id sid tid token lemma pos work_fc4vscbgnfdyhddwekhs4n7fcy 1 1 H h NN work_fc4vscbgnfdyhddwekhs4n7fcy 1 2 E e NN work_fc4vscbgnfdyhddwekhs4n7fcy 1 3 P p NN work_fc4vscbgnfdyhddwekhs4n7fcy 1 4 -P -P HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 1 5 H h NN work_fc4vscbgnfdyhddwekhs4n7fcy 1 6 -9 -9 : work_fc4vscbgnfdyhddwekhs4n7fcy 1 7 40 40 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 8 63 63 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 9 08 08 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 10 BA-94 BA-94 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 11 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 1 12 21 21 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 13 June June NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 14 14 14 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 1 16 1994 1994 CD work_fc4vscbgnfdyhddwekhs4n7fcy 1 17 Axion Axion NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 18 Dissipation Dissipation NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 19 Through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 1 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 1 21 Mixing Mixing NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 22 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 1 23 Goldstone Goldstone NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 24 Bosons Bosons NNP work_fc4vscbgnfdyhddwekhs4n7fcy 1 25 K.S. K.S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 2 1 Babu Babu NNP work_fc4vscbgnfdyhddwekhs4n7fcy 2 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 2 3 S.M. S.M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 1 Barr Barr NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 3 3 D. D. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 4 Seckel Seckel NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 5 Bartol Bartol NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 6 Research Research NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 7 Institute Institute NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 8 University University NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 9 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 10 Delaware Delaware NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 3 12 Newark Newark NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 3 14 DE DE NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 15 19716 19716 CD work_fc4vscbgnfdyhddwekhs4n7fcy 3 16 Abstract Abstract NNP work_fc4vscbgnfdyhddwekhs4n7fcy 3 17 By by IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 18 coupling couple VBG work_fc4vscbgnfdyhddwekhs4n7fcy 3 19 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 3 20 strongly strongly RB work_fc4vscbgnfdyhddwekhs4n7fcy 3 21 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 22 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 3 23 hidden hide VBN work_fc4vscbgnfdyhddwekhs4n7fcy 3 24 sector sector NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 3 26 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 3 27 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 28 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 29 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 30 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 3 31 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 3 32 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 3 33 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 3 34 converted convert VBN work_fc4vscbgnfdyhddwekhs4n7fcy 3 35 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 36 radiative radiative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 3 37 degrees degree NNS work_fc4vscbgnfdyhddwekhs4n7fcy 3 38 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 3 39 freedom freedom NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 40 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 3 41 alleviating alleviate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 3 42 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 3 43 \axion \axion CD work_fc4vscbgnfdyhddwekhs4n7fcy 3 44 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 45 crisis crisis NN work_fc4vscbgnfdyhddwekhs4n7fcy 3 46 " " '' work_fc4vscbgnfdyhddwekhs4n7fcy 3 47 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 4 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 4 2 strong strong JJ work_fc4vscbgnfdyhddwekhs4n7fcy 4 3 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 4 5 achieved achieve VBN work_fc4vscbgnfdyhddwekhs4n7fcy 4 6 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 4 7 mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 4 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 4 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 4 11 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 4 12 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 4 13 Goldstone Goldstone NNP work_fc4vscbgnfdyhddwekhs4n7fcy 4 14 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 15 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 4 16 their -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 4 17 kinetic kinetic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 4 18 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 19 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 4 20 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 4 21 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 4 22 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 4 23 manner manner NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 24 reminiscent reminiscent NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 25 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 4 26 paraphoton paraphoton NN work_fc4vscbgnfdyhddwekhs4n7fcy 4 27 models model NNS work_fc4vscbgnfdyhddwekhs4n7fcy 4 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 5 1 Even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 5 2 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 4 strong strong JJ work_fc4vscbgnfdyhddwekhs4n7fcy 5 5 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 6 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 5 7 proves prove VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 5 8 di di NNP work_fc4vscbgnfdyhddwekhs4n7fcy 5 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 5 10 cult cult NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 11 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 5 12 relax relax VB work_fc4vscbgnfdyhddwekhs4n7fcy 5 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 14 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 15 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 16 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 17 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 18 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 19 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 20 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 5 21 due due IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 22 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 23 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 24 derivative derivative NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 25 na- na- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 5 26 ture ture NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 27 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 28 Goldstone Goldstone NNP work_fc4vscbgnfdyhddwekhs4n7fcy 5 29 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 30 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 5 31 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 5 32 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 33 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 5 35 ect ect NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 36 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 37 back back JJ work_fc4vscbgnfdyhddwekhs4n7fcy 5 38 reactions reaction NNS work_fc4vscbgnfdyhddwekhs4n7fcy 5 39 on on IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 40 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 41 evolution evolution NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 42 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 5 43 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 5 44 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 45 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 46 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 5 47 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 6 1 However however RB work_fc4vscbgnfdyhddwekhs4n7fcy 6 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 6 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 6 4 distri- distri- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 6 5 bution bution NN work_fc4vscbgnfdyhddwekhs4n7fcy 6 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 6 7 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 6 8 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 6 9 species specie NNS work_fc4vscbgnfdyhddwekhs4n7fcy 6 10 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 6 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 6 12 hidden hidden JJ work_fc4vscbgnfdyhddwekhs4n7fcy 6 13 sector sector NN work_fc4vscbgnfdyhddwekhs4n7fcy 6 14 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 6 15 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 6 16 driven drive VBN work_fc4vscbgnfdyhddwekhs4n7fcy 6 17 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 6 18 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 6 19 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 6 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 6 21 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 6 22 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 6 23 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 6 24 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 6 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 7 1 Restoration restoration NN work_fc4vscbgnfdyhddwekhs4n7fcy 7 2 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 7 3 ther- ther- NN work_fc4vscbgnfdyhddwekhs4n7fcy 7 4 mal mal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 7 5 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 7 6 results result NNS work_fc4vscbgnfdyhddwekhs4n7fcy 7 7 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 7 8 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 7 9 being be VBG work_fc4vscbgnfdyhddwekhs4n7fcy 7 10 transferred transfer VBN work_fc4vscbgnfdyhddwekhs4n7fcy 7 11 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 7 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 7 13 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 7 14 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 7 15 massless massless NN work_fc4vscbgnfdyhddwekhs4n7fcy 7 16 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 7 17 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 7 18 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 7 19 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 7 20 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 7 21 redshift redshift VB work_fc4vscbgnfdyhddwekhs4n7fcy 7 22 harmlessly harmlessly RB work_fc4vscbgnfdyhddwekhs4n7fcy 7 23 without without IN work_fc4vscbgnfdyhddwekhs4n7fcy 7 24 causing cause VBG work_fc4vscbgnfdyhddwekhs4n7fcy 7 25 any any DT work_fc4vscbgnfdyhddwekhs4n7fcy 7 26 cosmological cosmological JJ work_fc4vscbgnfdyhddwekhs4n7fcy 7 27 problems problem NNS work_fc4vscbgnfdyhddwekhs4n7fcy 7 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 8 1 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 8 2 Introduction introduction NN work_fc4vscbgnfdyhddwekhs4n7fcy 8 3 Goldstone Goldstone NNP work_fc4vscbgnfdyhddwekhs4n7fcy 8 4 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 8 5 pseudo{goldstone pseudo{goldstone CD work_fc4vscbgnfdyhddwekhs4n7fcy 8 6 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 8 7 play play VBP work_fc4vscbgnfdyhddwekhs4n7fcy 8 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 8 9 large large JJ work_fc4vscbgnfdyhddwekhs4n7fcy 8 10 role role NN work_fc4vscbgnfdyhddwekhs4n7fcy 8 11 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 8 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 8 13 speculations speculation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 8 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 8 15 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 8 16 physicists physicist NNS work_fc4vscbgnfdyhddwekhs4n7fcy 8 17 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 8 18 cosmologists cosmologist NNS work_fc4vscbgnfdyhddwekhs4n7fcy 8 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 9 1 Some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 9 2 oft{discussed oft{discussed CD work_fc4vscbgnfdyhddwekhs4n7fcy 9 3 examples example NNS work_fc4vscbgnfdyhddwekhs4n7fcy 9 4 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 9 5 axions,1 axions,1 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 9 6 majorons,2 majorons,2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 9 7 familons,3 familons,3 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 9 8 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 9 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 9 10 non{abelian non{abelian JJ work_fc4vscbgnfdyhddwekhs4n7fcy 9 11 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 9 12 � � VBN work_fc4vscbgnfdyhddwekhs4n7fcy 9 13 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 9 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 9 15 texture texture NN work_fc4vscbgnfdyhddwekhs4n7fcy 9 16 models.4 models.4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 9 17 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 9 18 salient salient NN work_fc4vscbgnfdyhddwekhs4n7fcy 9 19 feature feature NN work_fc4vscbgnfdyhddwekhs4n7fcy 9 20 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 9 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 9 22 dynamics dynamic NNS work_fc4vscbgnfdyhddwekhs4n7fcy 9 23 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 9 24 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 9 25 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 9 26 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 9 27 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 9 28 they -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 9 29 couple couple VBP work_fc4vscbgnfdyhddwekhs4n7fcy 9 30 derivatively derivatively RB work_fc4vscbgnfdyhddwekhs4n7fcy 9 31 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 10 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 10 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 10 3 associated associate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 10 4 global global JJ work_fc4vscbgnfdyhddwekhs4n7fcy 10 5 continuous continuous JJ work_fc4vscbgnfdyhddwekhs4n7fcy 10 6 symmetryis symmetryi NNS work_fc4vscbgnfdyhddwekhs4n7fcy 10 7 broken break VBN work_fc4vscbgnfdyhddwekhs4n7fcy 10 8 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 10 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 10 10 scale scale NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 11 f f NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 10 13 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 10 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 10 15 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 16 always always RB work_fc4vscbgnfdyhddwekhs4n7fcy 10 17 involves involve VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 10 18 powers power NNS work_fc4vscbgnfdyhddwekhs4n7fcy 10 19 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 10 20 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 10 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 10 22 1@ 1@ CD work_fc4vscbgnfdyhddwekhs4n7fcy 10 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 10 24 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 10 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 10 26 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 10 27 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 28 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 10 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 10 30 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 31 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 10 32 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 11 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 11 2 consequence consequence NN work_fc4vscbgnfdyhddwekhs4n7fcy 11 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 11 4 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 11 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 11 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 11 7 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 11 8 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 11 9 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 11 10 very very RB work_fc4vscbgnfdyhddwekhs4n7fcy 11 11 large large JJ work_fc4vscbgnfdyhddwekhs4n7fcy 11 12 compared compare VBN work_fc4vscbgnfdyhddwekhs4n7fcy 11 13 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 11 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 11 15 relevant relevant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 11 16 masses masse NNS work_fc4vscbgnfdyhddwekhs4n7fcy 11 17 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 11 18 momenta momenta NNP work_fc4vscbgnfdyhddwekhs4n7fcy 11 19 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 11 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 11 21 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 11 22 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 11 23 decouples decouple VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 11 24 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 12 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 2 fact fact NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 3 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 12 4 exploited exploit VBN work_fc4vscbgnfdyhddwekhs4n7fcy 12 5 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 6 invisible invisible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 7 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 8 models,5 models,5 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 12 9 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 12 10 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 11 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 12 12 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 12 13 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 12 14 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 12 15 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 12 16 GeV gev NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 18 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 19 's 's POS work_fc4vscbgnfdyhddwekhs4n7fcy 12 20 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 12 21 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 12 22 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 23 enough enough RB work_fc4vscbgnfdyhddwekhs4n7fcy 12 24 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 25 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 12 26 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 12 27 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 12 28 evaded evade VBN work_fc4vscbgnfdyhddwekhs4n7fcy 12 29 detection detection NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 30 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 12 31 avoided avoided JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 32 con con NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 33 ict ict NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 34 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 35 astrophysical astrophysical JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 36 observations.6 observations.6 NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 37 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 38 fact fact NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 39 also also RB work_fc4vscbgnfdyhddwekhs4n7fcy 12 40 lies lie VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 12 41 behind behind IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 42 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 43 well well RB work_fc4vscbgnfdyhddwekhs4n7fcy 12 44 { { -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 12 45 known know VBN work_fc4vscbgnfdyhddwekhs4n7fcy 12 46 \axion \axion CD work_fc4vscbgnfdyhddwekhs4n7fcy 12 47 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 48 problem",7 problem",7 NNS work_fc4vscbgnfdyhddwekhs4n7fcy 12 49 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 12 50 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 12 51 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 52 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 53 fa fa PRP work_fc4vscbgnfdyhddwekhs4n7fcy 12 54 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 12 55 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 12 56 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 12 57 12 12 CD work_fc4vscbgnfdyhddwekhs4n7fcy 12 58 GeV GeV VBD work_fc4vscbgnfdyhddwekhs4n7fcy 12 59 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 60 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 61 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 62 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 63 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 12 64 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 65 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 66 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 67 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 12 68 eld eld VBN work_fc4vscbgnfdyhddwekhs4n7fcy 12 69 after after IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 70 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 71 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 12 72 phase phase NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 73 transition transition NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 74 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 75 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 76 early early JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 77 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 78 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 12 79 unable unable JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 80 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 12 81 dissipate dissipate VB work_fc4vscbgnfdyhddwekhs4n7fcy 12 82 due due IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 83 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 12 84 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 85 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 86 's 's POS work_fc4vscbgnfdyhddwekhs4n7fcy 12 87 weak weak JJ work_fc4vscbgnfdyhddwekhs4n7fcy 12 88 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 89 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 12 90 eventually eventually RB work_fc4vscbgnfdyhddwekhs4n7fcy 12 91 overcloses overclose VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 12 92 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 12 93 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 12 94 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 13 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 2 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 3 letter letter NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 4 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 13 5 show show VBP work_fc4vscbgnfdyhddwekhs4n7fcy 13 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 7 di di NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 9 erent erent NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 10 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 11 � � VBN work_fc4vscbgnfdyhddwekhs4n7fcy 13 12 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 13 13 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 13 14 mix mix VB work_fc4vscbgnfdyhddwekhs4n7fcy 13 15 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 16 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 17 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 13 18 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 19 kinetic kinetic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 13 20 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 13 21 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 22 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 23 Lagrangian Lagrangian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 24 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 25 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 26 way way NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 27 reminiscentof reminiscentof NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 28 photon photon NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 29 { { -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 13 30 paraphoton paraphoton NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 31 mixing,8 mixing,8 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 32 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 13 33 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 34 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 35 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 36 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 37 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 13 38 thus thus RB work_fc4vscbgnfdyhddwekhs4n7fcy 13 39 acquire acquire VB work_fc4vscbgnfdyhddwekhs4n7fcy 13 40 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 41 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 42 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 13 43 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 13 44 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 45 low low JJ work_fc4vscbgnfdyhddwekhs4n7fcy 13 46 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 47 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 48 certain certain JJ work_fc4vscbgnfdyhddwekhs4n7fcy 13 49 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 50 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 13 51 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 13 52 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 13 53 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 13 54 larger large JJR work_fc4vscbgnfdyhddwekhs4n7fcy 13 55 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 13 56 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 13 57 typical typical NNP work_fc4vscbgnfdyhddwekhs4n7fcy 13 58 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 13 59 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 13 60 f f XX work_fc4vscbgnfdyhddwekhs4n7fcy 13 61 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 14 1 After after IN work_fc4vscbgnfdyhddwekhs4n7fcy 14 2 demonstrating demonstrate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 14 3 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 14 4 point point NN work_fc4vscbgnfdyhddwekhs4n7fcy 14 5 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 14 6 show show VBP work_fc4vscbgnfdyhddwekhs4n7fcy 14 7 how how WRB work_fc4vscbgnfdyhddwekhs4n7fcy 14 8 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 14 9 makes make VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 14 10 possi- possi- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 14 11 ble ble VB work_fc4vscbgnfdyhddwekhs4n7fcy 14 12 scenarios scenario NNS work_fc4vscbgnfdyhddwekhs4n7fcy 14 13 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 14 14 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 14 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 14 16 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 14 17 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 14 18 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 14 19 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 14 20 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 14 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 14 22 cosmological cosmological JJ work_fc4vscbgnfdyhddwekhs4n7fcy 14 23 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 14 24 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 14 25 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 14 26 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 14 27 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 14 28 dissipated dissipate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 14 29 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 14 30 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 14 31 upper upper JJ work_fc4vscbgnfdyhddwekhs4n7fcy 14 32 limit limit NN work_fc4vscbgnfdyhddwekhs4n7fcy 14 33 on on IN work_fc4vscbgnfdyhddwekhs4n7fcy 14 34 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 14 35 removed remove VBN work_fc4vscbgnfdyhddwekhs4n7fcy 14 36 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 15 1 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 15 2 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 15 3 Mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 15 4 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 15 5 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 15 6 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 15 7 Consider consider VB work_fc4vscbgnfdyhddwekhs4n7fcy 15 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 15 9 theory theory NN work_fc4vscbgnfdyhddwekhs4n7fcy 15 10 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 15 11 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 15 12 global global JJ work_fc4vscbgnfdyhddwekhs4n7fcy 15 13 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 15 14 U(1)a U(1)a NNP work_fc4vscbgnfdyhddwekhs4n7fcy 15 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 15 16 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 15 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 16 1 Let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 16 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 16 3 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 16 4 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 16 5 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 16 6 scalar scalar JJ work_fc4vscbgnfdyhddwekhs4n7fcy 16 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 16 8 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 16 9 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 16 10 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 16 11 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 16 12 1,0 1,0 LS work_fc4vscbgnfdyhddwekhs4n7fcy 16 13 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 16 14 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 16 15 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 16 16 0,1 0,1 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 16 17 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 16 18 under under IN work_fc4vscbgnfdyhddwekhs4n7fcy 16 19 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 16 20 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 16 21 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 17 1 Suppose suppose VB work_fc4vscbgnfdyhddwekhs4n7fcy 17 2 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 17 3 jh jh NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 4 ij ij NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 6 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 17 8 jh jh NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 10 ij ij NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 11 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 12 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 17 14 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 17 15 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 16 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 17 17 assumed assume VBN work_fc4vscbgnfdyhddwekhs4n7fcy 17 18 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 17 19 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 17 20 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 17 21 smaller small JJR work_fc4vscbgnfdyhddwekhs4n7fcy 17 22 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 17 23 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 24 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 17 25 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 17 26 call call VB work_fc4vscbgnfdyhddwekhs4n7fcy 17 27 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 17 28 resulting result VBG work_fc4vscbgnfdyhddwekhs4n7fcy 17 29 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 17 30 modes mode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 17 31 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 17 32 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 17 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 17 34 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 17 35 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 17 36 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 17 37 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 17 38 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 17 39 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 17 40 b b LS work_fc4vscbgnfdyhddwekhs4n7fcy 17 41 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 17 42 respectively respectively RB work_fc4vscbgnfdyhddwekhs4n7fcy 17 43 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 18 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 18 2 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 18 3 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 18 4 clear clear JJ work_fc4vscbgnfdyhddwekhs4n7fcy 18 5 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 18 6 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 18 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 18 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 18 9 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 18 10 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 18 11 suppressed suppress VBN work_fc4vscbgnfdyhddwekhs4n7fcy 18 12 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 18 13 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 18 14 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 18 15 fa fa FW work_fc4vscbgnfdyhddwekhs4n7fcy 18 16 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 18 17 those those DT work_fc4vscbgnfdyhddwekhs4n7fcy 18 18 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 18 19 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 18 20 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 18 21 p p NNP work_fc4vscbgnfdyhddwekhs4n7fcy 18 22 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 18 23 fb fb UH work_fc4vscbgnfdyhddwekhs4n7fcy 18 24 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 19 1 It -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 19 2 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 19 3 happen happen VB work_fc4vscbgnfdyhddwekhs4n7fcy 19 4 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 5 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 6 integrating integrate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 19 7 out out RP work_fc4vscbgnfdyhddwekhs4n7fcy 19 8 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 10 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 19 11 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 12 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 13 M M NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 14 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 15 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 16 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 17 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 19 18 higher high JJR work_fc4vscbgnfdyhddwekhs4n7fcy 19 19 dimension dimension NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 20 operator operator NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 21 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 19 22 result result VB work_fc4vscbgnfdyhddwekhs4n7fcy 19 23 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 24 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 25 U(1)a U(1)a NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 27 U(1)b{invariant U(1)b{invariant '' work_fc4vscbgnfdyhddwekhs4n7fcy 19 28 form form NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 29 Lmix Lmix NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 30 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 19 31 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 32 M2 m2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 33 y@ y@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 35 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 19 36 y y LS work_fc4vscbgnfdyhddwekhs4n7fcy 19 37 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 38 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 39 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 40 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 19 41 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 42 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 19 43 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 44 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 19 45 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 46 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 19 47 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 48 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 49 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 19 50 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 51 fa+~ fa+~ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 52 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 53 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 54 ia ia XX work_fc4vscbgnfdyhddwekhs4n7fcy 19 55 = = FW work_fc4vscbgnfdyhddwekhs4n7fcy 19 56 fa fa FW work_fc4vscbgnfdyhddwekhs4n7fcy 19 57 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 19 58 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 59 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 19 60 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 61 fb+~ fb+~ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 62 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 63 )e )e . work_fc4vscbgnfdyhddwekhs4n7fcy 19 64 ib ib UH work_fc4vscbgnfdyhddwekhs4n7fcy 19 65 = = FW work_fc4vscbgnfdyhddwekhs4n7fcy 19 66 fb fb NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 67 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 19 68 substituted substitute VBN work_fc4vscbgnfdyhddwekhs4n7fcy 19 69 into into IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 70 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 71 expression expression NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 72 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 19 73 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 74 result result NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 75 contains contain VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 19 76 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 77 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 78 La;b La;b VBN work_fc4vscbgnfdyhddwekhs4n7fcy 19 79 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 19 80 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 81 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 82 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 83 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 84 a@ a@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 85 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 86 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 87 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 88 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 89 2 2 LS work_fc4vscbgnfdyhddwekhs4n7fcy 19 90 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 91 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 92 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 93 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 94 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 95 2c 2c CD work_fc4vscbgnfdyhddwekhs4n7fcy 19 96 fafb fafb VBD work_fc4vscbgnfdyhddwekhs4n7fcy 19 97 M2 M2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 98 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 19 99 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 100 3 3 LS work_fc4vscbgnfdyhddwekhs4n7fcy 19 101 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 102 Through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 103 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 104 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 105 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 106 a a NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 107 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 19 108 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 109 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 19 110 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 111 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 19 112 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 113 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 19 114 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 19 115 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 19 116 couple couple NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 117 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 118 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 19 119 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 19 120 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 19 121 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 122 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 19 123 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 124 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 125 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 126 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 19 127 strength strength NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 128 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 19 129 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 130 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 19 131 fb fb NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 132 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 19 133 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 19 134 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 19 135 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 19 136 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 19 137 greater great JJR work_fc4vscbgnfdyhddwekhs4n7fcy 19 138 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 19 139 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 19 140 = = : work_fc4vscbgnfdyhddwekhs4n7fcy 19 141 fa fa FW work_fc4vscbgnfdyhddwekhs4n7fcy 19 142 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 19 143 see see VB work_fc4vscbgnfdyhddwekhs4n7fcy 19 144 Fig Fig NNP work_fc4vscbgnfdyhddwekhs4n7fcy 19 145 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 20 1 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 20 2 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 20 3 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 21 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 21 2 example example NN work_fc4vscbgnfdyhddwekhs4n7fcy 21 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 21 4 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 21 5 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 21 6 such such JJ work_fc4vscbgnfdyhddwekhs4n7fcy 21 7 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 21 8 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 21 9 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 21 10 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 22 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 2 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 22 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 4 could could MD work_fc4vscbgnfdyhddwekhs4n7fcy 22 5 arise arise VB work_fc4vscbgnfdyhddwekhs4n7fcy 22 6 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 22 7 integrating integrate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 22 8 out out RP work_fc4vscbgnfdyhddwekhs4n7fcy 22 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 22 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 11 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 22 14 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 22 15 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 22 16 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 18 1=2; 1=2; CD work_fc4vscbgnfdyhddwekhs4n7fcy 22 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 20 1=2 1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 21 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 22 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 22 23 mass mass NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 24 M M NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 22 26 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 22 27 coupling couple VBG work_fc4vscbgnfdyhddwekhs4n7fcy 22 28 [ [ -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 30 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 22 33 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 22 34 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 35 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 22 36 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 22 37 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 22 38 c c LS work_fc4vscbgnfdyhddwekhs4n7fcy 22 39 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 22 40 ] ] -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 22 41 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 23 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 23 2 simplicity simplicity NN work_fc4vscbgnfdyhddwekhs4n7fcy 23 3 let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 23 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 23 5 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 23 6 positive positive JJ work_fc4vscbgnfdyhddwekhs4n7fcy 23 7 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 23 8 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 23 9 squared squared JJ work_fc4vscbgnfdyhddwekhs4n7fcy 23 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 23 11 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 23 12 VEV VEV NNP work_fc4vscbgnfdyhddwekhs4n7fcy 23 13 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 24 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 24 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 24 3 loop loop NN work_fc4vscbgnfdyhddwekhs4n7fcy 24 4 shown show VBN work_fc4vscbgnfdyhddwekhs4n7fcy 24 5 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 24 6 Fig Fig NNP work_fc4vscbgnfdyhddwekhs4n7fcy 24 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 25 1 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 2 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 25 3 produce produce VB work_fc4vscbgnfdyhddwekhs4n7fcy 25 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 25 5 following follow VBG work_fc4vscbgnfdyhddwekhs4n7fcy 25 6 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 8 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 25 9 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 25 10 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 11 among among IN work_fc4vscbgnfdyhddwekhs4n7fcy 25 12 others other NNS work_fc4vscbgnfdyhddwekhs4n7fcy 25 13 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 14 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 25 15 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 16 momenta momenta NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 17 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 25 18 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 25 19 M M NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 20 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 25 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 22 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 23 192 192 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 24 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 25 25 2M2 2m2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 26 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 27 y@ y@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 28 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 29 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 25 30 y y LS work_fc4vscbgnfdyhddwekhs4n7fcy 25 31 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 25 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 34 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 25 35 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 25 36 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 25 37 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 25 38 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 25 39 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 40 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 41 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 25 42 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 25 43 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 25 44 therefore therefore RB work_fc4vscbgnfdyhddwekhs4n7fcy 25 45 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 25 46 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 25 47 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 25 48 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 26 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 2 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 26 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 6 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 26 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 9 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 10 96 96 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 11 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 12 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 13 fafb fafb JJ work_fc4vscbgnfdyhddwekhs4n7fcy 26 14 M2 M2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 15 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 26 16 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 17 5 5 LS work_fc4vscbgnfdyhddwekhs4n7fcy 26 18 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 19 Now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 26 20 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 26 21 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 26 22 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 26 23 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 26 24 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 26 25 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 26 26 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 28 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 29 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 30 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 31 exists exist VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 26 32 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 26 33 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 26 34 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 26 35 require require VB work_fc4vscbgnfdyhddwekhs4n7fcy 26 36 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 26 37 arti arti NN work_fc4vscbgnfdyhddwekhs4n7fcy 26 38 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 26 39 cial cial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 26 40 can- can- NN work_fc4vscbgnfdyhddwekhs4n7fcy 26 41 cellation cellation NN work_fc4vscbgnfdyhddwekhs4n7fcy 26 42 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 26 43 M2 M2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 44 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 26 45 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 26 46 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 26 47 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 26 48 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 26 49 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 26 50 fafb fafb JJ work_fc4vscbgnfdyhddwekhs4n7fcy 26 51 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 26 52 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 26 53 hence hence RB work_fc4vscbgnfdyhddwekhs4n7fcy 26 54 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 26 55 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 56 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 26 57 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 26 58 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 26 59 larger large JJR work_fc4vscbgnfdyhddwekhs4n7fcy 26 60 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 26 61 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 62 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 26 63 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 64 96 96 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 65 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 26 66 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 67 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 26 68 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 69 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 70 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 26 71 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 26 72 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 27 1 There there EX work_fc4vscbgnfdyhddwekhs4n7fcy 27 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 27 3 also also RB work_fc4vscbgnfdyhddwekhs4n7fcy 27 4 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 5 absolute absolute JJ work_fc4vscbgnfdyhddwekhs4n7fcy 27 6 limit limit NN work_fc4vscbgnfdyhddwekhs4n7fcy 27 7 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 27 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 9 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 27 10 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 27 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 27 12 since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 27 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 14 kinetic kinetic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 27 15 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 27 16 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 27 17 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 18 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 27 19 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 27 20 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 27 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 22 form form NN work_fc4vscbgnfdyhddwekhs4n7fcy 27 23 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 27 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 27 25 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 27 26 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 27 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 28 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 29 @ @ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 27 30 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 31 b b LS work_fc4vscbgnfdyhddwekhs4n7fcy 27 32 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 27 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 34 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 27 35 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 27 36 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 37 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 27 38 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 27 39 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 27 40 @ @ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 27 41 � � : work_fc4vscbgnfdyhddwekhs4n7fcy 27 42 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 43 @ @ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 27 44 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 45 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 27 47 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 27 48 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 27 49 wrong{sign wrong{sign NN work_fc4vscbgnfdyhddwekhs4n7fcy 27 50 metric metric JJ work_fc4vscbgnfdyhddwekhs4n7fcy 27 51 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 27 52 otherwise otherwise RB work_fc4vscbgnfdyhddwekhs4n7fcy 27 53 result result VB work_fc4vscbgnfdyhddwekhs4n7fcy 27 54 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 28 1 There there EX work_fc4vscbgnfdyhddwekhs4n7fcy 28 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 28 3 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 28 4 reason reason NN work_fc4vscbgnfdyhddwekhs4n7fcy 28 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 28 6 however however RB work_fc4vscbgnfdyhddwekhs4n7fcy 28 7 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 28 8 why why WRB work_fc4vscbgnfdyhddwekhs4n7fcy 28 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 28 10 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 28 11 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 28 12 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 28 13 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 28 14 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 28 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 28 16 though though IN work_fc4vscbgnfdyhddwekhs4n7fcy 28 17 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 28 18 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 28 19 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 28 20 unity unity NN work_fc4vscbgnfdyhddwekhs4n7fcy 28 21 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 29 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 29 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 29 3 higher high JJR work_fc4vscbgnfdyhddwekhs4n7fcy 29 4 dimension dimension NN work_fc4vscbgnfdyhddwekhs4n7fcy 29 5 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 29 6 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 29 7 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 29 8 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 30 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 30 2 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 30 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 30 4 were be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 30 5 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 30 6 \hard \hard CD work_fc4vscbgnfdyhddwekhs4n7fcy 30 7 " " '' work_fc4vscbgnfdyhddwekhs4n7fcy 30 8 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 30 9 all all PDT work_fc4vscbgnfdyhddwekhs4n7fcy 30 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 30 11 way way NN work_fc4vscbgnfdyhddwekhs4n7fcy 30 12 up up IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 13 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 14 momenta momenta NNP work_fc4vscbgnfdyhddwekhs4n7fcy 30 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 16 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 30 17 fa fa UH work_fc4vscbgnfdyhddwekhs4n7fcy 30 18 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 30 19 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 30 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 30 21 theory theory NN work_fc4vscbgnfdyhddwekhs4n7fcy 30 22 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 30 23 become become VB work_fc4vscbgnfdyhddwekhs4n7fcy 30 24 strongly strongly RB work_fc4vscbgnfdyhddwekhs4n7fcy 30 25 coupled couple VBN work_fc4vscbgnfdyhddwekhs4n7fcy 30 26 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 30 27 physics physics NN work_fc4vscbgnfdyhddwekhs4n7fcy 30 28 uncalculable uncalculable JJ work_fc4vscbgnfdyhddwekhs4n7fcy 30 29 unless unless IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 30 M2 M2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 30 31 were be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 30 32 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 30 33 f2a f2a JJ work_fc4vscbgnfdyhddwekhs4n7fcy 30 34 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 30 35 hence hence RB work_fc4vscbgnfdyhddwekhs4n7fcy 30 36 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 30 37 were be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 30 38 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 30 39 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 40 about about IN work_fc4vscbgnfdyhddwekhs4n7fcy 30 41 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 30 42 = = FW work_fc4vscbgnfdyhddwekhs4n7fcy 30 43 fa fa XX work_fc4vscbgnfdyhddwekhs4n7fcy 30 44 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 31 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 31 2 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 31 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 31 4 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 31 5 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 31 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 31 7 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 31 8 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 31 9 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 31 10 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 31 11 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 31 12 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 31 13 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 31 14 mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 31 15 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 31 16 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 31 17 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 31 18 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 31 19 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 31 20 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 31 21 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 31 22 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 31 23 fb fb UH work_fc4vscbgnfdyhddwekhs4n7fcy 31 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 31 25 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 31 26 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 31 27 fa fa XX work_fc4vscbgnfdyhddwekhs4n7fcy 31 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 32 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 32 2 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 32 3 words word NNS work_fc4vscbgnfdyhddwekhs4n7fcy 32 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 32 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 32 6 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 32 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 32 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 32 9 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 32 10 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 32 11 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 32 12 enhanced enhance VBN work_fc4vscbgnfdyhddwekhs4n7fcy 32 13 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 32 14 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 32 15 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 32 16 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 33 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 33 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 33 3 on on IN work_fc4vscbgnfdyhddwekhs4n7fcy 33 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 33 5 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 33 6 hand hand NN work_fc4vscbgnfdyhddwekhs4n7fcy 33 7 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 33 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 33 9 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 33 10 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 33 11 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 33 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 34 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 34 2 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 34 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 34 4 arises arise VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 34 5 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 34 6 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 34 7 loop loop NN work_fc4vscbgnfdyhddwekhs4n7fcy 34 8 such such JJ work_fc4vscbgnfdyhddwekhs4n7fcy 34 9 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 34 10 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 34 11 shown show VBN work_fc4vscbgnfdyhddwekhs4n7fcy 34 12 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 34 13 Fig Fig NNP work_fc4vscbgnfdyhddwekhs4n7fcy 34 14 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 35 1 2 2 LS work_fc4vscbgnfdyhddwekhs4n7fcy 35 2 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 35 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 35 4 intermediate intermediate JJ work_fc4vscbgnfdyhddwekhs4n7fcy 35 5 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 35 6 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 35 7 mass mass NNP work_fc4vscbgnfdyhddwekhs4n7fcy 35 8 M2 M2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 35 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 35 10 fafb fafb JJ work_fc4vscbgnfdyhddwekhs4n7fcy 35 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 35 12 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 35 13 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 35 14 softens soften VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 35 15 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 35 16 momenta momenta NNP work_fc4vscbgnfdyhddwekhs4n7fcy 35 17 above above IN work_fc4vscbgnfdyhddwekhs4n7fcy 35 18 M M NNP work_fc4vscbgnfdyhddwekhs4n7fcy 35 19 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 35 20 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 35 21 problem problem NN work_fc4vscbgnfdyhddwekhs4n7fcy 35 22 arises arise VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 35 23 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 35 24 higher high JJR work_fc4vscbgnfdyhddwekhs4n7fcy 35 25 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 35 26 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 36 1 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 36 2 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 36 3 Alleviating alleviate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 36 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 36 5 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 6 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 7 crisis crisis NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 8 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 36 9 wish wish VBP work_fc4vscbgnfdyhddwekhs4n7fcy 36 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 36 11 make make VB work_fc4vscbgnfdyhddwekhs4n7fcy 36 12 use use NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 13 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 36 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 36 15 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 16 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 36 17 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 18 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 36 19 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 36 20 let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 36 21 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 36 22 couple couple VB work_fc4vscbgnfdyhddwekhs4n7fcy 36 23 strongly strongly RB work_fc4vscbgnfdyhddwekhs4n7fcy 36 24 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 36 25 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 36 26 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 36 27 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 36 28 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 36 29 thus thus RB work_fc4vscbgnfdyhddwekhs4n7fcy 36 30 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 36 31 somehow somehow RB work_fc4vscbgnfdyhddwekhs4n7fcy 36 32 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 36 33 allow allow VB work_fc4vscbgnfdyhddwekhs4n7fcy 36 34 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 36 35 primordial primordial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 36 36 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 37 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 36 38 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 36 39 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 36 40 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 36 41 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 36 42 dissipated dissipate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 36 43 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 37 1 Let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 37 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 37 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 37 4 eld eld VB work_fc4vscbgnfdyhddwekhs4n7fcy 37 5 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 37 6 be be NN work_fc4vscbgnfdyhddwekhs4n7fcy 37 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 37 8 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 37 9 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 37 10 solves solve VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 37 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 37 12 strong strong JJ work_fc4vscbgnfdyhddwekhs4n7fcy 37 13 CP CP NNP work_fc4vscbgnfdyhddwekhs4n7fcy 37 14 problem problem NN work_fc4vscbgnfdyhddwekhs4n7fcy 37 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 38 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 38 2 U(1)a U(1)a NNP work_fc4vscbgnfdyhddwekhs4n7fcy 38 3 has have VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 38 4 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 38 5 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 38 6 anomaly anomaly RB work_fc4vscbgnfdyhddwekhs4n7fcy 38 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 38 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 38 9 gets get VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 38 10 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 38 11 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 38 12 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 38 13 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 38 14 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 38 15 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 38 16 QCD QCD NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 38 17 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 38 18 fa fa XX work_fc4vscbgnfdyhddwekhs4n7fcy 38 19 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 38 20 instan- instan- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 38 21 ton ton NN work_fc4vscbgnfdyhddwekhs4n7fcy 38 22 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 38 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 38 24 ects ect NNS work_fc4vscbgnfdyhddwekhs4n7fcy 38 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 39 1 Several several JJ work_fc4vscbgnfdyhddwekhs4n7fcy 39 2 astrophysical astrophysical JJ work_fc4vscbgnfdyhddwekhs4n7fcy 39 3 arguments6 arguments6 NN work_fc4vscbgnfdyhddwekhs4n7fcy 39 4 suggest suggest VBP work_fc4vscbgnfdyhddwekhs4n7fcy 39 5 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 39 6 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 39 7 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 39 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 39 9 1010 1010 CD work_fc4vscbgnfdyhddwekhs4n7fcy 39 10 GeV GeV NNP work_fc4vscbgnfdyhddwekhs4n7fcy 39 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 39 12 otherwise otherwise RB work_fc4vscbgnfdyhddwekhs4n7fcy 39 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 39 14 evolution evolution NN work_fc4vscbgnfdyhddwekhs4n7fcy 39 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 39 16 stars star NNS work_fc4vscbgnfdyhddwekhs4n7fcy 39 17 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 39 18 their -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 39 19 remnants remnant NNS work_fc4vscbgnfdyhddwekhs4n7fcy 39 20 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 39 21 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 39 22 drastically drastically RB work_fc4vscbgnfdyhddwekhs4n7fcy 39 23 di di JJ work_fc4vscbgnfdyhddwekhs4n7fcy 39 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 39 25 er- er- XX work_fc4vscbgnfdyhddwekhs4n7fcy 39 26 ent ent NN work_fc4vscbgnfdyhddwekhs4n7fcy 39 27 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 39 28 observed observe VBN work_fc4vscbgnfdyhddwekhs4n7fcy 39 29 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 40 1 Thus thus RB work_fc4vscbgnfdyhddwekhs4n7fcy 40 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 40 3 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 40 4 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 40 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 40 6 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 40 7 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 40 8 ordinary ordinary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 40 9 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 40 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 40 11 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 40 12 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 40 13 proportional proportional JJ work_fc4vscbgnfdyhddwekhs4n7fcy 40 14 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 40 15 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 40 16 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 40 17 fa fa FW work_fc4vscbgnfdyhddwekhs4n7fcy 40 18 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 40 19 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 40 20 highly highly RB work_fc4vscbgnfdyhddwekhs4n7fcy 40 21 suppressed suppress VBN work_fc4vscbgnfdyhddwekhs4n7fcy 40 22 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 41 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 41 2 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 3 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 4 crisis crisis NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 5 arises arise VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 41 6 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 41 7 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 41 8 result result NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 9 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 41 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 41 11 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 41 12 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 13 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 41 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 41 15 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 41 16 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 17 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 41 18 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 41 19 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 41 20 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 42 1 At at IN work_fc4vscbgnfdyhddwekhs4n7fcy 42 2 temperatures temperature NNS work_fc4vscbgnfdyhddwekhs4n7fcy 42 3 above above IN work_fc4vscbgnfdyhddwekhs4n7fcy 42 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 42 5 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 42 6 phase phase NN work_fc4vscbgnfdyhddwekhs4n7fcy 42 7 transition transition NN work_fc4vscbgnfdyhddwekhs4n7fcy 42 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 42 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 42 10 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 42 11 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 42 12 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 42 13 enough enough RB work_fc4vscbgnfdyhddwekhs4n7fcy 42 14 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 42 15 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 42 16 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 42 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 42 18 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 42 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 43 1 As as IN work_fc4vscbgnfdyhddwekhs4n7fcy 43 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 43 3 universe universe JJ work_fc4vscbgnfdyhddwekhs4n7fcy 43 4 cools cools NNP work_fc4vscbgnfdyhddwekhs4n7fcy 43 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 43 6 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 43 7 increases increase VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 43 8 until until IN work_fc4vscbgnfdyhddwekhs4n7fcy 43 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 43 10 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 43 11 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 43 12 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 43 13 becomes become VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 43 14 dynamic dynamic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 43 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 43 16 i.e. i.e. FW work_fc4vscbgnfdyhddwekhs4n7fcy 44 1 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 44 2 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 44 3 H H NNP work_fc4vscbgnfdyhddwekhs4n7fcy 44 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 44 5 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 44 6 H h NN work_fc4vscbgnfdyhddwekhs4n7fcy 44 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 44 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 44 9 expansion expansion NN work_fc4vscbgnfdyhddwekhs4n7fcy 44 10 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 44 11 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 45 1 Barring bar VBG work_fc4vscbgnfdyhddwekhs4n7fcy 45 2 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 45 3 coincidence coincidence NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 4 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 45 5 alignment alignment NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 6 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 45 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 45 8 Peccei Peccei NNP work_fc4vscbgnfdyhddwekhs4n7fcy 45 9 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 45 10 Quinn Quinn NNP work_fc4vscbgnfdyhddwekhs4n7fcy 45 11 angle angle NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 45 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 45 14 initial initial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 45 15 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 16 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 45 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 45 18 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 19 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 45 20 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 45 21 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 45 22 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 45 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 45 24 fa fa NN work_fc4vscbgnfdyhddwekhs4n7fcy 45 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 46 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 46 2 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 46 3 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 46 4 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 46 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 46 6 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 46 7 na na IN work_fc4vscbgnfdyhddwekhs4n7fcy 46 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 46 9 f2aH. f2ah. CD work_fc4vscbgnfdyhddwekhs4n7fcy 47 1 After after IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 2 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 47 3 point point NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 47 5 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 7 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 47 8 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 47 10 comoving comoving JJ work_fc4vscbgnfdyhddwekhs4n7fcy 47 11 volume volume NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 12 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 47 13 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 47 14 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 47 15 while while IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 47 17 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 18 mass mass NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 19 increases increase NNS work_fc4vscbgnfdyhddwekhs4n7fcy 47 20 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 21 H h NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 22 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 47 23 its -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 47 24 zero zero CD work_fc4vscbgnfdyhddwekhs4n7fcy 47 25 temperature temperature NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 26 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 27 ma0 ma0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 47 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 48 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 48 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 48 3 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 4 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 48 6 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 48 7 after after IN work_fc4vscbgnfdyhddwekhs4n7fcy 48 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 48 9 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 10 phase phase NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 11 transition transition NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 12 exceeds exceed VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 48 13 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 48 14 critical critical JJ work_fc4vscbgnfdyhddwekhs4n7fcy 48 15 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 16 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 48 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 18 a;cr a;cr NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 20 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 48 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 22 7 7 CD work_fc4vscbgnfdyhddwekhs4n7fcy 48 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 48 24 4QCD 4qcd NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 48 26 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 48 27 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 48 28 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 48 29 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 30 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 48 31 become become VB work_fc4vscbgnfdyhddwekhs4n7fcy 48 32 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 48 33 dominated dominate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 48 34 too too RB work_fc4vscbgnfdyhddwekhs4n7fcy 48 35 early early RB work_fc4vscbgnfdyhddwekhs4n7fcy 48 36 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 48 37 i.e. i.e. FW work_fc4vscbgnfdyhddwekhs4n7fcy 49 1 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 49 2 temperatures temperature NNS work_fc4vscbgnfdyhddwekhs4n7fcy 49 3 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 49 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 49 5 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 49 6 eV eV NNS work_fc4vscbgnfdyhddwekhs4n7fcy 49 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 50 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 50 2 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 50 3 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 50 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 50 5 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 50 6 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 50 7 T T NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 10 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 11 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 50 12 roughly roughly RB work_fc4vscbgnfdyhddwekhs4n7fcy 50 13 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 50 14 a( a( JJ work_fc4vscbgnfdyhddwekhs4n7fcy 50 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 16 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 17 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 50 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 50 20 4QCDfa 4qcdfa CD work_fc4vscbgnfdyhddwekhs4n7fcy 50 21 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 50 22 MPl MPl NNS work_fc4vscbgnfdyhddwekhs4n7fcy 50 23 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 50 24 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 50 25 results result VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 50 26 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 50 27 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 50 28 constraint constraint NN work_fc4vscbgnfdyhddwekhs4n7fcy 50 29 fa fa FW work_fc4vscbgnfdyhddwekhs4n7fcy 50 30 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 50 31 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 50 32 12 12 CD work_fc4vscbgnfdyhddwekhs4n7fcy 50 33 GeV GeV NNS work_fc4vscbgnfdyhddwekhs4n7fcy 50 34 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 51 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 51 2 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 3 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 51 5 ationary ationary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 6 models model NNS work_fc4vscbgnfdyhddwekhs4n7fcy 51 7 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 51 8 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 51 9 bound bind VBN work_fc4vscbgnfdyhddwekhs4n7fcy 51 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 51 11 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 51 12 axionic axionic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 13 strings string NNS work_fc4vscbgnfdyhddwekhs4n7fcy 51 14 - - , work_fc4vscbgnfdyhddwekhs4n7fcy 51 15 whose whose WP$ work_fc4vscbgnfdyhddwekhs4n7fcy 51 16 decay decay JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 17 may9 may9 NN work_fc4vscbgnfdyhddwekhs4n7fcy 51 18 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 51 19 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 51 20 not10 not10 VB work_fc4vscbgnfdyhddwekhs4n7fcy 51 21 increase increase VB work_fc4vscbgnfdyhddwekhs4n7fcy 51 22 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 51 23 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 51 24 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 51 25 abundance abundance NN work_fc4vscbgnfdyhddwekhs4n7fcy 51 26 100-fold 100-fold CD work_fc4vscbgnfdyhddwekhs4n7fcy 51 27 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 51 28 lowering lower VBG work_fc4vscbgnfdyhddwekhs4n7fcy 51 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 51 30 cosmological cosmological JJ work_fc4vscbgnfdyhddwekhs4n7fcy 51 31 bound bind VBN work_fc4vscbgnfdyhddwekhs4n7fcy 51 32 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 51 33 fa fa NNP work_fc4vscbgnfdyhddwekhs4n7fcy 51 34 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 51 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 51 36 1010 1010 CD work_fc4vscbgnfdyhddwekhs4n7fcy 51 37 GeV GeV NNP work_fc4vscbgnfdyhddwekhs4n7fcy 51 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 52 1 There there EX work_fc4vscbgnfdyhddwekhs4n7fcy 52 2 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 52 3 been be VBN work_fc4vscbgnfdyhddwekhs4n7fcy 52 4 several several JJ work_fc4vscbgnfdyhddwekhs4n7fcy 52 5 approaches approach NNS work_fc4vscbgnfdyhddwekhs4n7fcy 52 6 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 52 7 solving solve VBG work_fc4vscbgnfdyhddwekhs4n7fcy 52 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 52 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 52 10 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 52 11 crisis crisis NN work_fc4vscbgnfdyhddwekhs4n7fcy 52 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 53 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 2 example example NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 53 4 entropy entropy JJ work_fc4vscbgnfdyhddwekhs4n7fcy 53 5 production11 production11 NNS work_fc4vscbgnfdyhddwekhs4n7fcy 53 6 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 53 7 dilute dilute VB work_fc4vscbgnfdyhddwekhs4n7fcy 53 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 53 9 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 10 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 11 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 12 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 53 13 relative relative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 53 14 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 15 ordinary ordinary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 53 16 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 17 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 53 18 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 53 19 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 20 ation ation NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 21 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 53 22 � � VB work_fc4vscbgnfdyhddwekhs4n7fcy 53 23 x x LS work_fc4vscbgnfdyhddwekhs4n7fcy 53 24 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 53 25 initial initial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 53 26 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 27 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 28 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 53 29 Peccei- Peccei- NNP work_fc4vscbgnfdyhddwekhs4n7fcy 53 30 Quinn Quinn NNP work_fc4vscbgnfdyhddwekhs4n7fcy 53 31 angle angle NN work_fc4vscbgnfdyhddwekhs4n7fcy 53 32 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 53 33 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 53 34 suitably suitably RB work_fc4vscbgnfdyhddwekhs4n7fcy 53 35 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 53 36 value12 value12 NNS work_fc4vscbgnfdyhddwekhs4n7fcy 53 37 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 54 1 However however RB work_fc4vscbgnfdyhddwekhs4n7fcy 54 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 54 3 attempts attempt VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 54 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 54 5 dissipate dissipate VB work_fc4vscbgnfdyhddwekhs4n7fcy 54 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 54 7 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 54 8 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 54 9 typically typically RB work_fc4vscbgnfdyhddwekhs4n7fcy 54 10 fail fail VBP work_fc4vscbgnfdyhddwekhs4n7fcy 54 11 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 55 1 Direct direct JJ work_fc4vscbgnfdyhddwekhs4n7fcy 55 2 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 55 3 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 55 4 presents present VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 55 5 several several JJ work_fc4vscbgnfdyhddwekhs4n7fcy 55 6 chal- chal- NN work_fc4vscbgnfdyhddwekhs4n7fcy 55 7 lenges lenge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 55 8 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 56 1 First first RB work_fc4vscbgnfdyhddwekhs4n7fcy 56 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 56 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 56 4 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 56 5 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 56 6 nature nature NN work_fc4vscbgnfdyhddwekhs4n7fcy 56 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 56 8 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 56 9 demands demand VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 56 10 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 56 11 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 56 12 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 56 13 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 56 14 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 56 15 fa fa CC work_fc4vscbgnfdyhddwekhs4n7fcy 56 16 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 56 17 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 56 18 vertex vertex NN work_fc4vscbgnfdyhddwekhs4n7fcy 56 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 57 1 Second second RB work_fc4vscbgnfdyhddwekhs4n7fcy 57 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 57 3 since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 57 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 57 5 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 57 6 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 57 7 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 57 8 absorbed absorb VBN work_fc4vscbgnfdyhddwekhs4n7fcy 57 9 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 57 10 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 57 11 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 57 12 relativistic relativistic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 57 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 57 14 derivative derivative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 57 15 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 57 16 demand demand VBP work_fc4vscbgnfdyhddwekhs4n7fcy 57 17 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 57 18 additional additional JJ work_fc4vscbgnfdyhddwekhs4n7fcy 57 19 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 57 20 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 57 21 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 57 22 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 57 23 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 57 24 vertex vertex NN work_fc4vscbgnfdyhddwekhs4n7fcy 57 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 58 1 Third third JJ work_fc4vscbgnfdyhddwekhs4n7fcy 58 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 58 3 any any DT work_fc4vscbgnfdyhddwekhs4n7fcy 58 4 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 5 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 58 6 single single JJ work_fc4vscbgnfdyhddwekhs4n7fcy 58 7 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 8 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 9 must must MD work_fc4vscbgnfdyhddwekhs4n7fcy 58 10 admit admit VB work_fc4vscbgnfdyhddwekhs4n7fcy 58 11 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 12 emission emission NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 13 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 58 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 58 15 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 58 16 reversed reverse VBD work_fc4vscbgnfdyhddwekhs4n7fcy 58 17 channel channel NNP work_fc4vscbgnfdyhddwekhs4n7fcy 58 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 59 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 2 leads lead VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 59 3 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 59 4 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 5 reduction reduction NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 6 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 59 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 8 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 9 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 10 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 59 11 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 12 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 13 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 59 14 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 59 15 = = NNP work_fc4vscbgnfdyhddwekhs4n7fcy 59 16 T T NNP work_fc4vscbgnfdyhddwekhs4n7fcy 59 17 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 59 18 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 19 naive naive JJ work_fc4vscbgnfdyhddwekhs4n7fcy 59 20 approach approach NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 21 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 59 22 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 59 23 ignore ignore VB work_fc4vscbgnfdyhddwekhs4n7fcy 59 24 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 59 25 back back NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 26 reac- reac- NN work_fc4vscbgnfdyhddwekhs4n7fcy 59 27 tions tion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 59 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 60 1 Flynn Flynn NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 60 3 Randall13 Randall13 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 4 considered consider VBD work_fc4vscbgnfdyhddwekhs4n7fcy 60 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 60 6 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 60 7 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 60 8 derivative derivative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 60 9 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 60 10 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 60 11 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 60 12 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 60 13 mesons14 mesons14 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 14 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 60 15 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 60 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 60 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 18 rst rst NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 19 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 60 20 third third JJ work_fc4vscbgnfdyhddwekhs4n7fcy 60 21 arguments argument NNS work_fc4vscbgnfdyhddwekhs4n7fcy 60 22 above above RB work_fc4vscbgnfdyhddwekhs4n7fcy 60 23 were be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 60 24 su su NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 60 26 cient cient NN work_fc4vscbgnfdyhddwekhs4n7fcy 60 27 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 60 28 leave leave VB work_fc4vscbgnfdyhddwekhs4n7fcy 60 29 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 60 30 undamped undampe VBN work_fc4vscbgnfdyhddwekhs4n7fcy 60 31 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 60 32 several several JJ work_fc4vscbgnfdyhddwekhs4n7fcy 60 33 orders order NNS work_fc4vscbgnfdyhddwekhs4n7fcy 60 34 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 60 35 magnitude magnitude NN work_fc4vscbgnfdyhddwekhs4n7fcy 60 36 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 61 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 61 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 61 3 present present JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 4 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 61 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 61 7 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 8 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 61 9 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 61 10 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 61 11 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 61 12 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 13 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 14 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 15 allows allow VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 61 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 61 17 possibility possibility NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 18 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 61 19 coupling couple VBG work_fc4vscbgnfdyhddwekhs4n7fcy 61 20 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 61 21 strongly strongly RB work_fc4vscbgnfdyhddwekhs4n7fcy 61 22 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 61 23 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 61 24 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 25 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 26 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 27 standard standard JJ work_fc4vscbgnfdyhddwekhs4n7fcy 61 28 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 61 29 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 62 1 However however RB work_fc4vscbgnfdyhddwekhs4n7fcy 62 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 62 3 without without IN work_fc4vscbgnfdyhddwekhs4n7fcy 62 4 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 62 5 explicit explicit JJ work_fc4vscbgnfdyhddwekhs4n7fcy 62 6 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 62 7 breaking break VBG work_fc4vscbgnfdyhddwekhs4n7fcy 62 8 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 62 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 62 10 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 62 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 62 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 62 13 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 62 14 must must MD work_fc4vscbgnfdyhddwekhs4n7fcy 62 15 couple couple VB work_fc4vscbgnfdyhddwekhs4n7fcy 62 16 derivatively derivatively RB work_fc4vscbgnfdyhddwekhs4n7fcy 62 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 63 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 63 2 combination combination NN work_fc4vscbgnfdyhddwekhs4n7fcy 63 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 4 powers power NNS work_fc4vscbgnfdyhddwekhs4n7fcy 63 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 6 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 63 7 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 63 9 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 63 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 63 11 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 12 consideration consideration NN work_fc4vscbgnfdyhddwekhs4n7fcy 63 13 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 14 back back JJ work_fc4vscbgnfdyhddwekhs4n7fcy 63 15 reactions reaction NNS work_fc4vscbgnfdyhddwekhs4n7fcy 63 16 has have VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 63 17 caused cause VBN work_fc4vscbgnfdyhddwekhs4n7fcy 63 18 all all PDT work_fc4vscbgnfdyhddwekhs4n7fcy 63 19 our -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 63 20 attempts attempt NNS work_fc4vscbgnfdyhddwekhs4n7fcy 63 21 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 63 22 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 63 23 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 63 24 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 63 25 fail fail VB work_fc4vscbgnfdyhddwekhs4n7fcy 63 26 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 64 1 Nonetheless nonetheless RB work_fc4vscbgnfdyhddwekhs4n7fcy 64 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 64 3 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 64 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 64 5 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 64 6 mechanism mechanism NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 7 whereby whereby WRB work_fc4vscbgnfdyhddwekhs4n7fcy 64 8 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 9 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 64 10 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 64 11 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 64 12 damped damp VBN work_fc4vscbgnfdyhddwekhs4n7fcy 64 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 64 14 allowing allow VBG work_fc4vscbgnfdyhddwekhs4n7fcy 64 15 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 64 16 fa fa NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 17 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 64 18 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 19 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 64 20 grand grand JJ work_fc4vscbgnfdyhddwekhs4n7fcy 64 21 uni uni NNP work_fc4vscbgnfdyhddwekhs4n7fcy 64 22 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 64 23 ed ed NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 24 scale scale NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 25 MGUT MGUT NNP work_fc4vscbgnfdyhddwekhs4n7fcy 64 26 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 64 27 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 64 28 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 64 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 64 30 Planck Planck NNP work_fc4vscbgnfdyhddwekhs4n7fcy 64 31 scale scale NN work_fc4vscbgnfdyhddwekhs4n7fcy 64 32 MPl MPl NNS work_fc4vscbgnfdyhddwekhs4n7fcy 64 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 65 1 Let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 65 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 65 3 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 65 4 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 65 5 mixed mix VBN work_fc4vscbgnfdyhddwekhs4n7fcy 65 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 65 7 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 65 8 described describe VBN work_fc4vscbgnfdyhddwekhs4n7fcy 65 9 above above RB work_fc4vscbgnfdyhddwekhs4n7fcy 65 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 65 11 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 65 12 strength strength NN work_fc4vscbgnfdyhddwekhs4n7fcy 65 13 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 65 14 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 65 15 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 65 16 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 65 17 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 65 18 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 65 19 arising arise VBG work_fc4vscbgnfdyhddwekhs4n7fcy 65 20 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 65 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 65 22 breaking breaking NN work_fc4vscbgnfdyhddwekhs4n7fcy 65 23 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 65 24 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 65 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 66 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 66 2 5 5 CD work_fc4vscbgnfdyhddwekhs4n7fcy 66 3 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 66 4 coupling couple VBG work_fc4vscbgnfdyhddwekhs4n7fcy 66 5 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 66 6 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 66 7 b{matter b{matter NNP work_fc4vscbgnfdyhddwekhs4n7fcy 66 8 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 66 9 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 66 10 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 66 11 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 66 12 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 66 13 call call VB work_fc4vscbgnfdyhddwekhs4n7fcy 66 14 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 66 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 66 16 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 66 17 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 66 18 vastly vastly RB work_fc4vscbgnfdyhddwekhs4n7fcy 66 19 stronger strong JJR work_fc4vscbgnfdyhddwekhs4n7fcy 66 20 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 66 21 its -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 66 22 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 66 23 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 66 24 ordinary ordinary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 66 25 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 66 26 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 67 1 Our -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 67 2 basic basic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 67 3 idea idea NN work_fc4vscbgnfdyhddwekhs4n7fcy 67 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 67 5 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 67 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 67 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 67 8 oscillating oscillating NN work_fc4vscbgnfdyhddwekhs4n7fcy 67 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 67 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 67 11 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 67 12 causes cause VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 67 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 67 14 energies energy NNS work_fc4vscbgnfdyhddwekhs4n7fcy 67 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 67 16 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 67 17 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 67 18 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 67 19 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 67 20 change change VB work_fc4vscbgnfdyhddwekhs4n7fcy 67 21 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 67 22 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 67 23 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 68 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 68 2 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 68 3 thermal thermal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 68 4 bath bath NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 68 6 such such JJ work_fc4vscbgnfdyhddwekhs4n7fcy 68 7 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 8 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 68 9 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 68 10 were be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 68 11 present present JJ work_fc4vscbgnfdyhddwekhs4n7fcy 68 12 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 68 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 68 14 early early JJ work_fc4vscbgnfdyhddwekhs4n7fcy 68 15 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 16 when when WRB work_fc4vscbgnfdyhddwekhs4n7fcy 68 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 68 18 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 19 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 68 20 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 68 21 started start VBD work_fc4vscbgnfdyhddwekhs4n7fcy 68 22 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 68 23 oscillate oscillate VB work_fc4vscbgnfdyhddwekhs4n7fcy 68 24 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 68 25 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 68 26 those those DT work_fc4vscbgnfdyhddwekhs4n7fcy 68 27 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 68 28 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 68 29 drive drive VB work_fc4vscbgnfdyhddwekhs4n7fcy 68 30 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 68 31 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 32 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 68 33 distribution distribution NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 34 out out IN work_fc4vscbgnfdyhddwekhs4n7fcy 68 35 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 68 36 thermal thermal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 68 37 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 68 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 69 1 By by IN work_fc4vscbgnfdyhddwekhs4n7fcy 69 2 adjusting adjust VBG work_fc4vscbgnfdyhddwekhs4n7fcy 69 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 69 4 interaction interaction NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 5 rates rate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 69 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 69 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 69 8 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 9 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 69 10 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 69 11 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 69 12 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 69 13 suitable suitable JJ work_fc4vscbgnfdyhddwekhs4n7fcy 69 14 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 69 16 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 17 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 18 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 69 19 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 69 20 dissipated dissipate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 69 21 into into IN work_fc4vscbgnfdyhddwekhs4n7fcy 69 22 thermal thermal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 69 23 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 24 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 69 25 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 69 26 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 69 27 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 70 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 70 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 70 3 nal nal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 70 4 step step NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 70 6 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 70 7 note note VB work_fc4vscbgnfdyhddwekhs4n7fcy 70 8 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 70 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 70 10 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 11 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 12 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 13 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 70 14 massless massless NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 70 16 so so IN work_fc4vscbgnfdyhddwekhs4n7fcy 70 17 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 70 18 all all DT work_fc4vscbgnfdyhddwekhs4n7fcy 70 19 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 20 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 21 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 70 22 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 70 23 principle principle JJ work_fc4vscbgnfdyhddwekhs4n7fcy 70 24 redshift redshift NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 25 away away RB work_fc4vscbgnfdyhddwekhs4n7fcy 70 26 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 70 27 radiation radiation NN work_fc4vscbgnfdyhddwekhs4n7fcy 70 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 71 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 71 2 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 71 3 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 71 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 71 5 thus thus RB work_fc4vscbgnfdyhddwekhs4n7fcy 71 6 put put VBN work_fc4vscbgnfdyhddwekhs4n7fcy 71 7 into into IN work_fc4vscbgnfdyhddwekhs4n7fcy 71 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 71 9 harmless harmless JJ work_fc4vscbgnfdyhddwekhs4n7fcy 71 10 form form NN work_fc4vscbgnfdyhddwekhs4n7fcy 71 11 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 71 12 never never RB work_fc4vscbgnfdyhddwekhs4n7fcy 71 13 dominates dominate VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 71 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 71 15 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 71 16 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 72 1 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 72 2 An an DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 3 explicit explicit JJ work_fc4vscbgnfdyhddwekhs4n7fcy 72 4 model model NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 5 To to TO work_fc4vscbgnfdyhddwekhs4n7fcy 72 6 illustrate illustrate VB work_fc4vscbgnfdyhddwekhs4n7fcy 72 7 how how WRB work_fc4vscbgnfdyhddwekhs4n7fcy 72 8 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 9 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 72 10 happen happen VB work_fc4vscbgnfdyhddwekhs4n7fcy 72 11 let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 72 12 us -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 72 13 calculate calculate VB work_fc4vscbgnfdyhddwekhs4n7fcy 72 14 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 72 15 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 16 simple simple JJ work_fc4vscbgnfdyhddwekhs4n7fcy 72 17 model model NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 18 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 72 19 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 72 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 21 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 72 22 b{matter b{matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 23 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 72 24 consists consist VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 72 25 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 72 26 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 28 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 30 whose whose WP$ work_fc4vscbgnfdyhddwekhs4n7fcy 72 31 vacuum vacuum NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 32 expectation expectation NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 33 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 34 breaks break VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 72 35 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 36 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 72 37 whose whose WP$ work_fc4vscbgnfdyhddwekhs4n7fcy 72 38 phase phase NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 39 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 72 40 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 41 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 72 42 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 72 43 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 44 scalar scalar NN work_fc4vscbgnfdyhddwekhs4n7fcy 72 45 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 72 46 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 47 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 48 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 72 49 has have VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 72 50 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 72 51 VEV VEV NNP work_fc4vscbgnfdyhddwekhs4n7fcy 72 52 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 73 1 Let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 73 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 73 3 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 73 4 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 73 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 73 6 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 73 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 73 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 73 9 both both DT work_fc4vscbgnfdyhddwekhs4n7fcy 73 10 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 73 11 +1 +1 NNS work_fc4vscbgnfdyhddwekhs4n7fcy 73 12 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 73 13 let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 73 14 them -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 73 15 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 73 16 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 73 17 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 73 18 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 73 19 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 73 20 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 73 21 g g NN work_fc4vscbgnfdyhddwekhs4n7fcy 73 22 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 73 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 73 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 73 25 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 73 26 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 73 27 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 73 28 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 73 29 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 73 30 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 73 31 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 73 32 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 73 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 74 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 74 2 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 74 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 74 5 Lagrangian Lagrangian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 6 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 74 7 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 74 8 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 74 9 relevant relevant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 74 10 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 11 our -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 74 12 analysis analysis NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 13 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 74 14 L l NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 15 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 74 16 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 17 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 18 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 19 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 20 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 21 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 74 22 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 23 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 25 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 26 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 27 m m CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 28 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 29 aa aa IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 30 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 31 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 74 32 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 33 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 34 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 35 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 36 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 37 b b LS work_fc4vscbgnfdyhddwekhs4n7fcy 74 38 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 39 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 40 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 74 41 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 74 42 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 43 @ @ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 74 44 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 45 a@ a@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 47 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 48 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 49 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 74 50 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 51 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 52 j@ j@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 53 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 54 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 55 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 56 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 57 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 58 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 59 m2j m2j NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 60 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 61 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 62 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 63 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 64 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 65 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 66 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 67 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 68 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 69 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 70 2ib 2ib NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 71 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 74 72 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 73 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 74 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 75 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 74 76 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 77 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 74 78 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 79 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 74 80 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 81 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 74 82 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 83 6 6 LS work_fc4vscbgnfdyhddwekhs4n7fcy 74 84 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 85 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 74 86 last last JJ work_fc4vscbgnfdyhddwekhs4n7fcy 74 87 term term NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 88 arises arise VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 74 89 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 90 expanding expand VBG work_fc4vscbgnfdyhddwekhs4n7fcy 74 91 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 92 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 93 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 74 94 fb fb NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 95 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 74 96 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 74 97 � � : work_fc4vscbgnfdyhddwekhs4n7fcy 74 98 )e )e . work_fc4vscbgnfdyhddwekhs4n7fcy 74 99 ib ib UH work_fc4vscbgnfdyhddwekhs4n7fcy 74 100 = = FW work_fc4vscbgnfdyhddwekhs4n7fcy 74 101 fb fb UH work_fc4vscbgnfdyhddwekhs4n7fcy 74 102 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 74 103 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 74 104 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 105 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 106 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 107 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 108 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 109 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 110 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 74 111 de de NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 112 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 113 ning ning NN work_fc4vscbgnfdyhddwekhs4n7fcy 74 114 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 115 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 74 116 � � NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 74 117 gf2b gf2b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 74 118 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 75 1 At at IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 2 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 75 3 point point NN work_fc4vscbgnfdyhddwekhs4n7fcy 75 4 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 75 5 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 75 6 free free JJ work_fc4vscbgnfdyhddwekhs4n7fcy 75 7 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 75 8 choose choose VB work_fc4vscbgnfdyhddwekhs4n7fcy 75 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 75 10 parameters parameter NNS work_fc4vscbgnfdyhddwekhs4n7fcy 75 11 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 12 L. L. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 13 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 14 purposes purpose NNS work_fc4vscbgnfdyhddwekhs4n7fcy 75 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 16 illustration illustration NN work_fc4vscbgnfdyhddwekhs4n7fcy 75 17 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 75 18 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 75 19 convenient convenient JJ work_fc4vscbgnfdyhddwekhs4n7fcy 75 20 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 75 21 choose choose VB work_fc4vscbgnfdyhddwekhs4n7fcy 75 22 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 24 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 25 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 75 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 27 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 75 28 6 6 CD work_fc4vscbgnfdyhddwekhs4n7fcy 75 29 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 75 30 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 75 31 choose choose VB work_fc4vscbgnfdyhddwekhs4n7fcy 75 32 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 75 33 somewhat somewhat RB work_fc4vscbgnfdyhddwekhs4n7fcy 75 34 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 75 35 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 36 m. m. NN work_fc4vscbgnfdyhddwekhs4n7fcy 75 37 These these DT work_fc4vscbgnfdyhddwekhs4n7fcy 75 38 values value NNS work_fc4vscbgnfdyhddwekhs4n7fcy 75 39 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 75 40 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 75 41 absolutely absolutely RB work_fc4vscbgnfdyhddwekhs4n7fcy 75 42 necessary necessary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 75 43 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 75 44 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 75 45 they -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 75 46 clearly clearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 75 47 show show VBP work_fc4vscbgnfdyhddwekhs4n7fcy 75 48 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 75 49 damping damp VBG work_fc4vscbgnfdyhddwekhs4n7fcy 75 50 mechanism mechanism NN work_fc4vscbgnfdyhddwekhs4n7fcy 75 51 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 75 52 work work NN work_fc4vscbgnfdyhddwekhs4n7fcy 75 53 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 76 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 76 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 76 3 rst rst NN work_fc4vscbgnfdyhddwekhs4n7fcy 76 4 task task NN work_fc4vscbgnfdyhddwekhs4n7fcy 76 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 76 6 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 76 7 resolve resolve VB work_fc4vscbgnfdyhddwekhs4n7fcy 76 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 76 9 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 76 10 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 76 11 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 76 12 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 76 13 b. b. NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 1 To to TO work_fc4vscbgnfdyhddwekhs4n7fcy 77 2 bring bring VB work_fc4vscbgnfdyhddwekhs4n7fcy 77 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 4 kinetic kinetic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 77 5 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 77 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 77 7 a a NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 8 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 77 9 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 10 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 77 11 canonical canonical JJ work_fc4vscbgnfdyhddwekhs4n7fcy 77 12 form form NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 13 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 77 14 perform perform VBP work_fc4vscbgnfdyhddwekhs4n7fcy 77 15 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 16 non{orthogonal non{orthogonal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 77 17 transformation transformation NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 18 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 19 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 20 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 21 a a NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 22 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 23 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 26 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 27 b0 b0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 28 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 29 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 30 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 32 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 33 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 77 34 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 77 35 7 7 LS work_fc4vscbgnfdyhddwekhs4n7fcy 77 36 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 77 37 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 38 gives give VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 77 39 L l NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 40 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 41 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 42 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 43 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 77 44 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 77 45 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 46 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 47 0)2 0)2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 48 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 49 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 50 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 51 m m CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 52 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 53 a(1 a(1 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 54 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 55 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 56 2) 2) CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 57 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 58 1a0 1a0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 59 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 60 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 61 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 62 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 63 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 77 64 @ @ IN work_fc4vscbgnfdyhddwekhs4n7fcy 77 65 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 66 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 67 0)2 0)2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 68 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 77 69 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 70 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 71 j@ j@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 72 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 73 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 74 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 75 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 76 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 77 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 78 m2j m2j NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 79 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 80 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 81 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 82 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 83 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 84 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 85 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 86 e e CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 87 2i 2i NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 88 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 89 fb( fb( NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 90 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 91 b0 b0 IN work_fc4vscbgnfdyhddwekhs4n7fcy 77 92 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 77 93 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 94 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 77 95 0p 0p NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 96 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 97 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 98 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 99 2 2 LS work_fc4vscbgnfdyhddwekhs4n7fcy 77 100 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 77 101 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 77 102 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 77 103 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 77 104 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 105 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 77 106 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 77 107 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 77 108 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 78 1 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 78 2 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 78 3 8) 8) CD work_fc4vscbgnfdyhddwekhs4n7fcy 78 4 At at IN work_fc4vscbgnfdyhddwekhs4n7fcy 78 5 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 78 6 point point NN work_fc4vscbgnfdyhddwekhs4n7fcy 78 7 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 78 8 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 78 9 convenient convenient JJ work_fc4vscbgnfdyhddwekhs4n7fcy 78 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 78 11 drop drop VB work_fc4vscbgnfdyhddwekhs4n7fcy 78 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 78 13 primes prime NNS work_fc4vscbgnfdyhddwekhs4n7fcy 78 14 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 78 15 work work VB work_fc4vscbgnfdyhddwekhs4n7fcy 78 16 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 78 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 78 18 canon- canon- NN work_fc4vscbgnfdyhddwekhs4n7fcy 78 19 ically ically RB work_fc4vscbgnfdyhddwekhs4n7fcy 78 20 normalized normalize VBD work_fc4vscbgnfdyhddwekhs4n7fcy 78 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 78 22 elds eld NNS work_fc4vscbgnfdyhddwekhs4n7fcy 78 23 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 79 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 2 further further JJ work_fc4vscbgnfdyhddwekhs4n7fcy 79 3 convenience convenience NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 4 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 79 5 represent represent VBP work_fc4vscbgnfdyhddwekhs4n7fcy 79 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 79 7 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 79 8 oscillation oscillation NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 9 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 79 11 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 12 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 79 13 eld eld VBN work_fc4vscbgnfdyhddwekhs4n7fcy 79 14 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 15 a(t a(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 16 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 17 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 79 18 a0 a0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 19 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 20 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 22 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 23 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 24 sin(mat sin(mat CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 25 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 26 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 79 27 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 28 9 9 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 29 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 30 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 79 31 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 79 32 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 34 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 79 35 Lagrangian Lagrangian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 36 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 37 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 38 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 39 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 79 40 presence presence NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 41 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 42 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 43 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 79 44 becomes become VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 79 45 Leff Leff NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 46 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 79 47 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 48 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 49 j@ j@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 50 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 51 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 52 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 53 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 54 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 55 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 56 m2j m2j NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 57 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 58 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 59 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 60 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 61 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 62 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 63 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 64 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 79 65 e2i e2i ADD work_fc4vscbgnfdyhddwekhs4n7fcy 79 66 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 67 (t) (t) ADD work_fc4vscbgnfdyhddwekhs4n7fcy 79 68 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 69 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 70 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 79 71 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 72 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 79 73 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 74 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 79 75 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 76 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 77 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 79 78 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 79 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 79 80 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 81 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 82 t t NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 83 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 84 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 85 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 86 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 87 a0 a0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 79 88 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 79 89 fb)sin(mat fb)sin(mat NN work_fc4vscbgnfdyhddwekhs4n7fcy 79 90 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 79 91 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 80 1 It -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 80 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 80 3 important important JJ work_fc4vscbgnfdyhddwekhs4n7fcy 80 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 80 5 note note VB work_fc4vscbgnfdyhddwekhs4n7fcy 80 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 80 7 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 80 8 though though IN work_fc4vscbgnfdyhddwekhs4n7fcy 80 9 a(t a(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 10 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 11 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 80 12 slowly slowly RB work_fc4vscbgnfdyhddwekhs4n7fcy 80 13 varying vary VBG work_fc4vscbgnfdyhddwekhs4n7fcy 80 14 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 15 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 80 16 frequency frequency NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 17 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 18 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 19 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 80 20 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 21 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 22 t t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 23 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 24 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 80 25 rapidly rapidly RB work_fc4vscbgnfdyhddwekhs4n7fcy 80 26 varying vary VBG work_fc4vscbgnfdyhddwekhs4n7fcy 80 27 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 80 28 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 30 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 32 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 33 t t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 34 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 35 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 80 36 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 37 a0mafb a0mafb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 80 38 cos(mat cos(mat NN work_fc4vscbgnfdyhddwekhs4n7fcy 80 39 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 80 40 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 81 1 Since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 81 2 a0ma a0ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 3 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 81 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 5 1=2 1=2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 81 6 axion axion VBP work_fc4vscbgnfdyhddwekhs4n7fcy 81 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 9 2QCD(fa 2qcd(fa CD work_fc4vscbgnfdyhddwekhs4n7fcy 81 10 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 81 11 Mpl)1=2 Mpl)1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 12 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 81 13 initially initially RB work_fc4vscbgnfdyhddwekhs4n7fcy 81 14 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 81 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 81 16 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 19 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 81 20 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 81 21 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 82 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 2 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 3 scales scale NNS work_fc4vscbgnfdyhddwekhs4n7fcy 82 4 short short RB work_fc4vscbgnfdyhddwekhs4n7fcy 82 5 compared compare VBN work_fc4vscbgnfdyhddwekhs4n7fcy 82 6 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 7 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 9 1a 1a NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 10 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 82 11 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 82 12 treat treat VB work_fc4vscbgnfdyhddwekhs4n7fcy 82 13 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 14 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 15 being be VBG work_fc4vscbgnfdyhddwekhs4n7fcy 82 16 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 82 17 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 82 18 write write VB work_fc4vscbgnfdyhddwekhs4n7fcy 82 19 L l NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 20 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 21 Leff Leff NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 22 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 82 23 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 25 j@ j@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 28 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 30 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 31 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 32 m2j m2j NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 34 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 36 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 37 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 38 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 39 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 40 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 41 e2iqt e2iqt NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 42 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 43 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 44 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 82 45 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 46 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 82 47 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 48 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 82 49 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 82 50 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 82 51 11 11 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 52 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 82 53 7 7 CD work_fc4vscbgnfdyhddwekhs4n7fcy 82 54 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 82 55 problem problem NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 56 now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 82 57 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 82 58 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 59 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 60 nd nd NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 61 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 82 62 evolution evolution NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 63 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 64 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 82 65 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 66 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 67 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 82 68 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 82 69 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 82 70 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 82 71 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 82 72 trivial trivial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 82 73 task task NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 74 because because IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 75 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 82 76 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 82 77 explicit explicit JJ work_fc4vscbgnfdyhddwekhs4n7fcy 82 78 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 79 dependence dependence NN work_fc4vscbgnfdyhddwekhs4n7fcy 82 80 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 83 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 83 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 83 3 done do VBN work_fc4vscbgnfdyhddwekhs4n7fcy 83 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 83 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 83 6 Appendix Appendix NNP work_fc4vscbgnfdyhddwekhs4n7fcy 83 7 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 83 8 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 83 9 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 83 10 give give VBP work_fc4vscbgnfdyhddwekhs4n7fcy 83 11 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 83 12 simpli simpli NN work_fc4vscbgnfdyhddwekhs4n7fcy 83 13 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 83 14 ed ed NNP work_fc4vscbgnfdyhddwekhs4n7fcy 83 15 version version NN work_fc4vscbgnfdyhddwekhs4n7fcy 83 16 here here RB work_fc4vscbgnfdyhddwekhs4n7fcy 83 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 84 1 First first RB work_fc4vscbgnfdyhddwekhs4n7fcy 84 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 84 3 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 84 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 84 5 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 84 6 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 84 7 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 84 8 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 84 9 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 84 10 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 84 11 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 84 12 ~k ~k . work_fc4vscbgnfdyhddwekhs4n7fcy 84 13 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 84 14 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 84 15 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 84 16 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 84 17 degenerate degenerate NN work_fc4vscbgnfdyhddwekhs4n7fcy 84 18 eigenstates eigenstate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 84 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 85 1 One one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 85 2 could could MD work_fc4vscbgnfdyhddwekhs4n7fcy 85 3 choose choose VB work_fc4vscbgnfdyhddwekhs4n7fcy 85 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 85 5 work work VB work_fc4vscbgnfdyhddwekhs4n7fcy 85 6 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 85 7 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 85 8 basis basis NN work_fc4vscbgnfdyhddwekhs4n7fcy 85 9 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 85 10 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 85 11 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 85 12 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 85 13 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 85 14 circularly circularly RB work_fc4vscbgnfdyhddwekhs4n7fcy 85 15 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 85 16 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 85 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 86 1 With with IN work_fc4vscbgnfdyhddwekhs4n7fcy 86 2 degenerate degenerate NN work_fc4vscbgnfdyhddwekhs4n7fcy 86 3 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 86 4 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 86 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 86 6 easy easy JJ work_fc4vscbgnfdyhddwekhs4n7fcy 86 7 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 86 8 show show VB work_fc4vscbgnfdyhddwekhs4n7fcy 86 9 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 86 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 86 11 Hamiltonian Hamiltonian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 86 12 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 86 13 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 86 14 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 86 15 any any DT work_fc4vscbgnfdyhddwekhs4n7fcy 86 16 linear linear JJ work_fc4vscbgnfdyhddwekhs4n7fcy 86 17 combination combination NN work_fc4vscbgnfdyhddwekhs4n7fcy 86 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 87 1 Next next RB work_fc4vscbgnfdyhddwekhs4n7fcy 87 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 87 3 consider consider VB work_fc4vscbgnfdyhddwekhs4n7fcy 87 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 87 5 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 87 6 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 87 7 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 87 8 6= 6= CD work_fc4vscbgnfdyhddwekhs4n7fcy 87 9 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 87 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 87 11 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 87 12 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 87 13 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 87 14 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 87 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 88 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 88 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 88 3 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 88 4 eigenstates eigenstate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 88 5 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 88 6 masses masse NNS work_fc4vscbgnfdyhddwekhs4n7fcy 88 7 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 88 8 m2 m2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 88 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 88 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 88 11 2)1=2 2)1=2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 88 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 88 13 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 88 14 correspond correspond VB work_fc4vscbgnfdyhddwekhs4n7fcy 88 15 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 88 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 88 17 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 88 18 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 88 19 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 88 20 along along IN work_fc4vscbgnfdyhddwekhs4n7fcy 88 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 88 22 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 88 23 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 88 24 imaginary imaginary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 88 25 components component NNS work_fc4vscbgnfdyhddwekhs4n7fcy 88 26 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 88 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 88 28 ; ; , work_fc4vscbgnfdyhddwekhs4n7fcy 88 29 i.e. i.e. FW work_fc4vscbgnfdyhddwekhs4n7fcy 89 1 they -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 89 2 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 89 3 A(x a(x NN work_fc4vscbgnfdyhddwekhs4n7fcy 89 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 5 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 6 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 89 7 B(x B(x NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 9 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 89 11 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 89 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 13 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 14 x x SYM work_fc4vscbgnfdyhddwekhs4n7fcy 89 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 16 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 17 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 89 18 A(x a(x NN work_fc4vscbgnfdyhddwekhs4n7fcy 89 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 20 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 21 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 89 22 iB(x ib(x NN work_fc4vscbgnfdyhddwekhs4n7fcy 89 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 89 24 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 89 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 90 1 Now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 90 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 90 3 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 90 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 90 5 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 90 6 explicit explicit JJ work_fc4vscbgnfdyhddwekhs4n7fcy 90 7 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 90 8 dependence dependence NN work_fc4vscbgnfdyhddwekhs4n7fcy 90 9 so so IN work_fc4vscbgnfdyhddwekhs4n7fcy 90 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 90 11 Hamiltonian Hamiltonian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 90 12 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 90 13 still still RB work_fc4vscbgnfdyhddwekhs4n7fcy 90 14 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 90 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 91 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 91 2 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 91 3 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 91 4 seen see VBN work_fc4vscbgnfdyhddwekhs4n7fcy 91 5 explicitly explicitly RB work_fc4vscbgnfdyhddwekhs4n7fcy 91 6 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 7 writing write VBG work_fc4vscbgnfdyhddwekhs4n7fcy 91 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 91 9 Hamiltonian Hamiltonian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 91 10 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 11 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 91 12 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 91 14 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 91 15 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 91 16 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 91 17 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 91 18 observing observe VBG work_fc4vscbgnfdyhddwekhs4n7fcy 91 19 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 20 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 91 21 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 91 22 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 91 23 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 91 24 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 25 di di NNP work_fc4vscbgnfdyhddwekhs4n7fcy 91 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 91 27 erent erent NN work_fc4vscbgnfdyhddwekhs4n7fcy 91 28 frequency frequency NN work_fc4vscbgnfdyhddwekhs4n7fcy 91 29 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 91 30 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 91 31 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 91 32 Hamiltonian Hamiltonian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 91 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 92 1 Finally finally RB work_fc4vscbgnfdyhddwekhs4n7fcy 92 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 92 3 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 92 4 non{zero non{zero NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 5 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 92 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 92 8 Hamiltonian Hamiltonian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 9 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 92 10 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 92 11 dependent dependent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 92 12 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 92 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 92 14 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 92 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 92 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 92 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 19 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 92 20 varies vary VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 92 21 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 92 22 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 92 23 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 93 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 93 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 93 3 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 93 4 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 93 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 93 6 evolution evolution NN work_fc4vscbgnfdyhddwekhs4n7fcy 93 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 93 8 well well RB work_fc4vscbgnfdyhddwekhs4n7fcy 93 9 approximated approximate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 93 10 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 93 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 93 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 93 13 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 93 14 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 93 15 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 93 16 eigenstates eigenstate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 93 17 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 93 18 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 93 19 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 93 20 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 93 21 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 93 22 qualitative qualitative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 93 23 di di NN work_fc4vscbgnfdyhddwekhs4n7fcy 93 24 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 93 25 erence erence NN work_fc4vscbgnfdyhddwekhs4n7fcy 93 26 between between IN work_fc4vscbgnfdyhddwekhs4n7fcy 93 27 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 93 28 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 93 29 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 93 30 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 93 31 circularly circularly RB work_fc4vscbgnfdyhddwekhs4n7fcy 93 32 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 93 33 solutions solution NNS work_fc4vscbgnfdyhddwekhs4n7fcy 93 34 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 94 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 94 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 94 3 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 94 4 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 94 5 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 94 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 94 8 potential potential NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 9 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 94 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 94 11 A a NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 12 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 94 13 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 94 14 B b NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 15 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 94 16 direction direction NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 17 has have VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 94 18 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 94 19 curvature curvature NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 20 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 94 21 varies vary VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 94 22 sinusoidally sinusoidally RB work_fc4vscbgnfdyhddwekhs4n7fcy 94 23 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 94 24 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 94 25 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 94 26 m2eff m2eff NNP work_fc4vscbgnfdyhddwekhs4n7fcy 94 27 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 94 28 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 94 29 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 94 30 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 94 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 94 32 2cos(2qt 2cos(2qt CD work_fc4vscbgnfdyhddwekhs4n7fcy 94 33 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 94 34 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 95 1 Since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 95 2 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 95 3 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 95 4 assume assume VB work_fc4vscbgnfdyhddwekhs4n7fcy 95 5 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 95 6 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 95 7 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 95 8 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 95 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 95 10 variation variation NN work_fc4vscbgnfdyhddwekhs4n7fcy 95 11 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 95 12 m2eff m2eff NNP work_fc4vscbgnfdyhddwekhs4n7fcy 95 13 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 95 14 adiabatic adiabatic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 95 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 96 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 96 2 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 96 3 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 4 one one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 96 5 expects expect VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 96 6 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 96 7 quantum quantum NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 8 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 96 9 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 96 10 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 11 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 12 m2 m2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 13 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 96 14 ~k2 ~k2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 15 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 96 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 17 2cos(2qt 2cos(2qt LS work_fc4vscbgnfdyhddwekhs4n7fcy 96 18 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 96 19 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 96 20 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 96 21 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 96 22 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 96 23 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 96 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 96 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 26 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 96 27 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 96 28 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 96 29 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 30 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 96 31 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 96 32 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 96 33 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 96 34 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 96 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 36 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 37 m2 m2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 96 38 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 96 39 ~k2 ~k2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 96 40 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 97 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 97 2 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 97 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 97 4 quanta quanta NNP work_fc4vscbgnfdyhddwekhs4n7fcy 97 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 97 6 oscillation oscillation NNP work_fc4vscbgnfdyhddwekhs4n7fcy 97 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 97 8 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 97 9 adiabatic adiabatic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 97 10 invariant invariant NN work_fc4vscbgnfdyhddwekhs4n7fcy 97 11 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 98 1 On on IN work_fc4vscbgnfdyhddwekhs4n7fcy 98 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 98 3 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 98 4 hand hand NN work_fc4vscbgnfdyhddwekhs4n7fcy 98 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 98 6 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 98 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 98 8 circularly circularly RB work_fc4vscbgnfdyhddwekhs4n7fcy 98 9 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 98 10 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 98 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 98 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 98 13 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 98 14 samples sample VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 98 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 98 16 potential potential NN work_fc4vscbgnfdyhddwekhs4n7fcy 98 17 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 98 18 all all DT work_fc4vscbgnfdyhddwekhs4n7fcy 98 19 phases phase NNS work_fc4vscbgnfdyhddwekhs4n7fcy 98 20 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 98 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 98 22 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 99 1 Since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 99 2 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 99 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 99 4 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 99 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 99 6 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 99 7 averaging averaging NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 8 takes take VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 99 9 place place NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 10 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 99 11 8 8 CD work_fc4vscbgnfdyhddwekhs4n7fcy 99 12 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 99 13 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 14 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 99 15 compared compare VBN work_fc4vscbgnfdyhddwekhs4n7fcy 99 16 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 99 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 99 18 evolution evolution NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 19 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 99 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 99 21 potential potential NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 22 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 99 23 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 99 24 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 99 25 little little JJ work_fc4vscbgnfdyhddwekhs4n7fcy 99 26 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 27 dependence dependence NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 28 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 99 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 99 30 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 99 31 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 100 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 100 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 100 3 Appendix Appendix NNP work_fc4vscbgnfdyhddwekhs4n7fcy 100 4 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 100 5 show show VBP work_fc4vscbgnfdyhddwekhs4n7fcy 100 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 100 7 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 100 8 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 100 9 fact fact NN work_fc4vscbgnfdyhddwekhs4n7fcy 100 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 100 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 100 12 true true JJ work_fc4vscbgnfdyhddwekhs4n7fcy 100 13 eigenmodes eigenmode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 100 14 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 100 15 approximately approximately RB work_fc4vscbgnfdyhddwekhs4n7fcy 100 16 circularly circularly RB work_fc4vscbgnfdyhddwekhs4n7fcy 100 17 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 100 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 101 1 There there EX work_fc4vscbgnfdyhddwekhs4n7fcy 101 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 101 3 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 101 4 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 101 5 dependence dependence NN work_fc4vscbgnfdyhddwekhs4n7fcy 101 6 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 101 7 pure pure JJ work_fc4vscbgnfdyhddwekhs4n7fcy 101 8 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 101 9 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 101 10 however however RB work_fc4vscbgnfdyhddwekhs4n7fcy 101 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 101 12 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 101 13 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 101 14 thermal thermal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 101 15 bath bath NN work_fc4vscbgnfdyhddwekhs4n7fcy 101 16 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 101 17 do do VBP work_fc4vscbgnfdyhddwekhs4n7fcy 101 18 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 101 19 expect expect VB work_fc4vscbgnfdyhddwekhs4n7fcy 101 20 pure pure JJ work_fc4vscbgnfdyhddwekhs4n7fcy 101 21 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 101 22 unless unless IN work_fc4vscbgnfdyhddwekhs4n7fcy 101 23 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 101 24 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 101 25 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 101 26 conserved conserve VBN work_fc4vscbgnfdyhddwekhs4n7fcy 101 27 quantum quantum NN work_fc4vscbgnfdyhddwekhs4n7fcy 101 28 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 101 29 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 102 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 102 2 corresponding correspond VBG work_fc4vscbgnfdyhddwekhs4n7fcy 102 3 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 102 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 102 5 our -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 102 6 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 102 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 102 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 102 9 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 102 10 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 102 11 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 102 12 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 102 13 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 102 14 broken break VBN work_fc4vscbgnfdyhddwekhs4n7fcy 102 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 102 16 so so IN work_fc4vscbgnfdyhddwekhs4n7fcy 102 17 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 102 18 b b CD work_fc4vscbgnfdyhddwekhs4n7fcy 102 19 charge charge NN work_fc4vscbgnfdyhddwekhs4n7fcy 102 20 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 102 21 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 102 22 conserved conserve VBN work_fc4vscbgnfdyhddwekhs4n7fcy 102 23 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 103 1 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 103 2 therefore therefore RB work_fc4vscbgnfdyhddwekhs4n7fcy 103 3 expect expect VBP work_fc4vscbgnfdyhddwekhs4n7fcy 103 4 all all DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 5 polarizations polarization NNS work_fc4vscbgnfdyhddwekhs4n7fcy 103 6 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 103 7 play play VB work_fc4vscbgnfdyhddwekhs4n7fcy 103 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 9 role role NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 103 11 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 103 12 having have VBG work_fc4vscbgnfdyhddwekhs4n7fcy 103 13 identi identi NNP work_fc4vscbgnfdyhddwekhs4n7fcy 103 14 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 103 15 ed ed NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 17 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 103 18 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 103 19 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 103 20 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 103 21 having have VBG work_fc4vscbgnfdyhddwekhs4n7fcy 103 22 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 23 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 24 dependence dependence NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 25 driven drive VBN work_fc4vscbgnfdyhddwekhs4n7fcy 103 26 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 103 27 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 28 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 29 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 103 30 eld eld VBN work_fc4vscbgnfdyhddwekhs4n7fcy 103 31 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 103 32 look look VBP work_fc4vscbgnfdyhddwekhs4n7fcy 103 33 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 103 34 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 35 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 103 36 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 37 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 38 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 103 39 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 103 40 those those DT work_fc4vscbgnfdyhddwekhs4n7fcy 103 41 modes mode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 103 42 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 104 1 Time Time NNP work_fc4vscbgnfdyhddwekhs4n7fcy 104 2 variation variation NN work_fc4vscbgnfdyhddwekhs4n7fcy 104 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 104 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 104 5 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 104 6 levels level NNS work_fc4vscbgnfdyhddwekhs4n7fcy 104 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 104 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 104 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 104 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 104 11 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 104 12 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 104 13 lead lead VB work_fc4vscbgnfdyhddwekhs4n7fcy 104 14 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 104 15 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 104 16 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 105 1 Suppose suppose VB work_fc4vscbgnfdyhddwekhs4n7fcy 105 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 105 3 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 105 4 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 105 5 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 105 6 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 105 7 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 105 8 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 105 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 105 10 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 105 11 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 105 12 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 105 13 ~k ~k . work_fc4vscbgnfdyhddwekhs4n7fcy 105 14 scatters scatter NNS work_fc4vscbgnfdyhddwekhs4n7fcy 105 15 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 105 16 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 105 17 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 105 18 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 105 19 ~k ~k NFP work_fc4vscbgnfdyhddwekhs4n7fcy 105 20 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 105 21 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 106 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 106 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 106 3 occupation occupation NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 4 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 5 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 6 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 7 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 8 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 106 9 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 106 10 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 106 11 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 12 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 106 13 obey obey VB work_fc4vscbgnfdyhddwekhs4n7fcy 106 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 106 15 di di NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 17 erential erential JJ work_fc4vscbgnfdyhddwekhs4n7fcy 106 18 equation equation NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 19 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 20 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 21 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 22 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 23 = = FW work_fc4vscbgnfdyhddwekhs4n7fcy 106 24 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 25 ~k ~k NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 26 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 27 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 28 4f0 4f0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 29 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 30 @E(~k;t @E(~k;t . work_fc4vscbgnfdyhddwekhs4n7fcy 106 31 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 32 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 33 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 34 A a NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 36 f f NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 37 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 38 k(t k(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 39 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 40 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 41 5 5 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 42 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 43 12 12 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 44 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 45 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 106 46 E(~k;t e(~k;t NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 47 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 48 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 49 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 106 50 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 51 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 106 52 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 53 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 54 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 55 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 106 56 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 106 57 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 106 58 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 59 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 60 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 106 61 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 62 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 106 63 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 106 64 equilibriumoccupation equilibriumoccupation NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 65 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 106 66 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 67 Bose{Einstein Bose{Einstein NNP work_fc4vscbgnfdyhddwekhs4n7fcy 106 68 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 106 69 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 107 1 Treating treat VBG work_fc4vscbgnfdyhddwekhs4n7fcy 107 2 � � HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 107 3 E e NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 4 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 5 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 107 6 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 7 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 9 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 10 T!0 t!0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 11 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 107 12 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 107 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 107 14 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 107 15 has have VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 107 16 solution solution NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 17 f f XX work_fc4vscbgnfdyhddwekhs4n7fcy 107 18 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 107 19 k(t k(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 20 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 107 21 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 107 22 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 24 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 107 25 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 107 26 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 27 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 28 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 107 29 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 30 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 32 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 107 33 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 107 34 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 36 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 37 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 38 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 107 39 4q2 4q2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 40 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 41 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 42 2T!0 2t!0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 43 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 107 44 + + CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 45 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 46 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 107 47 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 107 48 13 13 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 49 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 107 50 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 107 51 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 52 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 53 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 54 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 107 55 @f0=@x @f0=@x NFP work_fc4vscbgnfdyhddwekhs4n7fcy 107 56 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 107 57 tan tan NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 58 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 59 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 107 60 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 107 61 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 107 62 2q)= 2q)= CD work_fc4vscbgnfdyhddwekhs4n7fcy 107 63 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 108 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 108 2 occupation occupation NN work_fc4vscbgnfdyhddwekhs4n7fcy 108 3 numbers number NNS work_fc4vscbgnfdyhddwekhs4n7fcy 108 4 thus thus RB work_fc4vscbgnfdyhddwekhs4n7fcy 108 5 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 108 6 lag lag VBP work_fc4vscbgnfdyhddwekhs4n7fcy 108 7 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 108 8 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 108 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 108 10 phase phase NN work_fc4vscbgnfdyhddwekhs4n7fcy 108 11 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 108 12 behind behind IN work_fc4vscbgnfdyhddwekhs4n7fcy 108 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 108 14 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 108 15 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 108 16 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 108 17 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 108 18 oscillates oscillate VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 108 19 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 108 20 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 108 21 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 109 1 As as IN work_fc4vscbgnfdyhddwekhs4n7fcy 109 2 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 110 1 1 1 LS work_fc4vscbgnfdyhddwekhs4n7fcy 110 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 110 3 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 110 4 lag lag NN work_fc4vscbgnfdyhddwekhs4n7fcy 110 5 goes go VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 110 6 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 110 7 zero zero CD work_fc4vscbgnfdyhddwekhs4n7fcy 110 8 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 110 9 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 110 10 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 110 11 k(t k(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 110 12 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 110 13 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 111 1 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 111 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 111 3 E(~k;t E(~k;t . work_fc4vscbgnfdyhddwekhs4n7fcy 111 4 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 111 5 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 111 6 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 111 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 111 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 111 9 system system NN work_fc4vscbgnfdyhddwekhs4n7fcy 111 10 remains remain VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 111 11 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 111 12 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 111 13 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 112 1 As as IN work_fc4vscbgnfdyhddwekhs4n7fcy 112 2 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 113 1 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 113 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 113 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 113 4 interactions interaction NNS work_fc4vscbgnfdyhddwekhs4n7fcy 113 5 turn turn VBP work_fc4vscbgnfdyhddwekhs4n7fcy 113 6 o o DT work_fc4vscbgnfdyhddwekhs4n7fcy 113 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 113 8 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 113 9 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 113 10 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 113 11 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 113 12 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 113 13 variation variation NN work_fc4vscbgnfdyhddwekhs4n7fcy 113 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 113 15 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 113 16 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 113 17 k(t k(t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 113 18 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 113 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 114 1 Maximum maximum JJ work_fc4vscbgnfdyhddwekhs4n7fcy 114 2 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 114 3 occurs occur VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 114 4 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 114 5 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 114 6 2q 2q NNS work_fc4vscbgnfdyhddwekhs4n7fcy 114 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 115 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 2 average average JJ work_fc4vscbgnfdyhddwekhs4n7fcy 115 3 9 9 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 4 power power NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 5 dissipated dissipate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 115 6 over over IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 7 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 8 period period NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 9 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 10 2q) 2q) NNS work_fc4vscbgnfdyhddwekhs4n7fcy 115 11 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 12 1by 1by NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 14 mode mode NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 15 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 16 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 17 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 18 k k XX work_fc4vscbgnfdyhddwekhs4n7fcy 115 19 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 115 20 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 115 21 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 22 P p NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 23 = = NNS work_fc4vscbgnfdyhddwekhs4n7fcy 115 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 25 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 26 2q 2q LS work_fc4vscbgnfdyhddwekhs4n7fcy 115 27 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 28 Z z NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 29 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 30 2q) 2q) CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 32 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 33 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 34 dt dt NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 35 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 36 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 37 ~ ~ NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 38 k(t)E k(t)E NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 39 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 40 ~k;t ~k;t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 41 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 42 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 43 f f NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 44 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 45 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 47 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 115 48 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 49 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 50 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 115 51 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 52 2q)2q 2q)2q CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 53 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 54 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 115 55 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 56 2q)2 2q)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 57 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 58 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 59 4!2 4!2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 60 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 61 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 62 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 115 63 Z z NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 64 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 65 2q) 2q) CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 66 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 67 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 68 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 69 dt dt NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 70 sin(2qt sin(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 71 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 115 72 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 73 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 74 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 75 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 76 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 77 14 14 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 78 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 79 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 115 80 P p NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 81 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 115 82 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 83 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 84 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 85 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 86 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 115 87 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 88 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 89 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 115 90 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 91 2q)2 2q)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 92 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 93 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 115 94 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 95 2q)2 2q)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 96 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 97 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 98 8!2 8!2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 99 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 100 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 101 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 115 102 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 103 15 15 LS work_fc4vscbgnfdyhddwekhs4n7fcy 115 104 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 105 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 106 total total JJ work_fc4vscbgnfdyhddwekhs4n7fcy 115 107 power power NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 108 dissipated dissipate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 115 109 per per IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 110 unit unit NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 111 volume volume NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 112 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 115 113 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 115 114 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 115 115 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 116 P p NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 117 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 115 118 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 119 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 120 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 121 Z z NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 122 d3~k d3~k NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 123 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 124 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 125 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 126 )3 )3 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 127 f f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 128 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 129 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 130 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 131 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 115 132 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 133 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 134 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 135 " " '' work_fc4vscbgnfdyhddwekhs4n7fcy 115 136 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 137 2q)2 2q)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 138 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 139 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 115 140 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 141 2q)2 2q)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 142 # # NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 143 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 144 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 115 145 8!2 8!2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 146 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 115 147 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 148 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 115 149 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 150 16 16 LS work_fc4vscbgnfdyhddwekhs4n7fcy 115 151 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 115 152 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 153 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 115 154 1=3 1=3 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 155 comes come VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 115 156 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 157 averaging average VBG work_fc4vscbgnfdyhddwekhs4n7fcy 115 158 over over IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 159 all all DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 160 possible possible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 115 161 polarizations polarization NNS work_fc4vscbgnfdyhddwekhs4n7fcy 115 162 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 115 163 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 115 164 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 115 165 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 115 166 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 116 1 Equating equate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 116 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 3 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 4 power power NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 5 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 116 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 7 change change NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 8 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 116 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 10 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 11 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 116 13 P p NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 14 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 15 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 17 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 18 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 116 19 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 116 20 using use VBG work_fc4vscbgnfdyhddwekhs4n7fcy 116 21 hq2i hq2i NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 22 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 116 23 D d NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 24 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 27 1=2a 1=2a JJ work_fc4vscbgnfdyhddwekhs4n7fcy 116 28 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 29 fbcos(mat fbcos(mat . work_fc4vscbgnfdyhddwekhs4n7fcy 116 30 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 31 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 32 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 33 E e NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 34 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 35 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 36 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 37 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 38 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 39 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 40 f2 f2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 41 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 42 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 43 a a NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 44 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 116 45 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 46 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 47 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 116 48 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 116 49 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 50 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 116 51 evolves evolve NNS work_fc4vscbgnfdyhddwekhs4n7fcy 116 52 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 116 53 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 54 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 55 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 56 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 116 57 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 58 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 59 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 60 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 61 C(m;T c(m;t CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 62 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 63 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 64 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 65 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 66 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 67 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 68 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 69 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 70 2f2b 2f2b CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 71 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 72 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 73 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 74 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 75 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 116 76 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 116 77 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 116 78 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 79 17 17 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 80 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 81 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 116 82 C(m;T c(m;t NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 83 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 84 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 116 85 R r NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 86 dx dx NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 87 x x SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 88 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 89 c2+x2 c2+x2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 90 f0 f0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 91 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 116 92 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 93 p p NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 94 c2 c2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 95 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 116 96 x2 x2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 97 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 116 98 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 116 99 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 116 100 c c NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 101 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 102 m m NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 103 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 104 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 105 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 116 106 x x SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 107 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 108 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 116 109 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 116 110 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 116 111 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 117 1 Let let VB work_fc4vscbgnfdyhddwekhs4n7fcy 117 2 us -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 117 3 now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 117 4 make make VB work_fc4vscbgnfdyhddwekhs4n7fcy 117 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 117 6 approximation approximation NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 7 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 8 whatever whatever WDT work_fc4vscbgnfdyhddwekhs4n7fcy 117 9 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 10 occurs occur VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 117 11 takes take VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 117 12 place place NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 13 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 14 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 117 15 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 16 an an DT work_fc4vscbgnfdyhddwekhs4n7fcy 117 17 expansion expansion NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 18 period period NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 19 - - : work_fc4vscbgnfdyhddwekhs4n7fcy 117 20 so so IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 21 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 22 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 117 23 functions function NNS work_fc4vscbgnfdyhddwekhs4n7fcy 117 24 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 117 25 C(m;T c(m;t NN work_fc4vscbgnfdyhddwekhs4n7fcy 117 26 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 117 27 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 117 28 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 117 29 approximated approximate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 117 30 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 117 31 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 117 32 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 118 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 118 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 118 3 taking take VBG work_fc4vscbgnfdyhddwekhs4n7fcy 118 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 118 5 integral integral JJ work_fc4vscbgnfdyhddwekhs4n7fcy 118 6 R R NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 7 dt dt NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 8 � � '' work_fc4vscbgnfdyhddwekhs4n7fcy 118 9 0:1Mpl 0:1Mpl . work_fc4vscbgnfdyhddwekhs4n7fcy 118 10 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 118 11 T2 t2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 118 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 118 14 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 15 nal nal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 118 16 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 17 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 18 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 19 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 118 20 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 118 21 a;fe a;fe NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 22 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 26 a;f a;f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 27 f2 f2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 28 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 29 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 30 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 118 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 32 a;ie a;ie NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 33 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 35 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 36 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 37 a;i a;i NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 38 f2 f2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 39 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 40 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 41 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 42 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 43 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 44 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 45 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 47 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 48 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 49 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 50 Mpl Mpl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 51 f2 f2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 52 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 53 T2 t2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 54 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 118 55 18 18 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 56 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 118 57 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 58 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 118 59 solution solution NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 60 embodies embody VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 118 61 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 118 62 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 63 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 118 64 special special JJ work_fc4vscbgnfdyhddwekhs4n7fcy 118 65 cases case NNS work_fc4vscbgnfdyhddwekhs4n7fcy 118 66 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 118 67 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 118 68 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 118 69 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 118 70 mostly mostly RB work_fc4vscbgnfdyhddwekhs4n7fcy 118 71 in- in- RB work_fc4vscbgnfdyhddwekhs4n7fcy 118 72 terested tereste VBN work_fc4vscbgnfdyhddwekhs4n7fcy 118 73 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 118 74 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 118 75 cases case NNS work_fc4vscbgnfdyhddwekhs4n7fcy 118 76 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 118 77 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 118 78 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 118 79 treat treat VB work_fc4vscbgnfdyhddwekhs4n7fcy 118 80 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 118 81 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 82 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 83 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 84 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 85 a)=(f a)=(f NNP work_fc4vscbgnfdyhddwekhs4n7fcy 118 86 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 87 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 118 88 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 118 89 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 118 90 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 118 91 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 118 92 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 119 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 119 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 119 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 119 4 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 119 5 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 119 6 decreases decrease VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 119 7 exponentially exponentially RB work_fc4vscbgnfdyhddwekhs4n7fcy 119 8 during during IN work_fc4vscbgnfdyhddwekhs4n7fcy 119 9 one one CD work_fc4vscbgnfdyhddwekhs4n7fcy 119 10 expansion expansion NN work_fc4vscbgnfdyhddwekhs4n7fcy 119 11 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 119 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 120 1 Given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 120 2 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 120 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 120 4 maximum maximum JJ work_fc4vscbgnfdyhddwekhs4n7fcy 120 5 initial initial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 120 6 value value NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 120 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 120 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 120 10 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 120 11 approximately approximately RB work_fc4vscbgnfdyhddwekhs4n7fcy 120 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 120 13 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 14 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 120 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 120 16 as as RB work_fc4vscbgnfdyhddwekhs4n7fcy 120 17 long long RB work_fc4vscbgnfdyhddwekhs4n7fcy 120 18 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 120 19 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 120 20 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 120 22 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 23 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 25 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 120 26 4Mpl)=(f 4mpl)=(f NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 27 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 28 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 29 T t NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 30 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 31 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 120 32 > > XX work_fc4vscbgnfdyhddwekhs4n7fcy 120 33 20 20 CD work_fc4vscbgnfdyhddwekhs4n7fcy 120 34 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 120 35 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 120 36 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 37 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 120 38 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 120 39 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 120 40 reduced reduce VBN work_fc4vscbgnfdyhddwekhs4n7fcy 120 41 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 120 42 accept- accept- VB work_fc4vscbgnfdyhddwekhs4n7fcy 120 43 able able JJ work_fc4vscbgnfdyhddwekhs4n7fcy 120 44 levels level NNS work_fc4vscbgnfdyhddwekhs4n7fcy 120 45 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 121 1 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 121 2 take take VBP work_fc4vscbgnfdyhddwekhs4n7fcy 121 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 121 4 temperature temperature NN work_fc4vscbgnfdyhddwekhs4n7fcy 121 5 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 121 6 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 121 7 about about IN work_fc4vscbgnfdyhddwekhs4n7fcy 121 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 121 9 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 121 10 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 122 1 Dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 122 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 122 3 fastest fast JJS work_fc4vscbgnfdyhddwekhs4n7fcy 122 4 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 122 5 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 122 6 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 122 7 small small JJ work_fc4vscbgnfdyhddwekhs4n7fcy 122 8 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 123 1 On on IN work_fc4vscbgnfdyhddwekhs4n7fcy 123 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 123 3 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 123 4 hand hand NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 123 6 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 123 7 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 123 8 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 123 9 T T NNP work_fc4vscbgnfdyhddwekhs4n7fcy 123 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 123 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 123 12 U(1)b U(1)b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 123 13 symmetry symmetry NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 14 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 123 15 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 123 16 unbroken unbroken JJ work_fc4vscbgnfdyhddwekhs4n7fcy 123 17 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 123 18 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 123 19 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 20 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 123 21 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 123 22 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 123 23 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 24 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 123 26 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 123 27 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 123 28 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 123 29 mix mix VB work_fc4vscbgnfdyhddwekhs4n7fcy 123 30 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 123 31 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 123 32 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 123 33 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 123 34 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 35 mechanism mechanism NN work_fc4vscbgnfdyhddwekhs4n7fcy 123 36 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 123 37 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 123 38 operate operate VB work_fc4vscbgnfdyhddwekhs4n7fcy 123 39 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 124 1 So so RB work_fc4vscbgnfdyhddwekhs4n7fcy 124 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 124 3 greatest great JJS work_fc4vscbgnfdyhddwekhs4n7fcy 124 4 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 124 5 should should MD work_fc4vscbgnfdyhddwekhs4n7fcy 124 6 exist exist VB work_fc4vscbgnfdyhddwekhs4n7fcy 124 7 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 124 8 fb fb NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 10 T T NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 11 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 124 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 13 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 14 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 124 15 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 124 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 17 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 124 18 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 124 19 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 124 20 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 124 21 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 125 1 4 4 LS work_fc4vscbgnfdyhddwekhs4n7fcy 125 2 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 125 3 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 4 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 125 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 6 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 125 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 8 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 125 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 10 16 16 CD work_fc4vscbgnfdyhddwekhs4n7fcy 125 11 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 125 12 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 125 13 19 19 CD work_fc4vscbgnfdyhddwekhs4n7fcy 125 14 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 125 15 On on IN work_fc4vscbgnfdyhddwekhs4n7fcy 125 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 125 17 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 125 18 hand hand NN work_fc4vscbgnfdyhddwekhs4n7fcy 125 19 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 125 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 125 21 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 125 22 cuts cut VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 125 23 o o XX work_fc4vscbgnfdyhddwekhs4n7fcy 125 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 25 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 125 26 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 28 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 125 29 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 125 30 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 125 31 m m NN work_fc4vscbgnfdyhddwekhs4n7fcy 125 32 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 126 1 So so RB work_fc4vscbgnfdyhddwekhs4n7fcy 126 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 126 3 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 126 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 126 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 126 6 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 126 7 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 126 8 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 126 9 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 126 10 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 126 11 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 126 12 reduced reduce VBN work_fc4vscbgnfdyhddwekhs4n7fcy 126 13 below below IN work_fc4vscbgnfdyhddwekhs4n7fcy 126 14 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 126 15 f;min f;min DT work_fc4vscbgnfdyhddwekhs4n7fcy 126 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 126 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 126 18 4f2b 4f2b CD work_fc4vscbgnfdyhddwekhs4n7fcy 126 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 126 20 2m2 2m2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 126 21 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 126 22 20 20 CD work_fc4vscbgnfdyhddwekhs4n7fcy 126 23 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 126 24 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 126 25 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 126 26 mechanism mechanism NN work_fc4vscbgnfdyhddwekhs4n7fcy 126 27 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 127 1 Demanding demand VBG work_fc4vscbgnfdyhddwekhs4n7fcy 127 2 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 127 3 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 127 4 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 127 5 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 127 6 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 127 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 8 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 127 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 10 8 8 CD work_fc4vscbgnfdyhddwekhs4n7fcy 127 11 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 127 12 4QCD 4qcd NN work_fc4vscbgnfdyhddwekhs4n7fcy 127 13 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 127 14 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 127 15 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 127 16 comfortably comfortably RB work_fc4vscbgnfdyhddwekhs4n7fcy 127 17 solve solve VB work_fc4vscbgnfdyhddwekhs4n7fcy 127 18 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 127 19 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 127 20 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 127 21 problem problem NN work_fc4vscbgnfdyhddwekhs4n7fcy 127 22 gives give VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 127 23 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 127 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 25 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 127 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 27 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 28 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 127 29 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 127 30 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 127 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 32 210 210 CD work_fc4vscbgnfdyhddwekhs4n7fcy 127 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 34 8 8 CD work_fc4vscbgnfdyhddwekhs4n7fcy 127 35 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 127 36 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 127 37 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 127 38 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 127 39 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 128 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 128 2 19 19 CD work_fc4vscbgnfdyhddwekhs4n7fcy 128 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 128 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 128 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 6 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 128 7 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 128 8 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 128 9 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 10 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 11 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 128 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 13 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 128 14 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 15 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 128 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 128 17 8 8 CD work_fc4vscbgnfdyhddwekhs4n7fcy 128 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 129 1 These these DT work_fc4vscbgnfdyhddwekhs4n7fcy 129 2 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 3 constraints constraint NNS work_fc4vscbgnfdyhddwekhs4n7fcy 129 4 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 129 5 easily easily RB work_fc4vscbgnfdyhddwekhs4n7fcy 129 6 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 129 7 satis sati VBN work_fc4vscbgnfdyhddwekhs4n7fcy 129 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 9 ed ed NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 129 11 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 129 12 example example NN work_fc4vscbgnfdyhddwekhs4n7fcy 129 13 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 129 14 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 16 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 18 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 19 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 129 20 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 129 21 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 22 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 23 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 24 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 129 25 QCD QCD NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 26 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 129 27 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 129 28 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 29 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 30 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 31 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 33 7 7 CD work_fc4vscbgnfdyhddwekhs4n7fcy 129 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 129 35 2QCD 2qcd NN work_fc4vscbgnfdyhddwekhs4n7fcy 129 36 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 130 1 5 5 CD work_fc4vscbgnfdyhddwekhs4n7fcy 130 2 Discussion discussion NN work_fc4vscbgnfdyhddwekhs4n7fcy 130 3 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 130 4 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 130 5 established establish VBN work_fc4vscbgnfdyhddwekhs4n7fcy 130 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 130 7 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 130 8 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 130 9 possible possible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 130 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 130 11 dissipate dissipate VB work_fc4vscbgnfdyhddwekhs4n7fcy 130 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 130 13 primordial primordial JJ work_fc4vscbgnfdyhddwekhs4n7fcy 130 14 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 130 15 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 130 16 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 130 17 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 130 18 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 130 19 their -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 130 20 interactions interaction NNS work_fc4vscbgnfdyhddwekhs4n7fcy 130 21 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 130 22 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 130 23 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 130 24 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 131 1 A a DT work_fc4vscbgnfdyhddwekhs4n7fcy 131 2 key key JJ work_fc4vscbgnfdyhddwekhs4n7fcy 131 3 fea- fea- NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 4 11 11 CD work_fc4vscbgnfdyhddwekhs4n7fcy 131 5 ture ture NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 131 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 131 8 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 9 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 131 10 envision envision VBP work_fc4vscbgnfdyhddwekhs4n7fcy 131 11 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 131 12 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 131 13 mix mix VB work_fc4vscbgnfdyhddwekhs4n7fcy 131 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 131 15 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 16 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 131 17 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 131 18 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 131 19 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 20 boson boson NNP work_fc4vscbgnfdyhddwekhs4n7fcy 131 21 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 131 22 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 131 23 whose whose WP$ work_fc4vscbgnfdyhddwekhs4n7fcy 131 24 decay decay JJ work_fc4vscbgnfdyhddwekhs4n7fcy 131 25 constant constant JJ work_fc4vscbgnfdyhddwekhs4n7fcy 131 26 fb fb NN work_fc4vscbgnfdyhddwekhs4n7fcy 131 27 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 131 28 much much RB work_fc4vscbgnfdyhddwekhs4n7fcy 131 29 smaller small JJR work_fc4vscbgnfdyhddwekhs4n7fcy 131 30 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 131 31 fa fa PRP work_fc4vscbgnfdyhddwekhs4n7fcy 131 32 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 132 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 132 2 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 132 3 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 132 4 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 132 5 large large JJ work_fc4vscbgnfdyhddwekhs4n7fcy 132 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 132 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 132 8 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 132 9 allow allow VB work_fc4vscbgnfdyhddwekhs4n7fcy 132 10 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 132 11 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 132 12 couple couple VB work_fc4vscbgnfdyhddwekhs4n7fcy 132 13 strongly strongly RB work_fc4vscbgnfdyhddwekhs4n7fcy 132 14 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 132 15 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 132 16 b b CC work_fc4vscbgnfdyhddwekhs4n7fcy 132 17 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 132 18 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 132 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 133 1 By by IN work_fc4vscbgnfdyhddwekhs4n7fcy 133 2 adjusting adjust VBG work_fc4vscbgnfdyhddwekhs4n7fcy 133 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 133 4 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 5 content content NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 133 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 133 8 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 9 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 133 10 sector sector NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 11 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 133 12 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 133 13 arrange arrange VB work_fc4vscbgnfdyhddwekhs4n7fcy 133 14 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 133 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 133 16 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 17 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 133 18 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 133 19 drive drive VB work_fc4vscbgnfdyhddwekhs4n7fcy 133 20 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 133 21 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 133 22 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 133 23 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 24 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 133 25 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 133 26 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 133 27 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 134 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 134 2 pushes push VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 134 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 134 4 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 5 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 6 out out IN work_fc4vscbgnfdyhddwekhs4n7fcy 134 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 134 8 thermal thermal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 134 9 equilibrium equilibrium NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 134 11 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 134 12 ultimately ultimately RB work_fc4vscbgnfdyhddwekhs4n7fcy 134 13 allows allow VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 134 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 134 15 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 16 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 17 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 18 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 134 19 dissipate dissipate VB work_fc4vscbgnfdyhddwekhs4n7fcy 134 20 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 134 21 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 134 22 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 23 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 134 24 sector sector NN work_fc4vscbgnfdyhddwekhs4n7fcy 134 25 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 135 1 Although although IN work_fc4vscbgnfdyhddwekhs4n7fcy 135 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 135 3 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 135 4 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 135 5 constructed construct VBN work_fc4vscbgnfdyhddwekhs4n7fcy 135 6 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 135 7 model model NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 8 whereby whereby WRB work_fc4vscbgnfdyhddwekhs4n7fcy 135 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 135 10 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 135 11 dissipate dissipate NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 135 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 135 14 addition addition NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 135 16 new new JJ work_fc4vscbgnfdyhddwekhs4n7fcy 135 17 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 135 18 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 135 19 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 135 20 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 135 21 troublesome troublesome JJ work_fc4vscbgnfdyhddwekhs4n7fcy 135 22 consequences consequence NNS work_fc4vscbgnfdyhddwekhs4n7fcy 135 23 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 135 24 chief chief NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 25 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 135 26 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 135 27 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 135 28 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 135 29 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 135 30 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 31 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 135 32 itself -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 135 33 come come VB work_fc4vscbgnfdyhddwekhs4n7fcy 135 34 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 135 35 dominate dominate VB work_fc4vscbgnfdyhddwekhs4n7fcy 135 36 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 135 37 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 135 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 136 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 2 easiest easy JJS work_fc4vscbgnfdyhddwekhs4n7fcy 136 3 way way NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 136 5 avoid avoid VB work_fc4vscbgnfdyhddwekhs4n7fcy 136 6 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 136 8 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 136 9 adjust adjust VB work_fc4vscbgnfdyhddwekhs4n7fcy 136 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 11 masses masse NNS work_fc4vscbgnfdyhddwekhs4n7fcy 136 12 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 136 13 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 136 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 136 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 16 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 17 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 136 18 sector sector NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 19 so so IN work_fc4vscbgnfdyhddwekhs4n7fcy 136 20 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 21 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 136 22 part part NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 23 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 136 24 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 136 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 136 27 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 136 28 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 136 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 30 lightest light JJS work_fc4vscbgnfdyhddwekhs4n7fcy 136 31 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 32 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 136 33 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 34 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 136 35 than than IN work_fc4vscbgnfdyhddwekhs4n7fcy 136 36 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 136 37 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 38 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 39 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 136 40 itself -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 136 41 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 137 1 Then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 137 2 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 137 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 137 4 universe universe JJ work_fc4vscbgnfdyhddwekhs4n7fcy 137 5 cools cool VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 137 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 137 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 137 8 rst rst VB work_fc4vscbgnfdyhddwekhs4n7fcy 137 9 all all DT work_fc4vscbgnfdyhddwekhs4n7fcy 137 10 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 11 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 12 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 137 13 end end VB work_fc4vscbgnfdyhddwekhs4n7fcy 137 14 up up RP work_fc4vscbgnfdyhddwekhs4n7fcy 137 15 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 137 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 137 17 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 137 18 's 's POS work_fc4vscbgnfdyhddwekhs4n7fcy 137 19 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 137 20 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 137 21 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 137 22 decay decay VB work_fc4vscbgnfdyhddwekhs4n7fcy 137 23 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 137 24 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 137 25 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 26 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 137 27 order order NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 28 fb fb NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 29 into into IN work_fc4vscbgnfdyhddwekhs4n7fcy 137 30 b b NNP work_fc4vscbgnfdyhddwekhs4n7fcy 137 31 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 137 32 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 137 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 138 1 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 138 2 argued argue VBD work_fc4vscbgnfdyhddwekhs4n7fcy 138 3 earlier early RBR work_fc4vscbgnfdyhddwekhs4n7fcy 138 4 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 138 5 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 138 6 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 138 7 di di NNP work_fc4vscbgnfdyhddwekhs4n7fcy 138 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 138 9 cult cult NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 138 11 dissipate dissipate VB work_fc4vscbgnfdyhddwekhs4n7fcy 138 12 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 13 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 14 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 138 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 138 16 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 17 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 138 18 single single JJ work_fc4vscbgnfdyhddwekhs4n7fcy 138 19 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 20 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 21 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 138 22 yet yet RB work_fc4vscbgnfdyhddwekhs4n7fcy 138 23 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 138 24 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 138 25 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 138 26 present present JJ work_fc4vscbgnfdyhddwekhs4n7fcy 138 27 scenario scenario NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 28 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 29 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 138 30 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 138 31 indeed indeed RB work_fc4vscbgnfdyhddwekhs4n7fcy 138 32 absorbed absorb VBN work_fc4vscbgnfdyhddwekhs4n7fcy 138 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 139 1 It -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 139 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 139 3 natural natural JJ work_fc4vscbgnfdyhddwekhs4n7fcy 139 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 139 5 ask ask VB work_fc4vscbgnfdyhddwekhs4n7fcy 139 6 if if IN work_fc4vscbgnfdyhddwekhs4n7fcy 139 7 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 139 8 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 139 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 139 10 \Feynman \Feynman NNP work_fc4vscbgnfdyhddwekhs4n7fcy 139 11 diagram diagram NN work_fc4vscbgnfdyhddwekhs4n7fcy 139 12 " " '' work_fc4vscbgnfdyhddwekhs4n7fcy 139 13 explanation explanation NN work_fc4vscbgnfdyhddwekhs4n7fcy 139 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 139 15 our -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 139 16 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 139 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 140 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 140 2 answer answer NN work_fc4vscbgnfdyhddwekhs4n7fcy 140 3 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 140 4 yes yes UH work_fc4vscbgnfdyhddwekhs4n7fcy 140 5 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 141 1 Imagine imagine VB work_fc4vscbgnfdyhddwekhs4n7fcy 141 2 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 141 3 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 141 4 whereby whereby WRB work_fc4vscbgnfdyhddwekhs4n7fcy 141 5 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 141 6 single single JJ work_fc4vscbgnfdyhddwekhs4n7fcy 141 7 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 141 8 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 141 9 absorbed absorb VBN work_fc4vscbgnfdyhddwekhs4n7fcy 141 10 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 141 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 141 12 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 141 13 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 141 14 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 141 15 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 141 16 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 141 17 Fig Fig NNP work_fc4vscbgnfdyhddwekhs4n7fcy 141 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 142 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 142 2 3a 3a NN work_fc4vscbgnfdyhddwekhs4n7fcy 142 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 142 4 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 142 5 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 142 6 second second JJ work_fc4vscbgnfdyhddwekhs4n7fcy 142 7 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 142 8 whereby whereby WRB work_fc4vscbgnfdyhddwekhs4n7fcy 142 9 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 142 10 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 142 11 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 142 12 absorbed absorb VBN work_fc4vscbgnfdyhddwekhs4n7fcy 142 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 142 14 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 142 15 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 142 16 Fig Fig NNP work_fc4vscbgnfdyhddwekhs4n7fcy 142 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 143 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 143 2 3b 3b NN work_fc4vscbgnfdyhddwekhs4n7fcy 143 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 143 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 144 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 144 2 ratio ratio NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 3 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 144 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 144 5 rates rate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 144 6 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 144 7 these these DT work_fc4vscbgnfdyhddwekhs4n7fcy 144 8 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 144 9 processes process NNS work_fc4vscbgnfdyhddwekhs4n7fcy 144 10 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 144 11 R r NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 12 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 144 13 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 144 14 2= 2= CD work_fc4vscbgnfdyhddwekhs4n7fcy 144 15 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 16 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 144 17 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 144 18 na na IN work_fc4vscbgnfdyhddwekhs4n7fcy 144 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 144 20 2m2a 2m2a CD work_fc4vscbgnfdyhddwekhs4n7fcy 144 21 f2b f2b NNS work_fc4vscbgnfdyhddwekhs4n7fcy 144 22 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 144 23 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 144 24 21 21 LS work_fc4vscbgnfdyhddwekhs4n7fcy 144 25 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 144 26 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 144 27 na na NNP work_fc4vscbgnfdyhddwekhs4n7fcy 144 28 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 144 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 144 30 occupation occupation NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 31 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 32 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 144 33 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 144 34 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 144 35 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 145 1 As as IN work_fc4vscbgnfdyhddwekhs4n7fcy 145 2 stated state VBN work_fc4vscbgnfdyhddwekhs4n7fcy 145 3 earlier early RBR work_fc4vscbgnfdyhddwekhs4n7fcy 145 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 145 5 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 145 6 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 145 7 ec- ec- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 145 8 tive tive JJ work_fc4vscbgnfdyhddwekhs4n7fcy 145 9 single single JJ work_fc4vscbgnfdyhddwekhs4n7fcy 145 10 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 145 11 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 145 12 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 145 13 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 145 14 reduced reduce VBN work_fc4vscbgnfdyhddwekhs4n7fcy 145 15 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 145 16 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 145 17 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 145 18 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 145 19 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 145 20 = = NNP work_fc4vscbgnfdyhddwekhs4n7fcy 145 21 T T NNP work_fc4vscbgnfdyhddwekhs4n7fcy 145 22 when when WRB work_fc4vscbgnfdyhddwekhs4n7fcy 145 23 back back RB work_fc4vscbgnfdyhddwekhs4n7fcy 145 24 12 12 CD work_fc4vscbgnfdyhddwekhs4n7fcy 145 25 reactions reaction NNS work_fc4vscbgnfdyhddwekhs4n7fcy 145 26 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 145 27 included include VBN work_fc4vscbgnfdyhddwekhs4n7fcy 145 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 146 1 However however RB work_fc4vscbgnfdyhddwekhs4n7fcy 146 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 146 3 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 146 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 146 5 also also RB work_fc4vscbgnfdyhddwekhs4n7fcy 146 6 true true JJ work_fc4vscbgnfdyhddwekhs4n7fcy 146 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 146 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 146 9 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 146 10 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 146 11 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 146 12 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 146 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 146 14 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 146 15 so so RB work_fc4vscbgnfdyhddwekhs4n7fcy 146 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 146 17 ratio ratio NN work_fc4vscbgnfdyhddwekhs4n7fcy 146 18 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 146 19 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 146 20 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 147 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 147 2 21 21 CD work_fc4vscbgnfdyhddwekhs4n7fcy 147 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 147 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 147 5 correct correct JJ work_fc4vscbgnfdyhddwekhs4n7fcy 147 6 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 147 7 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 147 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 147 9 presence presence NN work_fc4vscbgnfdyhddwekhs4n7fcy 147 10 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 147 11 backre- backre- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 147 12 actions action NNS work_fc4vscbgnfdyhddwekhs4n7fcy 147 13 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 148 1 Now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 148 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 148 3 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 148 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 148 5 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 148 6 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 148 7 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 148 8 na na NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 9 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 148 10 approximated approximate VBN work_fc4vscbgnfdyhddwekhs4n7fcy 148 11 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 148 12 na na IN work_fc4vscbgnfdyhddwekhs4n7fcy 148 13 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 14 f2a f2a . work_fc4vscbgnfdyhddwekhs4n7fcy 148 15 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 148 16 H2 H2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 17 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 148 18 so so CC work_fc4vscbgnfdyhddwekhs4n7fcy 148 19 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 148 20 ratio ratio NN work_fc4vscbgnfdyhddwekhs4n7fcy 148 21 becomes become VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 148 22 R R NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 24 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 25 2M2pl= 2m2pl= CD work_fc4vscbgnfdyhddwekhs4n7fcy 148 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 148 27 2QCD 2qcd NN work_fc4vscbgnfdyhddwekhs4n7fcy 148 28 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 148 29 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 148 30 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 148 31 quite quite RB work_fc4vscbgnfdyhddwekhs4n7fcy 148 32 large large JJ work_fc4vscbgnfdyhddwekhs4n7fcy 148 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 149 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 149 2 leads lead VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 149 3 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 149 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 149 5 situtation situtation NN work_fc4vscbgnfdyhddwekhs4n7fcy 149 6 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 149 7 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 149 8 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 149 9 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 149 10 formally formally RB work_fc4vscbgnfdyhddwekhs4n7fcy 149 11 exceeds exceed VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 149 12 one one CD work_fc4vscbgnfdyhddwekhs4n7fcy 149 13 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 149 14 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 149 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 150 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 150 2 three three CD work_fc4vscbgnfdyhddwekhs4n7fcy 150 3 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 150 4 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 150 5 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 150 6 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 150 7 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 150 8 larger large JJR work_fc4vscbgnfdyhddwekhs4n7fcy 150 9 ... ... . work_fc4vscbgnfdyhddwekhs4n7fcy 151 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 151 2 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 151 3 situation situation NN work_fc4vscbgnfdyhddwekhs4n7fcy 151 4 what what WP work_fc4vscbgnfdyhddwekhs4n7fcy 151 5 one one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 151 6 must must MD work_fc4vscbgnfdyhddwekhs4n7fcy 151 7 do do VB work_fc4vscbgnfdyhddwekhs4n7fcy 151 8 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 151 9 sum sum NN work_fc4vscbgnfdyhddwekhs4n7fcy 151 10 over over RP work_fc4vscbgnfdyhddwekhs4n7fcy 151 11 diagrams diagram NNS work_fc4vscbgnfdyhddwekhs4n7fcy 151 12 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 151 13 any any DT work_fc4vscbgnfdyhddwekhs4n7fcy 151 14 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 151 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 151 16 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 151 17 attached attach VBN work_fc4vscbgnfdyhddwekhs4n7fcy 151 18 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 151 19 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 151 20 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 151 21 participating participate VBG work_fc4vscbgnfdyhddwekhs4n7fcy 151 22 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 151 23 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 151 24 scattering scattering NN work_fc4vscbgnfdyhddwekhs4n7fcy 151 25 process process NN work_fc4vscbgnfdyhddwekhs4n7fcy 151 26 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 152 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 2 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 152 3 equivalent equivalent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 152 4 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 5 solving solve VBG work_fc4vscbgnfdyhddwekhs4n7fcy 152 6 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 8 propagator propagator NN work_fc4vscbgnfdyhddwekhs4n7fcy 152 9 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 10 these these DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 11 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 152 12 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 14 presence presence NN work_fc4vscbgnfdyhddwekhs4n7fcy 152 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 17 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 152 18 oscillating oscillating NN work_fc4vscbgnfdyhddwekhs4n7fcy 152 19 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 152 20 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 152 21 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 152 22 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 152 23 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 24 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 152 25 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 152 26 done do VBN work_fc4vscbgnfdyhddwekhs4n7fcy 152 27 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 152 28 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 152 29 paper paper NN work_fc4vscbgnfdyhddwekhs4n7fcy 152 30 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 153 1 Along along IN work_fc4vscbgnfdyhddwekhs4n7fcy 153 2 these these DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 3 lines line NNS work_fc4vscbgnfdyhddwekhs4n7fcy 153 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 153 5 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 153 6 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 153 7 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 8 normal normal JJ work_fc4vscbgnfdyhddwekhs4n7fcy 153 9 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 10 model model NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 11 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 153 12 no no DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 13 mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 153 14 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 15 additional additional JJ work_fc4vscbgnfdyhddwekhs4n7fcy 153 16 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 17 brings bring VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 153 18 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 19 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 20 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 153 21 Mpl Mpl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 153 22 = = NNP work_fc4vscbgnfdyhddwekhs4n7fcy 153 23 fa fa XX work_fc4vscbgnfdyhddwekhs4n7fcy 153 24 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 153 25 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 153 26 amplitude amplitude NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 27 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 153 28 so so CC work_fc4vscbgnfdyhddwekhs4n7fcy 153 29 here here RB work_fc4vscbgnfdyhddwekhs4n7fcy 153 30 also also RB work_fc4vscbgnfdyhddwekhs4n7fcy 153 31 one one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 153 32 should should MD work_fc4vscbgnfdyhddwekhs4n7fcy 153 33 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 153 34 calculate calculate VB work_fc4vscbgnfdyhddwekhs4n7fcy 153 35 individual individual JJ work_fc4vscbgnfdyhddwekhs4n7fcy 153 36 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 153 37 rates rate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 153 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 154 1 Rather rather RB work_fc4vscbgnfdyhddwekhs4n7fcy 154 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 154 3 one one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 154 4 should should MD work_fc4vscbgnfdyhddwekhs4n7fcy 154 5 calculate calculate VB work_fc4vscbgnfdyhddwekhs4n7fcy 154 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 154 7 propagators propagator NNS work_fc4vscbgnfdyhddwekhs4n7fcy 154 8 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 154 9 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 154 10 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 154 11 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 154 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 154 13 including include VBG work_fc4vscbgnfdyhddwekhs4n7fcy 154 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 154 15 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 154 16 dependent dependent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 154 17 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 154 18 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 154 19 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 154 20 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 154 21 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 154 22 arrive arrive VB work_fc4vscbgnfdyhddwekhs4n7fcy 154 23 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 154 24 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 154 25 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 154 26 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 154 27 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 154 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 155 1 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 155 2 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 155 3 presently presently RB work_fc4vscbgnfdyhddwekhs4n7fcy 155 4 considering consider VBG work_fc4vscbgnfdyhddwekhs4n7fcy 155 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 155 6 question question NN work_fc4vscbgnfdyhddwekhs4n7fcy 155 7 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 155 8 what what WDT work_fc4vscbgnfdyhddwekhs4n7fcy 155 9 dissipation dissipation NN work_fc4vscbgnfdyhddwekhs4n7fcy 155 10 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 155 11 result result VB work_fc4vscbgnfdyhddwekhs4n7fcy 155 12 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 155 13 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 155 14 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 155 15 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 155 16 derivative derivative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 155 17 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 155 18 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 155 19 mesons meson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 155 20 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 155 21 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 155 22 plan plan VBP work_fc4vscbgnfdyhddwekhs4n7fcy 155 23 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 155 24 present present VB work_fc4vscbgnfdyhddwekhs4n7fcy 155 25 results result NNS work_fc4vscbgnfdyhddwekhs4n7fcy 155 26 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 155 27 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 155 28 separate separate JJ work_fc4vscbgnfdyhddwekhs4n7fcy 155 29 paper paper NN work_fc4vscbgnfdyhddwekhs4n7fcy 155 30 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 156 1 Although although IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 2 derivative derivative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 3 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 156 4 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 156 5 seem seem VB work_fc4vscbgnfdyhddwekhs4n7fcy 156 6 important important JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 7 too too RB work_fc4vscbgnfdyhddwekhs4n7fcy 156 8 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 156 9 one one PRP work_fc4vscbgnfdyhddwekhs4n7fcy 156 10 must must MD work_fc4vscbgnfdyhddwekhs4n7fcy 156 11 remember remember VB work_fc4vscbgnfdyhddwekhs4n7fcy 156 12 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 13 such such JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 14 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 156 15 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 156 16 less less JJR work_fc4vscbgnfdyhddwekhs4n7fcy 156 17 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 156 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 156 19 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 20 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 21 damping damp VBG work_fc4vscbgnfdyhddwekhs4n7fcy 156 22 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 156 23 non non JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 24 - - JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 25 relativistic relativistic JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 26 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 27 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 156 28 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 156 29 due due JJ work_fc4vscbgnfdyhddwekhs4n7fcy 156 30 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 31 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 156 32 factor factor NN work_fc4vscbgnfdyhddwekhs4n7fcy 156 33 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 34 ma ma NNP work_fc4vscbgnfdyhddwekhs4n7fcy 156 35 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 156 36 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 156 37 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 156 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 157 1 Besides besides IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 2 damping damp VBG work_fc4vscbgnfdyhddwekhs4n7fcy 157 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 157 4 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 157 5 oscillations oscillation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 157 6 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 157 8 early early JJ work_fc4vscbgnfdyhddwekhs4n7fcy 157 9 universe universe NN work_fc4vscbgnfdyhddwekhs4n7fcy 157 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 157 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 157 12 kind kind NN work_fc4vscbgnfdyhddwekhs4n7fcy 157 13 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 14 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 157 15 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 16 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 157 17 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 18 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 157 19 goldstone goldstone NN work_fc4vscbgnfdyhddwekhs4n7fcy 157 20 bosons boson NNS work_fc4vscbgnfdyhddwekhs4n7fcy 157 21 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 157 22 have have VBP work_fc4vscbgnfdyhddwekhs4n7fcy 157 23 been be VBN work_fc4vscbgnfdyhddwekhs4n7fcy 157 24 discussing discuss VBG work_fc4vscbgnfdyhddwekhs4n7fcy 157 25 could could MD work_fc4vscbgnfdyhddwekhs4n7fcy 157 26 lead lead VB work_fc4vscbgnfdyhddwekhs4n7fcy 157 27 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 157 28 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 157 29 interesting interesting JJ work_fc4vscbgnfdyhddwekhs4n7fcy 157 30 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 157 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 157 32 ects ect NNS work_fc4vscbgnfdyhddwekhs4n7fcy 157 33 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 158 1 In in IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 2 particular particular JJ work_fc4vscbgnfdyhddwekhs4n7fcy 158 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 158 4 it -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 158 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 158 6 possible possible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 158 7 now now RB work_fc4vscbgnfdyhddwekhs4n7fcy 158 8 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 158 9 contemplate contemplate VB work_fc4vscbgnfdyhddwekhs4n7fcy 158 10 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 11 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 158 12 invisible invisible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 158 13 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 14 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 15 fa fa IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 158 17 MGUT MGUT NNP work_fc4vscbgnfdyhddwekhs4n7fcy 158 18 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 158 19 MPl MPl NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 20 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 158 21 have have VB work_fc4vscbgnfdyhddwekhs4n7fcy 158 22 sizable sizable JJ work_fc4vscbgnfdyhddwekhs4n7fcy 158 23 couplings coupling NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 24 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 25 some some DT work_fc4vscbgnfdyhddwekhs4n7fcy 158 26 kinds kind NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 27 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 28 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 158 29 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 158 30 perhaps perhaps RB work_fc4vscbgnfdyhddwekhs4n7fcy 158 31 even even RB work_fc4vscbgnfdyhddwekhs4n7fcy 158 32 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 33 particles particle NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 34 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 158 35 13 13 CD work_fc4vscbgnfdyhddwekhs4n7fcy 158 36 carry carry VBP work_fc4vscbgnfdyhddwekhs4n7fcy 158 37 standard standard JJ work_fc4vscbgnfdyhddwekhs4n7fcy 158 38 model model NN work_fc4vscbgnfdyhddwekhs4n7fcy 158 39 gauge gauge NN work_fc4vscbgnfdyhddwekhs4n7fcy 158 40 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 158 41 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 159 1 This this DT work_fc4vscbgnfdyhddwekhs4n7fcy 159 2 would would MD work_fc4vscbgnfdyhddwekhs4n7fcy 159 3 mean mean VB work_fc4vscbgnfdyhddwekhs4n7fcy 159 4 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 159 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 159 6 \invisible \invisible CD work_fc4vscbgnfdyhddwekhs4n7fcy 159 7 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 159 8 " " `` work_fc4vscbgnfdyhddwekhs4n7fcy 159 9 may may MD work_fc4vscbgnfdyhddwekhs4n7fcy 159 10 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 159 11 be be VB work_fc4vscbgnfdyhddwekhs4n7fcy 159 12 quite quite RB work_fc4vscbgnfdyhddwekhs4n7fcy 159 13 as as RB work_fc4vscbgnfdyhddwekhs4n7fcy 159 14 invisible invisible JJ work_fc4vscbgnfdyhddwekhs4n7fcy 159 15 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 159 16 was be VBD work_fc4vscbgnfdyhddwekhs4n7fcy 159 17 thought think VBN work_fc4vscbgnfdyhddwekhs4n7fcy 159 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 160 1 Also also RB work_fc4vscbgnfdyhddwekhs4n7fcy 160 2 worth worth JJ work_fc4vscbgnfdyhddwekhs4n7fcy 160 3 further further JJ work_fc4vscbgnfdyhddwekhs4n7fcy 160 4 investigation investigation NN work_fc4vscbgnfdyhddwekhs4n7fcy 160 5 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 160 6 whether whether IN work_fc4vscbgnfdyhddwekhs4n7fcy 160 7 similar similar JJ work_fc4vscbgnfdyhddwekhs4n7fcy 160 8 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 160 9 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 160 10 familiar familiar JJ work_fc4vscbgnfdyhddwekhs4n7fcy 160 11 majoron majoron NNP work_fc4vscbgnfdyhddwekhs4n7fcy 160 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 160 13 familon familon NN work_fc4vscbgnfdyhddwekhs4n7fcy 160 14 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 160 15 texture texture NN work_fc4vscbgnfdyhddwekhs4n7fcy 160 16 models model NNS work_fc4vscbgnfdyhddwekhs4n7fcy 160 17 could could MD work_fc4vscbgnfdyhddwekhs4n7fcy 160 18 lead lead VB work_fc4vscbgnfdyhddwekhs4n7fcy 160 19 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 160 20 interesting interesting JJ work_fc4vscbgnfdyhddwekhs4n7fcy 160 21 phenomena phenomenon NNS work_fc4vscbgnfdyhddwekhs4n7fcy 160 22 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 161 1 Appendix Appendix NNP work_fc4vscbgnfdyhddwekhs4n7fcy 161 2 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 161 3 easiest easy JJS work_fc4vscbgnfdyhddwekhs4n7fcy 161 4 way way NN work_fc4vscbgnfdyhddwekhs4n7fcy 161 5 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 161 6 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 161 7 nd nd NNP work_fc4vscbgnfdyhddwekhs4n7fcy 161 8 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 161 9 eigenstates eigenstate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 161 10 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 161 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 161 12 Lagrangian Lagrangian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 161 13 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 161 14 Eq Eq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 161 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 162 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 2 11 11 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 4 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 162 5 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 162 6 make make VB work_fc4vscbgnfdyhddwekhs4n7fcy 162 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 162 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 9 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 10 rede rede NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 11 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 12 nition nition NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 13 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 14 eiqt eiqt NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 16 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 162 17 after after IN work_fc4vscbgnfdyhddwekhs4n7fcy 162 18 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 162 19 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 162 20 Lagrangian Lagrangian NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 21 becomes become VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 162 22 L0 L0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 23 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 24 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 25 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 26 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 27 j@ j@ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 28 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 29 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 30 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 31 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 32 m2 m2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 33 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 34 q2 q2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 35 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 36 j j NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 37 j2 j2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 38 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 162 39 iq iq NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 40 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 41 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 42 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 43 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 44 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 45 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 47 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 48 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 49 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 50 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 51 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 52 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 53 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 54 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 55 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 56 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 57 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 58 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 162 59 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 60 A1 A1 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 61 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 62 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 162 63 equations equation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 64 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 162 65 motion motion NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 66 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 162 67 L0 L0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 68 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 162 69 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 70 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 71 52 52 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 72 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 73 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 74 m2 m2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 75 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 76 q2 q2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 77 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 78 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 79 2iq 2iq NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 80 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 81 + + NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 82 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 83 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 84 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 85 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 86 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 162 87 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 88 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 89 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 90 52 52 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 91 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 92 + + NFP work_fc4vscbgnfdyhddwekhs4n7fcy 162 93 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 94 m2 m2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 95 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 96 q2 q2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 97 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 98 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 99 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 162 100 2iq 2iq JJ work_fc4vscbgnfdyhddwekhs4n7fcy 162 101 _ _ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 102 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 103 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 104 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 105 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 106 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 107 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 108 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 162 109 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 110 A2 A2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 111 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 112 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 162 113 solutions solution NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 114 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 162 115 these these DT work_fc4vscbgnfdyhddwekhs4n7fcy 162 116 equations equation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 117 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 162 118 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 162 119 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 120 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 121 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 162 122 � � : work_fc4vscbgnfdyhddwekhs4n7fcy 162 123 ei(!+t ei(!+t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 124 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 125 k k NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 126 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 127 x x NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 128 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 129 + + CD work_fc4vscbgnfdyhddwekhs4n7fcy 162 130 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 131 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 132 e e NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 133 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 134 i(!+t i(!+t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 135 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 136 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 137 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 138 x x LS work_fc4vscbgnfdyhddwekhs4n7fcy 162 139 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 140 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 141 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 162 142 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 162 143 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 144 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 162 145 � � VBP work_fc4vscbgnfdyhddwekhs4n7fcy 162 146 e e LS work_fc4vscbgnfdyhddwekhs4n7fcy 162 147 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 148 i(! i(! '' work_fc4vscbgnfdyhddwekhs4n7fcy 162 149 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 150 t t NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 151 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 152 k k NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 153 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 162 154 x x NN work_fc4vscbgnfdyhddwekhs4n7fcy 162 155 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 156 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 162 157 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 158 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 159 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 162 160 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 162 161 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 162 162 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 163 1 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 2 t t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 4 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 5 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 163 6 x x LS work_fc4vscbgnfdyhddwekhs4n7fcy 163 7 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 163 8 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 9 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 163 10 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 163 11 A3 a3 NN work_fc4vscbgnfdyhddwekhs4n7fcy 163 12 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 163 13 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 163 14 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 163 15 index index NN work_fc4vscbgnfdyhddwekhs4n7fcy 163 16 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 163 17 denotes denote VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 163 18 one one CD work_fc4vscbgnfdyhddwekhs4n7fcy 163 19 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 163 20 four four CD work_fc4vscbgnfdyhddwekhs4n7fcy 163 21 solutions solution NNS work_fc4vscbgnfdyhddwekhs4n7fcy 163 22 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 163 23 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 163 24 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 163 25 wave wave NN work_fc4vscbgnfdyhddwekhs4n7fcy 163 26 vector vector NN work_fc4vscbgnfdyhddwekhs4n7fcy 163 27 ~k ~k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 163 28 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 164 1 Due due IN work_fc4vscbgnfdyhddwekhs4n7fcy 164 2 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 164 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 164 4 mixing mixing NN work_fc4vscbgnfdyhddwekhs4n7fcy 164 5 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 164 6 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 164 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 164 8 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 164 9 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 164 10 simultaneously simultaneously RB work_fc4vscbgnfdyhddwekhs4n7fcy 164 11 solve solve VB work_fc4vscbgnfdyhddwekhs4n7fcy 164 12 both both DT work_fc4vscbgnfdyhddwekhs4n7fcy 164 13 equations equation NNS work_fc4vscbgnfdyhddwekhs4n7fcy 164 14 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 164 15 motion motion NN work_fc4vscbgnfdyhddwekhs4n7fcy 164 16 requires require VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 164 17 that that IN work_fc4vscbgnfdyhddwekhs4n7fcy 164 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 164 19 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 164 20 be be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 164 21 either either CC work_fc4vscbgnfdyhddwekhs4n7fcy 164 22 pure pure JJ work_fc4vscbgnfdyhddwekhs4n7fcy 164 23 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 164 24 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 164 25 pure pure JJ work_fc4vscbgnfdyhddwekhs4n7fcy 164 26 imaginary imaginary NN work_fc4vscbgnfdyhddwekhs4n7fcy 164 27 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 164 28 but but CC work_fc4vscbgnfdyhddwekhs4n7fcy 164 29 otherwise otherwise RB work_fc4vscbgnfdyhddwekhs4n7fcy 164 30 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 164 31 normalization normalization NN work_fc4vscbgnfdyhddwekhs4n7fcy 164 32 amplitude amplitude NN work_fc4vscbgnfdyhddwekhs4n7fcy 164 33 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 164 34 arbitrary arbitrary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 164 35 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 165 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 165 2 positive positive JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 3 eigenfrequencies eigenfrequencie NNS work_fc4vscbgnfdyhddwekhs4n7fcy 165 4 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 165 5 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 165 6 by by RP work_fc4vscbgnfdyhddwekhs4n7fcy 165 7 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 165 8 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 165 9 � � JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 165 11 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 165 12 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 13 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 14 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 165 15 q2 q2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 165 17 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 18 4!2 4!2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 19 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 20 q2 q2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 21 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 165 22 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 23 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 24 i i CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 25 1=2 1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 165 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 165 27 1=2 1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 165 28 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 165 29 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 165 30 A4 a4 NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 31 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 165 32 14 14 CD work_fc4vscbgnfdyhddwekhs4n7fcy 165 33 Negative negative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 34 frequency frequency NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 35 solutions solution NNS work_fc4vscbgnfdyhddwekhs4n7fcy 165 36 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 165 37 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 38 ~k ~k NNS work_fc4vscbgnfdyhddwekhs4n7fcy 165 39 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 165 40 equivalent equivalent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 41 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 165 42 positive positive JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 43 fre- fre- NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 44 quency quency NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 45 solutions solution NNS work_fc4vscbgnfdyhddwekhs4n7fcy 165 46 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 165 47 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 165 48 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 165 49 ~k ~k NNS work_fc4vscbgnfdyhddwekhs4n7fcy 165 50 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 165 51 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 165 52 so so RB work_fc4vscbgnfdyhddwekhs4n7fcy 165 53 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 165 54 not not RB work_fc4vscbgnfdyhddwekhs4n7fcy 165 55 distinct distinct JJ work_fc4vscbgnfdyhddwekhs4n7fcy 165 56 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 166 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 166 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 166 3 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 166 4 when when WRB work_fc4vscbgnfdyhddwekhs4n7fcy 166 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 6 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 166 7 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 166 8 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 166 9 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 166 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 166 11 mixings mixing NNS work_fc4vscbgnfdyhddwekhs4n7fcy 166 12 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 166 13 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 166 14 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 166 15 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 17 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 166 18 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 20 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 166 21 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 166 22 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 166 23 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 166 24 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 166 25 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 166 26 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 166 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 28 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 166 29 q)2 q)2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 166 30 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 166 31 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 166 32 A5 a5 NN work_fc4vscbgnfdyhddwekhs4n7fcy 166 33 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 166 34 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 166 35 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 166 36 case case NN work_fc4vscbgnfdyhddwekhs4n7fcy 166 37 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 166 38 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 39 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 166 40 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 166 41 imaginary imaginary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 166 42 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 166 43 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 166 44 sign sign NN work_fc4vscbgnfdyhddwekhs4n7fcy 166 45 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 166 46 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 166 47 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 166 48 changed change VBN work_fc4vscbgnfdyhddwekhs4n7fcy 166 49 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 167 1 Counting counting NN work_fc4vscbgnfdyhddwekhs4n7fcy 167 2 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 167 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 167 5 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 167 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 7 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 8 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 167 9 imaginary imaginary JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 11 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 167 12 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 167 13 there there EX work_fc4vscbgnfdyhddwekhs4n7fcy 167 14 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 167 15 eight eight CD work_fc4vscbgnfdyhddwekhs4n7fcy 167 16 eigenfunc- eigenfunc- JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 17 tions tion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 167 18 combining combine VBG work_fc4vscbgnfdyhddwekhs4n7fcy 167 19 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 20 wavenumbers wavenumber NNS work_fc4vscbgnfdyhddwekhs4n7fcy 167 21 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 22 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 167 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 24 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 25 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 167 26 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 167 27 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 167 28 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 29 right right JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 30 number number NN work_fc4vscbgnfdyhddwekhs4n7fcy 167 31 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 167 32 determine determine VB work_fc4vscbgnfdyhddwekhs4n7fcy 167 33 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 35 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 36 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 167 37 its -PRON- PRP$ work_fc4vscbgnfdyhddwekhs4n7fcy 167 38 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 39 rst rst NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 40 time time NN work_fc4vscbgnfdyhddwekhs4n7fcy 167 41 derivative derivative JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 42 at at IN work_fc4vscbgnfdyhddwekhs4n7fcy 167 43 each each DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 44 point point NN work_fc4vscbgnfdyhddwekhs4n7fcy 167 45 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 167 46 so so CC work_fc4vscbgnfdyhddwekhs4n7fcy 167 47 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 48 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 167 49 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 50 complete complete JJ work_fc4vscbgnfdyhddwekhs4n7fcy 167 51 set set NN work_fc4vscbgnfdyhddwekhs4n7fcy 167 52 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 167 53 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 167 54 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 167 55 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 167 56 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 57 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 167 58 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 168 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 168 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 168 3 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 5 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 168 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 168 8 states state NNS work_fc4vscbgnfdyhddwekhs4n7fcy 168 9 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 168 10 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 168 11 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 168 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 13 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 168 14 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 168 15 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 168 17 iqt iqt NN work_fc4vscbgnfdyhddwekhs4n7fcy 168 18 i. i. NN work_fc4vscbgnfdyhddwekhs4n7fcy 169 1 We -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 169 2 can can MD work_fc4vscbgnfdyhddwekhs4n7fcy 169 3 choose choose VB work_fc4vscbgnfdyhddwekhs4n7fcy 169 4 any any DT work_fc4vscbgnfdyhddwekhs4n7fcy 169 5 four four CD work_fc4vscbgnfdyhddwekhs4n7fcy 169 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 169 7 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 169 8 eight eight CD work_fc4vscbgnfdyhddwekhs4n7fcy 169 9 eigenstates eigenstate NNS work_fc4vscbgnfdyhddwekhs4n7fcy 169 10 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 169 11 characterize characterize VB work_fc4vscbgnfdyhddwekhs4n7fcy 169 12 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 169 13 momentumk momentumk NN work_fc4vscbgnfdyhddwekhs4n7fcy 169 14 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 169 15 using use VBG work_fc4vscbgnfdyhddwekhs4n7fcy 169 16 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 169 17 other other JJ work_fc4vscbgnfdyhddwekhs4n7fcy 169 18 four four CD work_fc4vscbgnfdyhddwekhs4n7fcy 169 19 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 169 20 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 169 21 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 169 22 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 169 23 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 170 1 It -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 170 2 seems seem VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 170 3 natural natural JJ work_fc4vscbgnfdyhddwekhs4n7fcy 170 4 to to TO work_fc4vscbgnfdyhddwekhs4n7fcy 170 5 chose chose VB work_fc4vscbgnfdyhddwekhs4n7fcy 170 6 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 170 7 set set NN work_fc4vscbgnfdyhddwekhs4n7fcy 170 8 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 170 9 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 171 1 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 171 2 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 171 3 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 172 1 ! ! NFP work_fc4vscbgnfdyhddwekhs4n7fcy 172 2 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 172 3 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 172 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 172 5 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 172 6 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 173 1 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 173 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 173 3 since since IN work_fc4vscbgnfdyhddwekhs4n7fcy 173 4 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 173 5 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 173 6 limit limit NN work_fc4vscbgnfdyhddwekhs4n7fcy 173 7 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 173 8 must must MD work_fc4vscbgnfdyhddwekhs4n7fcy 173 9 get get VB work_fc4vscbgnfdyhddwekhs4n7fcy 173 10 back back RB work_fc4vscbgnfdyhddwekhs4n7fcy 173 11 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 173 12 free free JJ work_fc4vscbgnfdyhddwekhs4n7fcy 173 13 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 173 14 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 173 15 theory theory NN work_fc4vscbgnfdyhddwekhs4n7fcy 173 16 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 173 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 173 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 174 1 With with IN work_fc4vscbgnfdyhddwekhs4n7fcy 174 2 this this DT work_fc4vscbgnfdyhddwekhs4n7fcy 174 3 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 174 4 mind mind NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 174 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 174 7 general general JJ work_fc4vscbgnfdyhddwekhs4n7fcy 174 8 solution solution NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 9 that that WDT work_fc4vscbgnfdyhddwekhs4n7fcy 174 10 we -PRON- PRP work_fc4vscbgnfdyhddwekhs4n7fcy 174 11 will will MD work_fc4vscbgnfdyhddwekhs4n7fcy 174 12 associate associate VB work_fc4vscbgnfdyhddwekhs4n7fcy 174 13 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 174 14 momentum momentum NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 15 k k NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 16 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 174 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 18 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 174 19 X x NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 20 s= s= NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 21 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 22 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 23 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 24 s+ s+ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 25 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 26 s+ s+ NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 27 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 174 28 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 174 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 30 s s NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 31 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 33 s s NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 34 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 35 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 36 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 37 A6 A6 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 38 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 39 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 174 40 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 174 41 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 42 ss0 ss0 NNS work_fc4vscbgnfdyhddwekhs4n7fcy 174 43 are be VBP work_fc4vscbgnfdyhddwekhs4n7fcy 174 44 real real JJ work_fc4vscbgnfdyhddwekhs4n7fcy 174 45 numbers number NNS work_fc4vscbgnfdyhddwekhs4n7fcy 174 46 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 174 47 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 174 48 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 49 ss0 ss0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 50 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 174 51 N n CD work_fc4vscbgnfdyhddwekhs4n7fcy 174 52 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 53 1=2 1=2 NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 174 54 ss0 ss0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 55 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 56 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 57 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 174 58 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 59 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 60 ss0 ss0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 61 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 62 ei(!s ei(!s CD work_fc4vscbgnfdyhddwekhs4n7fcy 174 63 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 64 q)t q)t NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 65 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 66 ik ik IN work_fc4vscbgnfdyhddwekhs4n7fcy 174 67 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 68 x x NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 69 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 174 70 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 71 ss0e ss0e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 72 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 73 i(!s+q)t+ik i(!s+q)t+ik CD work_fc4vscbgnfdyhddwekhs4n7fcy 174 74 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 75 x x NNS work_fc4vscbgnfdyhddwekhs4n7fcy 174 76 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 174 77 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 174 78 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 79 A7 A7 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 80 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 81 Here here RB work_fc4vscbgnfdyhddwekhs4n7fcy 174 82 Nss0 Nss0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 83 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 174 84 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 85 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 174 86 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 87 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 88 ss0)2 ss0)2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 174 89 + + NFP work_fc4vscbgnfdyhddwekhs4n7fcy 174 90 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 174 91 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 92 ss0)2 ss0)2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 93 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 174 94 s s NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 95 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 96 s s NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 97 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 174 98 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 175 1 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 2 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 3 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 175 4 q2 q2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 5 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 175 6 s s NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 7 h h NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 8 4!2 4!2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 9 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 10 q q NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 11 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 12 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 175 13 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 14 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 15 i i CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 16 1=2 1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 18 1=2 1=2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 19 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 20 ss0 ss0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 22 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 175 23 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 24 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 25 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 175 26 s0 s0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 27 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 28 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 30 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 175 31 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 33 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 175 34 s)2 s)2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 35 4q!s 4q!s CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 36 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 175 37 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 175 38 A8 a8 NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 39 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 175 40 15 15 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 41 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 175 42 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 43 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 175 44 < < XX work_fc4vscbgnfdyhddwekhs4n7fcy 175 45 mq mq NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 46 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 175 47 which which WDT work_fc4vscbgnfdyhddwekhs4n7fcy 175 48 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 175 49 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 175 50 limit limit NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 51 taken take VBN work_fc4vscbgnfdyhddwekhs4n7fcy 175 52 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 175 53 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 175 54 text text NN work_fc4vscbgnfdyhddwekhs4n7fcy 175 55 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 175 56 Eqs Eqs NNP work_fc4vscbgnfdyhddwekhs4n7fcy 175 57 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 176 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 2 A8 a8 NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 4 reduce reduce VB work_fc4vscbgnfdyhddwekhs4n7fcy 176 5 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 176 6 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 176 7 s s NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 176 8 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 176 9 sm sm NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 10 + + NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 11 q q NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 12 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 13 A9 A9 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 14 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 15 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 176 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 17 ss0 ss0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 18 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 176 19 ss0 ss0 NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 20 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 21 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 176 22 4q(m 4q(m CD work_fc4vscbgnfdyhddwekhs4n7fcy 176 23 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 176 24 sq sq XX work_fc4vscbgnfdyhddwekhs4n7fcy 176 25 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 26 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 28 4 4 CD work_fc4vscbgnfdyhddwekhs4n7fcy 176 29 16q2(m 16q2(m CD work_fc4vscbgnfdyhddwekhs4n7fcy 176 30 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 176 31 sq)2 sq)2 NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 32 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 176 33 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 34 A10 A10 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 176 35 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 176 36 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 176 37 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 38 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 176 39 computed compute VBN work_fc4vscbgnfdyhddwekhs4n7fcy 176 40 by by IN work_fc4vscbgnfdyhddwekhs4n7fcy 176 41 just just RB work_fc4vscbgnfdyhddwekhs4n7fcy 176 42 substituting substitute VBG work_fc4vscbgnfdyhddwekhs4n7fcy 176 43 Eq Eq NNS work_fc4vscbgnfdyhddwekhs4n7fcy 176 44 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 177 1 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 177 2 A6 A6 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 3 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 177 4 into into IN work_fc4vscbgnfdyhddwekhs4n7fcy 177 5 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 177 6 Hamil- Hamil- NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 7 tonian tonian JJ work_fc4vscbgnfdyhddwekhs4n7fcy 177 8 density density NN work_fc4vscbgnfdyhddwekhs4n7fcy 177 9 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 177 10 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 177 11 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 177 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 13 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 177 14 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 177 15 Re re NN work_fc4vscbgnfdyhddwekhs4n7fcy 177 16 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 17 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 18 2qe 2qe JJ work_fc4vscbgnfdyhddwekhs4n7fcy 177 19 2iqt 2iqt CD work_fc4vscbgnfdyhddwekhs4n7fcy 177 20 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 177 21 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 177 22 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 177 23 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 177 24 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 177 25 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 177 26 A11 A11 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 27 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 177 28 where where WRB work_fc4vscbgnfdyhddwekhs4n7fcy 177 29 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 177 30 ellipses ellipsis NNS work_fc4vscbgnfdyhddwekhs4n7fcy 177 31 represent represent VBP work_fc4vscbgnfdyhddwekhs4n7fcy 177 32 more more RBR work_fc4vscbgnfdyhddwekhs4n7fcy 177 33 rapidly rapidly RB work_fc4vscbgnfdyhddwekhs4n7fcy 177 34 varying vary VBG work_fc4vscbgnfdyhddwekhs4n7fcy 177 35 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 177 36 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 177 37 eg eg NNP work_fc4vscbgnfdyhddwekhs4n7fcy 177 38 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 178 1 terms term NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 2 varying vary VBG work_fc4vscbgnfdyhddwekhs4n7fcy 178 3 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 178 4 frequency frequency NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 5 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 178 6 + + NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 8 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 178 9 � � , work_fc4vscbgnfdyhddwekhs4n7fcy 178 10 or or CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 11 2!s 2!s NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 12 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 13 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 14 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 15 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 16 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 17 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 18 4X 4X NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 19 s;s0 s;s0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 20 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 21 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 22 ss0 ss0 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 23 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 24 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 25 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 26 5!2 5!2 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 27 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 28 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 178 29 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 30 2q 2q NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 31 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 32 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 33 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 34 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 35 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 36 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 37 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 38 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 39 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 40 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 41 + + DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 42 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 43 )( )( NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 178 44 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 45 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 46 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 47 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 48 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 49 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 50 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 178 51 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 52 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 53 : : : work_fc4vscbgnfdyhddwekhs4n7fcy 178 54 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 55 A12 A12 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 56 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 57 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 58 approximately approximately RB work_fc4vscbgnfdyhddwekhs4n7fcy 178 59 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 178 60 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 178 61 polarized polarize VBD work_fc4vscbgnfdyhddwekhs4n7fcy 178 62 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 178 63 modes mode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 64 with with IN work_fc4vscbgnfdyhddwekhs4n7fcy 178 65 arg arg NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 66 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 67 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 68 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 69 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 178 70 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 71 = = SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 72 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 178 73 correspond correspond NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 74 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 178 75 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 76 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 77 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 78 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 79 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 80 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 81 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 82 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 83 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 84 )=( )=( : work_fc4vscbgnfdyhddwekhs4n7fcy 178 85 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 86 ++ ++ . work_fc4vscbgnfdyhddwekhs4n7fcy 178 87 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 88 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 89 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 90 + + DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 91 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 92 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 93 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 94 e e NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 95 i i NN work_fc4vscbgnfdyhddwekhs4n7fcy 178 96 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 97 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 178 98 whereas whereas IN work_fc4vscbgnfdyhddwekhs4n7fcy 178 99 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 100 approximately approximately RB work_fc4vscbgnfdyhddwekhs4n7fcy 178 101 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 178 102 circularly circularly RB work_fc4vscbgnfdyhddwekhs4n7fcy 178 103 polarized polarize VBD work_fc4vscbgnfdyhddwekhs4n7fcy 178 104 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 178 105 modes mode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 106 correspond correspond VBP work_fc4vscbgnfdyhddwekhs4n7fcy 178 107 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 178 108 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 109 cases case NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 110 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 111 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 112 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 113 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 114 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 115 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 116 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 117 + + DT work_fc4vscbgnfdyhddwekhs4n7fcy 178 118 � � NNS work_fc4vscbgnfdyhddwekhs4n7fcy 178 119 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 120 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 121 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 122 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 123 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 124 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 125 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 126 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 178 127 + + CC work_fc4vscbgnfdyhddwekhs4n7fcy 178 128 i i PRP work_fc4vscbgnfdyhddwekhs4n7fcy 178 129 � � . work_fc4vscbgnfdyhddwekhs4n7fcy 178 130 � � ADD work_fc4vscbgnfdyhddwekhs4n7fcy 178 131 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 178 132 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 178 133 = = NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 134 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 178 135 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 179 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 179 2 linearly linearly RB work_fc4vscbgnfdyhddwekhs4n7fcy 179 3 polarized polarize VBN work_fc4vscbgnfdyhddwekhs4n7fcy 179 4 modes mode NNS work_fc4vscbgnfdyhddwekhs4n7fcy 179 5 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 179 6 / / SYM work_fc4vscbgnfdyhddwekhs4n7fcy 179 7 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 179 8 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 180 1 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 2 0 0 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 3 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 180 4 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 5 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 6 � � NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 7 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 8 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 9 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 10 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 180 11 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 12 A13 A13 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 180 13 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 14 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 180 15 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 180 16 energy energy NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 17 per per IN work_fc4vscbgnfdyhddwekhs4n7fcy 180 18 quantum quantum NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 19 is be VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 180 20 E e NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 21 = = NNS work_fc4vscbgnfdyhddwekhs4n7fcy 180 22 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 180 23 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 180 24 + + SYM work_fc4vscbgnfdyhddwekhs4n7fcy 180 25 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 26 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 27 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 180 28 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 180 29 ! ! . work_fc4vscbgnfdyhddwekhs4n7fcy 180 30 0 0 NFP work_fc4vscbgnfdyhddwekhs4n7fcy 180 31 cos(2qt cos(2qt NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 32 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 33 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 34 A14 A14 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 180 35 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 180 36 as as IN work_fc4vscbgnfdyhddwekhs4n7fcy 180 37 given give VBN work_fc4vscbgnfdyhddwekhs4n7fcy 180 38 in in IN work_fc4vscbgnfdyhddwekhs4n7fcy 180 39 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 180 40 text text NN work_fc4vscbgnfdyhddwekhs4n7fcy 180 41 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 181 1 16 16 CD work_fc4vscbgnfdyhddwekhs4n7fcy 181 2 References reference NNS work_fc4vscbgnfdyhddwekhs4n7fcy 181 3 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 181 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 182 1 R.D. R.D. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 183 1 Peccei Peccei NNP work_fc4vscbgnfdyhddwekhs4n7fcy 183 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 183 3 H. H. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 183 4 Quinn Quinn NNP work_fc4vscbgnfdyhddwekhs4n7fcy 183 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 183 6 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 183 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 184 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 185 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 185 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 186 1 38 38 CD work_fc4vscbgnfdyhddwekhs4n7fcy 186 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 186 3 1440 1440 CD work_fc4vscbgnfdyhddwekhs4n7fcy 186 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 186 5 1977 1977 CD work_fc4vscbgnfdyhddwekhs4n7fcy 186 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 186 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 186 8 S. S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 186 9 Weinberg Weinberg NNP work_fc4vscbgnfdyhddwekhs4n7fcy 186 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 186 11 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 186 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 187 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 188 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 188 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 189 1 40 40 CD work_fc4vscbgnfdyhddwekhs4n7fcy 189 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 189 3 223 223 CD work_fc4vscbgnfdyhddwekhs4n7fcy 189 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 189 5 1978 1978 CD work_fc4vscbgnfdyhddwekhs4n7fcy 189 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 189 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 189 8 F. F. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 189 9 Wilczek Wilczek NNP work_fc4vscbgnfdyhddwekhs4n7fcy 189 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 189 11 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 189 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 190 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 191 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 191 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 192 1 40 40 CD work_fc4vscbgnfdyhddwekhs4n7fcy 192 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 192 3 271 271 CD work_fc4vscbgnfdyhddwekhs4n7fcy 192 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 192 5 1978 1978 CD work_fc4vscbgnfdyhddwekhs4n7fcy 192 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 192 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 193 1 2 2 LS work_fc4vscbgnfdyhddwekhs4n7fcy 193 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 194 1 Y. Y. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 194 2 Chikashige Chikashige NNP work_fc4vscbgnfdyhddwekhs4n7fcy 194 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 194 4 R.N. R.N. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 195 1 Mohapatra Mohapatra NNP work_fc4vscbgnfdyhddwekhs4n7fcy 195 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 195 3 R. R. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 195 4 Peccei Peccei NNP work_fc4vscbgnfdyhddwekhs4n7fcy 195 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 195 6 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 195 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 196 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 196 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 197 1 98B 98b CD work_fc4vscbgnfdyhddwekhs4n7fcy 197 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 197 3 265 265 CD work_fc4vscbgnfdyhddwekhs4n7fcy 197 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 197 5 1981 1981 CD work_fc4vscbgnfdyhddwekhs4n7fcy 197 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 197 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 197 8 G. G. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 197 9 Gelmini Gelmini NNP work_fc4vscbgnfdyhddwekhs4n7fcy 197 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 197 11 M. M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 197 12 Roncadelli Roncadelli NNP work_fc4vscbgnfdyhddwekhs4n7fcy 197 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 197 14 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 197 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 198 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 198 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 199 1 99B 99B NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 199 3 411 411 CD work_fc4vscbgnfdyhddwekhs4n7fcy 199 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 199 5 1981 1981 CD work_fc4vscbgnfdyhddwekhs4n7fcy 199 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 199 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 199 8 H. H. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 9 Georgi Georgi NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 199 11 S. S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 12 Glashow Glashow NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 199 14 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 199 15 S. S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 16 Nussinov Nussinov NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 17 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 199 18 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 199 19 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 200 1 Phys phys NN work_fc4vscbgnfdyhddwekhs4n7fcy 200 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 201 1 B193 B193 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 201 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 201 3 297 297 CD work_fc4vscbgnfdyhddwekhs4n7fcy 201 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 201 5 1981 1981 CD work_fc4vscbgnfdyhddwekhs4n7fcy 201 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 201 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 202 1 3 3 LS work_fc4vscbgnfdyhddwekhs4n7fcy 202 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 203 1 F. F. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 203 2 Wilczek Wilczek NNP work_fc4vscbgnfdyhddwekhs4n7fcy 203 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 203 4 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 203 5 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 204 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 205 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 205 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 206 1 49 49 CD work_fc4vscbgnfdyhddwekhs4n7fcy 206 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 206 3 1549 1549 CD work_fc4vscbgnfdyhddwekhs4n7fcy 206 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 206 5 1982 1982 CD work_fc4vscbgnfdyhddwekhs4n7fcy 206 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 206 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 206 8 D.B. D.B. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 207 1 Reiss Reiss NNP work_fc4vscbgnfdyhddwekhs4n7fcy 207 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 207 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 207 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 208 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 208 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 209 1 115B 115b CD work_fc4vscbgnfdyhddwekhs4n7fcy 209 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 209 3 217 217 CD work_fc4vscbgnfdyhddwekhs4n7fcy 209 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 209 5 1982 1982 CD work_fc4vscbgnfdyhddwekhs4n7fcy 209 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 209 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 209 8 G. G. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 9 Gelmini Gelmini NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 209 11 S. S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 12 Nussinov Nussinov NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 13 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 209 14 T. T. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 15 Yanagida Yanagida NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 16 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 209 17 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 209 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 210 1 Phys phys NN work_fc4vscbgnfdyhddwekhs4n7fcy 210 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 211 1 B219 B219 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 211 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 211 3 31 31 CD work_fc4vscbgnfdyhddwekhs4n7fcy 211 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 211 5 1983 1983 CD work_fc4vscbgnfdyhddwekhs4n7fcy 211 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 211 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 212 1 4 4 LS work_fc4vscbgnfdyhddwekhs4n7fcy 212 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 213 1 N. N. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 213 2 Turok Turok NNP work_fc4vscbgnfdyhddwekhs4n7fcy 213 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 213 4 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 213 5 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 214 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 215 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 215 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 216 1 63 63 CD work_fc4vscbgnfdyhddwekhs4n7fcy 216 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 216 3 2625 2625 CD work_fc4vscbgnfdyhddwekhs4n7fcy 216 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 216 5 1989 1989 CD work_fc4vscbgnfdyhddwekhs4n7fcy 216 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 216 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 216 8 N. N. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 216 9 Turok Turok NNP work_fc4vscbgnfdyhddwekhs4n7fcy 216 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 216 11 D. D. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 216 12 Spergel Spergel NNP work_fc4vscbgnfdyhddwekhs4n7fcy 216 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 216 14 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 216 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 217 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 218 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 218 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 219 1 64 64 CD work_fc4vscbgnfdyhddwekhs4n7fcy 219 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 219 3 2736 2736 CD work_fc4vscbgnfdyhddwekhs4n7fcy 219 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 219 5 1990 1990 CD work_fc4vscbgnfdyhddwekhs4n7fcy 219 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 219 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 220 1 5 5 CD work_fc4vscbgnfdyhddwekhs4n7fcy 220 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 221 1 J.E. J.E. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 222 1 Kim Kim NNP work_fc4vscbgnfdyhddwekhs4n7fcy 222 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 222 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 222 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 223 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 224 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 224 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 225 1 43 43 CD work_fc4vscbgnfdyhddwekhs4n7fcy 225 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 225 3 103 103 CD work_fc4vscbgnfdyhddwekhs4n7fcy 225 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 225 5 1979 1979 CD work_fc4vscbgnfdyhddwekhs4n7fcy 225 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 225 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 225 8 M.A. M.A. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 226 1 Shifman Shifman NNP work_fc4vscbgnfdyhddwekhs4n7fcy 226 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 226 3 A.I. A.I. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 227 1 Vainshtein Vainshtein NNP work_fc4vscbgnfdyhddwekhs4n7fcy 227 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 227 3 V.I. V.I. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 228 1 Zakharov Zakharov NNP work_fc4vscbgnfdyhddwekhs4n7fcy 228 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 228 3 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 228 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 229 1 Phys phys NN work_fc4vscbgnfdyhddwekhs4n7fcy 229 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 230 1 B166 B166 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 230 3 199 199 CD work_fc4vscbgnfdyhddwekhs4n7fcy 230 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 230 5 1981 1981 CD work_fc4vscbgnfdyhddwekhs4n7fcy 230 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 230 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 230 8 M. M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 9 Dine Dine NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 230 11 W. W. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 12 Fischler Fischler NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 13 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 230 14 M. M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 15 Srednicki Srednicki NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 16 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 230 17 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 230 18 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 231 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 231 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 232 1 104B 104b CD work_fc4vscbgnfdyhddwekhs4n7fcy 232 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 232 3 199 199 CD work_fc4vscbgnfdyhddwekhs4n7fcy 232 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 232 5 1981 1981 CD work_fc4vscbgnfdyhddwekhs4n7fcy 232 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 232 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 232 8 A.P. A.P. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 233 1 Zhitniskii Zhitniskii NNP work_fc4vscbgnfdyhddwekhs4n7fcy 233 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 233 3 Sov Sov NNP work_fc4vscbgnfdyhddwekhs4n7fcy 233 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 234 1 J. J. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 234 2 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 234 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 234 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 235 1 31 31 CD work_fc4vscbgnfdyhddwekhs4n7fcy 235 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 235 3 260 260 CD work_fc4vscbgnfdyhddwekhs4n7fcy 235 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 235 5 1980 1980 CD work_fc4vscbgnfdyhddwekhs4n7fcy 235 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 235 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 236 1 6 6 CD work_fc4vscbgnfdyhddwekhs4n7fcy 236 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 237 1 For for IN work_fc4vscbgnfdyhddwekhs4n7fcy 237 2 reviews review NNS work_fc4vscbgnfdyhddwekhs4n7fcy 237 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 237 4 see see VB work_fc4vscbgnfdyhddwekhs4n7fcy 237 5 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 237 6 J.E. J.E. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 238 1 Kim Kim NNP work_fc4vscbgnfdyhddwekhs4n7fcy 238 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 238 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 238 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 239 1 Rept Rept NNP work_fc4vscbgnfdyhddwekhs4n7fcy 239 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 240 1 149 149 CD work_fc4vscbgnfdyhddwekhs4n7fcy 240 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 240 3 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 240 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 240 5 1987 1987 CD work_fc4vscbgnfdyhddwekhs4n7fcy 240 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 240 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 240 8 M.S. M.S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 241 1 Turner Turner NNP work_fc4vscbgnfdyhddwekhs4n7fcy 241 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 241 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 241 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 242 1 Rept Rept NNP work_fc4vscbgnfdyhddwekhs4n7fcy 242 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 243 1 197 197 CD work_fc4vscbgnfdyhddwekhs4n7fcy 243 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 243 3 67 67 CD work_fc4vscbgnfdyhddwekhs4n7fcy 243 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 243 5 1990 1990 CD work_fc4vscbgnfdyhddwekhs4n7fcy 243 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 243 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 243 8 G.G. G.G. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 244 1 Ra Ra NNP work_fc4vscbgnfdyhddwekhs4n7fcy 244 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 244 3 elt elt NN work_fc4vscbgnfdyhddwekhs4n7fcy 244 4 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 244 5 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 244 6 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 245 1 Rept Rept NNP work_fc4vscbgnfdyhddwekhs4n7fcy 245 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 246 1 198 198 CD work_fc4vscbgnfdyhddwekhs4n7fcy 246 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 246 3 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 246 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 246 5 1990 1990 CD work_fc4vscbgnfdyhddwekhs4n7fcy 246 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 246 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 247 1 17 17 CD work_fc4vscbgnfdyhddwekhs4n7fcy 247 2 7 7 CD work_fc4vscbgnfdyhddwekhs4n7fcy 247 3 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 248 1 J. J. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 2 Preskill Preskill NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 248 4 M. M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 5 Wise Wise NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 6 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 248 7 F. F. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 8 Wilczek Wilczek NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 9 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 248 10 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 248 11 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 249 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 249 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 250 1 120B 120b CD work_fc4vscbgnfdyhddwekhs4n7fcy 250 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 250 3 127 127 CD work_fc4vscbgnfdyhddwekhs4n7fcy 250 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 250 5 1983 1983 CD work_fc4vscbgnfdyhddwekhs4n7fcy 250 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 250 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 250 8 L.F. L.F. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 250 9 Abbott Abbott NNP work_fc4vscbgnfdyhddwekhs4n7fcy 250 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 250 11 P. P. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 250 12 Sikivie Sikivie NNP work_fc4vscbgnfdyhddwekhs4n7fcy 250 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 250 14 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 250 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 251 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 251 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 252 1 120B 120b CD work_fc4vscbgnfdyhddwekhs4n7fcy 252 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 252 3 133 133 CD work_fc4vscbgnfdyhddwekhs4n7fcy 252 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 252 5 1983 1983 CD work_fc4vscbgnfdyhddwekhs4n7fcy 252 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 252 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 252 8 M. M. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 252 9 Dine Dine NNP work_fc4vscbgnfdyhddwekhs4n7fcy 252 10 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 252 11 W. W. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 252 12 Fischler Fischler NNP work_fc4vscbgnfdyhddwekhs4n7fcy 252 13 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 252 14 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 252 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 253 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 253 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 254 1 120B 120b CD work_fc4vscbgnfdyhddwekhs4n7fcy 254 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 254 3 137 137 CD work_fc4vscbgnfdyhddwekhs4n7fcy 254 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 254 5 1983 1983 CD work_fc4vscbgnfdyhddwekhs4n7fcy 254 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 254 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 255 1 8 8 LS work_fc4vscbgnfdyhddwekhs4n7fcy 255 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 256 1 B. B. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 256 2 Holdom Holdom NNP work_fc4vscbgnfdyhddwekhs4n7fcy 256 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 256 4 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 256 5 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 257 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 257 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 258 1 166B 166b CD work_fc4vscbgnfdyhddwekhs4n7fcy 258 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 258 3 196 196 CD work_fc4vscbgnfdyhddwekhs4n7fcy 258 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 258 5 1986 1986 CD work_fc4vscbgnfdyhddwekhs4n7fcy 258 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 258 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 259 1 9 9 CD work_fc4vscbgnfdyhddwekhs4n7fcy 259 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 260 1 R.L. R.L. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 261 1 Davis Davis NNP work_fc4vscbgnfdyhddwekhs4n7fcy 261 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 261 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 261 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 262 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 263 1 D32 D32 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 263 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 263 3 3172 3172 CD work_fc4vscbgnfdyhddwekhs4n7fcy 263 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 263 5 1985 1985 CD work_fc4vscbgnfdyhddwekhs4n7fcy 263 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 263 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 263 8 R.L. R.L. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 264 1 Davis Davis NNP work_fc4vscbgnfdyhddwekhs4n7fcy 264 2 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 264 3 E.P.S. E.P.S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 265 1 Shellard Shellard NNP work_fc4vscbgnfdyhddwekhs4n7fcy 265 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 265 3 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 265 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 266 1 Phys phys NN work_fc4vscbgnfdyhddwekhs4n7fcy 266 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 267 1 B324 B324 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 267 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 267 3 167 167 CD work_fc4vscbgnfdyhddwekhs4n7fcy 267 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 267 5 1989 1989 CD work_fc4vscbgnfdyhddwekhs4n7fcy 267 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 267 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 268 1 10 10 CD work_fc4vscbgnfdyhddwekhs4n7fcy 268 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 269 1 D. D. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 269 2 Harari Harari NNP work_fc4vscbgnfdyhddwekhs4n7fcy 269 3 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 269 4 P. P. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 269 5 Sikivie Sikivie NNP work_fc4vscbgnfdyhddwekhs4n7fcy 269 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 269 7 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 269 8 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 270 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 270 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 271 1 195B 195b CD work_fc4vscbgnfdyhddwekhs4n7fcy 271 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 271 3 361 361 CD work_fc4vscbgnfdyhddwekhs4n7fcy 271 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 271 5 1987 1987 CD work_fc4vscbgnfdyhddwekhs4n7fcy 271 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 271 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 272 1 11 11 CD work_fc4vscbgnfdyhddwekhs4n7fcy 272 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 273 1 P. P. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 273 2 Steinhardt Steinhardt NNP work_fc4vscbgnfdyhddwekhs4n7fcy 273 3 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 273 4 M.S. M.S. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 274 1 Turner Turner NNP work_fc4vscbgnfdyhddwekhs4n7fcy 274 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 274 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 274 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 275 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 275 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 276 1 129B 129b CD work_fc4vscbgnfdyhddwekhs4n7fcy 276 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 276 3 51 51 CD work_fc4vscbgnfdyhddwekhs4n7fcy 276 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 276 5 1983 1983 CD work_fc4vscbgnfdyhddwekhs4n7fcy 276 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 276 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 276 8 G. G. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 9 Lazarides Lazarides NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 276 11 et et NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 12 al al NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 13 . . NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 14 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 276 15 Nucl Nucl NNP work_fc4vscbgnfdyhddwekhs4n7fcy 276 16 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 277 1 Phys phys NN work_fc4vscbgnfdyhddwekhs4n7fcy 277 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 278 1 B346 B346 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 278 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 278 3 193 193 CD work_fc4vscbgnfdyhddwekhs4n7fcy 278 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 278 5 1990 1990 CD work_fc4vscbgnfdyhddwekhs4n7fcy 278 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 278 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 279 1 12 12 CD work_fc4vscbgnfdyhddwekhs4n7fcy 279 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 280 1 S.-Y. s.-y. XX work_fc4vscbgnfdyhddwekhs4n7fcy 281 1 Pi pi NN work_fc4vscbgnfdyhddwekhs4n7fcy 281 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 281 3 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 281 4 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 282 1 Rev. Rev. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 283 1 D24 D24 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 283 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 283 3 1725 1725 CD work_fc4vscbgnfdyhddwekhs4n7fcy 283 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 283 5 1984 1984 CD work_fc4vscbgnfdyhddwekhs4n7fcy 283 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 283 7 ; ; : work_fc4vscbgnfdyhddwekhs4n7fcy 283 8 A. A. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 283 9 Linde Linde NNP work_fc4vscbgnfdyhddwekhs4n7fcy 283 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 283 11 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 283 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 284 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 284 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 285 1 201B 201b CD work_fc4vscbgnfdyhddwekhs4n7fcy 285 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 285 3 437 437 CD work_fc4vscbgnfdyhddwekhs4n7fcy 285 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 285 5 1988 1988 CD work_fc4vscbgnfdyhddwekhs4n7fcy 285 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 285 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 286 1 13 13 CD work_fc4vscbgnfdyhddwekhs4n7fcy 286 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 287 1 J. J. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 2 Flynn Flynn NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 3 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 287 4 L. L. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 5 Randall Randall NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 287 7 LBL LBL NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 8 preprint preprint NN work_fc4vscbgnfdyhddwekhs4n7fcy 287 9 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 287 10 LBL-25115 LBL-25115 NNP work_fc4vscbgnfdyhddwekhs4n7fcy 287 11 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 287 12 1988 1988 CD work_fc4vscbgnfdyhddwekhs4n7fcy 287 13 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 287 14 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 288 1 14 14 CD work_fc4vscbgnfdyhddwekhs4n7fcy 288 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 289 1 H. H. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 2 Georgi Georgi NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 3 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 289 4 D. D. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 5 Kaplan Kaplan NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 6 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 289 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 289 8 L. L. NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 9 Randall Randall NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 10 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 289 11 Phys Phys NNP work_fc4vscbgnfdyhddwekhs4n7fcy 289 12 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 290 1 Lett Lett NNP work_fc4vscbgnfdyhddwekhs4n7fcy 290 2 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 291 1 169B 169b CD work_fc4vscbgnfdyhddwekhs4n7fcy 291 2 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 291 3 73 73 CD work_fc4vscbgnfdyhddwekhs4n7fcy 291 4 ( ( -LRB- work_fc4vscbgnfdyhddwekhs4n7fcy 291 5 1986 1986 CD work_fc4vscbgnfdyhddwekhs4n7fcy 291 6 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 291 7 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 292 1 18 18 CD work_fc4vscbgnfdyhddwekhs4n7fcy 292 2 Figure Figure NNP work_fc4vscbgnfdyhddwekhs4n7fcy 292 3 Captions Captions NNPS work_fc4vscbgnfdyhddwekhs4n7fcy 292 4 Figure Figure NNP work_fc4vscbgnfdyhddwekhs4n7fcy 292 5 1 1 CD work_fc4vscbgnfdyhddwekhs4n7fcy 292 6 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 293 1 E E NNP work_fc4vscbgnfdyhddwekhs4n7fcy 293 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 293 3 ective ective JJ work_fc4vscbgnfdyhddwekhs4n7fcy 293 4 coupling coupling NN work_fc4vscbgnfdyhddwekhs4n7fcy 293 5 to to IN work_fc4vscbgnfdyhddwekhs4n7fcy 293 6 ` ` '' work_fc4vscbgnfdyhddwekhs4n7fcy 293 7 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 293 8 - - HYPH work_fc4vscbgnfdyhddwekhs4n7fcy 293 9 matter matter NN work_fc4vscbgnfdyhddwekhs4n7fcy 293 10 ' ' '' work_fc4vscbgnfdyhddwekhs4n7fcy 293 11 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 293 12 goldstone goldstone NNP work_fc4vscbgnfdyhddwekhs4n7fcy 293 13 boson boson NN work_fc4vscbgnfdyhddwekhs4n7fcy 293 14 mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 293 15 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 294 1 Figure figure NN work_fc4vscbgnfdyhddwekhs4n7fcy 294 2 2 2 CD work_fc4vscbgnfdyhddwekhs4n7fcy 294 3 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 295 1 Mixing mix VBG work_fc4vscbgnfdyhddwekhs4n7fcy 295 2 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 295 3 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 295 4 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 295 5 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 295 6 scalars scalar VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 295 7 through through IN work_fc4vscbgnfdyhddwekhs4n7fcy 295 8 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 295 9 loop loop NN work_fc4vscbgnfdyhddwekhs4n7fcy 295 10 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 296 1 The the DT work_fc4vscbgnfdyhddwekhs4n7fcy 296 2 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 296 3 particle particle NN work_fc4vscbgnfdyhddwekhs4n7fcy 296 4 carries carry VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 296 5 both both CC work_fc4vscbgnfdyhddwekhs4n7fcy 296 6 a a NN work_fc4vscbgnfdyhddwekhs4n7fcy 296 7 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 296 8 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 296 9 charges charge NNS work_fc4vscbgnfdyhddwekhs4n7fcy 296 10 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 297 1 Figure figure NN work_fc4vscbgnfdyhddwekhs4n7fcy 297 2 3 3 CD work_fc4vscbgnfdyhddwekhs4n7fcy 297 3 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 298 1 Similar similar JJ work_fc4vscbgnfdyhddwekhs4n7fcy 298 2 processes process NNS work_fc4vscbgnfdyhddwekhs4n7fcy 298 3 involving involve VBG work_fc4vscbgnfdyhddwekhs4n7fcy 298 4 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 298 5 absorption absorption NN work_fc4vscbgnfdyhddwekhs4n7fcy 298 6 of of IN work_fc4vscbgnfdyhddwekhs4n7fcy 298 7 a a LS work_fc4vscbgnfdyhddwekhs4n7fcy 298 8 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 298 9 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 298 10 single single JJ work_fc4vscbgnfdyhddwekhs4n7fcy 298 11 axion axion NN work_fc4vscbgnfdyhddwekhs4n7fcy 298 12 and and CC work_fc4vscbgnfdyhddwekhs4n7fcy 298 13 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 298 14 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 298 15 two two CD work_fc4vscbgnfdyhddwekhs4n7fcy 298 16 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 298 17 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 299 1 If if IN work_fc4vscbgnfdyhddwekhs4n7fcy 299 2 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 3 axions axion NNS work_fc4vscbgnfdyhddwekhs4n7fcy 299 4 come come VBP work_fc4vscbgnfdyhddwekhs4n7fcy 299 5 from from IN work_fc4vscbgnfdyhddwekhs4n7fcy 299 6 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 7 coherent coherent JJ work_fc4vscbgnfdyhddwekhs4n7fcy 299 8 state state NN work_fc4vscbgnfdyhddwekhs4n7fcy 299 9 describing describe VBG work_fc4vscbgnfdyhddwekhs4n7fcy 299 10 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 11 classical classical JJ work_fc4vscbgnfdyhddwekhs4n7fcy 299 12 � � NNP work_fc4vscbgnfdyhddwekhs4n7fcy 299 13 eld eld NNP work_fc4vscbgnfdyhddwekhs4n7fcy 299 14 oscillation oscillation NN work_fc4vscbgnfdyhddwekhs4n7fcy 299 15 , , , work_fc4vscbgnfdyhddwekhs4n7fcy 299 16 then then RB work_fc4vscbgnfdyhddwekhs4n7fcy 299 17 the the DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 18 rate rate NN work_fc4vscbgnfdyhddwekhs4n7fcy 299 19 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 299 20 b b NN work_fc4vscbgnfdyhddwekhs4n7fcy 299 21 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 299 22 exceeds exceed VBZ work_fc4vscbgnfdyhddwekhs4n7fcy 299 23 that that DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 24 for for IN work_fc4vscbgnfdyhddwekhs4n7fcy 299 25 a a DT work_fc4vscbgnfdyhddwekhs4n7fcy 299 26 ) ) -RRB- work_fc4vscbgnfdyhddwekhs4n7fcy 299 27 . . . work_fc4vscbgnfdyhddwekhs4n7fcy 300 1 19 19 CD