No title February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke BEAUTY PRODUCTION AT HERA O. BEHNKE Physik. Institut Uni Heidelberg Philosophenweg 12, 69120 Heidelberg E-mail: obehnke@mail.desy.de A review is given on beauty production at HERA. Many new results have recently become available based on various tagging techniques and covering altogether a wide kinematic phase space in photon virtualities and b quark transverse mo- menta. Differential beauty production cross sections are presented and compared to perturbative QCD predictions. The first measurements of the structure function F bb̄ 2 are shown. 1. Introduction The dominant beauty production mechanism at HERA is photon gluon fusion (PGF), which is shown in the left diagram in figure 1. The total Figure 1. Comparison of kinematical thresholds for charm and beauty production at HERA in terms of the minimum proton momentum fraction xg of the gluon that enters the hard interaction. The left plot shows the PGF process where the energies are indi- cated that enter the heavy quark pair production process. The threshold formula for xg in the middle of the figure is calculated from (xgp + q) 2 ≈ 2xg pq = 4xgEγ Ep ≥ (2mQ) 2, where p and q are the four vectors of the proton and photon, respectively. The right plot shows the gluon density in the proton as determined from scaling violations of F2. The vertical line indicates the minimum fraction Xg = 10 −3 for beauty production at HERA. 1 February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 2 production rates of light, charm and beauty quarks at HERA scale roughly like σuds : σc : σb ∼ 2000 : 200 : 1. The strong suppression of beauty events is mostly due to the limited kine- matic phase space, as illustrated in figure 1. To produce two beauty quarks in the PGF process a minimal proton momentum fraction of the gluon of 10−3 is needed, while for charm the threshold is one order of magnitude lower. A further suppression factor of four for beauty production relative to charm production is due to the smaller electric charge of down type quarks compared to up type quarks. Since the last Ringberg workshop in 2003 a wealth of new beauty pro- duction measurements have become available at HERA, which will be summarised here. The results are based on a variety of tagging meth- ods and cover in total a large kinematic phase space of photon virtualities 0 < Q2 < 1000 GeV2 and b quark transverse momenta 0 < pT < 30 GeV. 2. Theory Since the large b mass provides a hard scale, rendering a small αs, it would be expected that beauty production can be accurately calculated using perturbative QCD (pQCD). Calculations are available in Next to Leading Order (NLO) in the massive scheme, where the b quark mass is fully taken into account. For photoproduction the program FMNR 1 is used and for deep inelastic scattering (DIS) HVQDIS 2. In the massive scheme, u, d and s are the only active flavours in the proton and the photon, and charm and beauty are produced dynamically in the hard scattering as shown in figure 1. These predictions are expected to be reliable for the largest part of the kinematic phase space at HERA. However, at very large transverse momenta pt,b ≫ mb or photon virtualities Q 2 ≫ m2 b , the predictions of the massive scheme are expected to become unreliable due to neglected higher order terms in the perturbation series of the form [αs ln(p 2 t,b /m2 b )]n or [αs ln(Q 2/m2 b )]n, which appear to any order n and represent collinear gluon radiation from the heavy quark lines. In this kinematic range, the massless scheme can be used, in which charm and beauty are treated as active flavours in both the proton and also in the hadronic structure of the photon, in addition to u, d and s. The kinematics of the heavy quarks is treated massless in this scheme, mass effects are taken into account as effective cutoffs for the dynamic evolution of the heavy quarks in the proton and photon parton density functions. In this scheme the above higher order February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 3 terms are resummed to all orders. Unfortunately there are at the present time no results from massless scheme calculations available which could be compared to the HERA beauty measurements. Results are available from mixed scheme calculations, which apply the massive (massless) scheme for small (large) high transverse momenta and photon virtualities with suitable interpolations in intermediate regions. The measurements of the proton structure function F bb̄2 , presented below, are compared to the mixed scheme predictions from MRST 3 and CTEQ 4 in NLO and to the first Next to Next to Leading Order (NNLO) calculation, provided by MRST 5. 3. Overview of measurements and the tagging techniques used The table below gives an overview of the beauty measurements presented in this review. The analyses are ordered with respect to the minimum b quark transverse momentum pT which is probed and the covered range of the photon virtuality Q2. Note, that the numbers in the table are only approximative values. The following tagging techniques are applied: • (µ+Jets): The measurements 6,7,8 use events with a muon from semileptonic b decay associated to a jet. The separation of beauty events from charm and light quark background is based on the large b quark mass, leading to large transverse momenta prelt of the muon with respect to the axis of the associated jet. In 8 the long lifetime of the b quark is additionally exploited, leading to relatively large displacements of the muon track from the primary vertex. • (Incl. Lifet.) The inclusive lifetime measurements 9,10,11 are based on the displacements of charged tracks from beauty decays from the primary vertex. Events are selected with at least one charged track measured with high quality in the vertex detector. February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 4 • (µµ, D∗µ) The double tag measurements use events with two muons 12 or with one muon and a fully reconstructed D∗+ 13,14. The separation of the beauty events from the background exploits the charge correlations (µµ) or charge and angular correlations (D∗µ) between the two particles. All presented measurements are based on HERA I data. The achieved experimental accuracies are ≥ 20% for inclusive measurements and for dif- ferential bins sometimes only ∼ 50%. 4. Results The results section is ordered as follows: In 4.1 a selection of differential re- sults of the µ+Jets analyses is presented. In 4.2 summary plots of all recent HERA measurements are shown, as a function of photon virtuality Q2 and separately for photoproduction as a function of the b quark transverse mo- mentum pT . In 4.3 the results are concluded with the first measurements of the structure function F bb̄2 . 4.1. µ+Jets analyses: Photoproduction: For the H1 and ZEUS photoproduction analyses 8,6 (Q2 < 1 GeV2) at least two jets are required in the final state with trans- verse momenta p jet1(2) t > 7(6) GeV. Figure 2 shows the differential cross sections as a function of the muon pseudorapidity (left) and transverse momentum (right). The H1 and ZEUS measurements agree well in the overlapping region. The data are also compared to a massive scheme NLO calculation, based on the program 1. The estimated errors of the theory prediction are dominated by the uncertainties of the renormalisation and factorisation scales and of the b quark mass. The data tend to lie slightly above this calculation, however, within the errors the calculation describes all data points. The measured cross sections as a function of the muon transverse momentum are compared in figure 2 (right) to the NLO predic- tions in the respective kinematic ranges of the H1 and ZEUS measurements. In the lowest bin from 2.5 to 3.3 GeV the H1 measurement exceeds the pre- diction by a factor of ∼ 2.5, while at higher transverse momenta a better agreement is observed. Such an excess is not seen in the ZEUS data. This discrepancy needs to be clarified in the future. Deep inelastic scattering: For the H1 and ZEUS DIS analyses 8,7 (Q2 > 2 GeV2) the jet algorithm is applied in the Breit frame and at least one jet February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 5 0 20 40 -1 0 1 2 H1 ZEUS NLO QCD ⊗ Had ep → ebb − X → ejjµX ηµ d σ /d η µ [p b ] Q 2 < 1 GeV2 0.2 < y < 0.8 p µ t > 2.5 GeV p jet1(2) t > 7(6) GeV |ηjet| < 2.5 1 10 2.5 5 7.5 10 H1 -0.55 < η µ < 1.1 ZEUS -1.6 < η µ < 2.3 NLO QCD ⊗ Had: -0.55 < ηµ < 1.1 -1.6 < ηµ < 2.3 p µ t [GeV] d σ /d p µ t [p b /G e V ] Q 2 < 1 GeV2; 0.2 < y < 0.8 p jet1(2) t > 7(6) GeV; |ηjet| < 2.5 Figure 2. Differential beauty cross sections in photoproduction, for dijet events with a muon associated to one of the jets, as a function of (left) muon pseudorapidity and (right) muon transverse momentum. The H1 and ZEUS data are compared to predictions from a massive scheme NLO calculation. with transverse momentum pBreitt,jet > 6 GeV is required. Figure 3 shows the differential cross sections of the H1 (top) and ZEUS (bottom) measurements as a function of (left) jet transverse momentum in the Breit frame, (middle) muon transverse momentum and (right) muon pseudorapidity. The data are compared to a massive scheme NLO calculation using the program 2. The H1 and ZEUS measurements are performed in similar kinematic regions and also most of the observations are similar: (1) An excess of data over NLO prediction by a factor ∼ 2 is observed towards smaller muon transverse momenta below 4 GeV. (2) A rise of the differential cross sections is observed towards more positive muon pseudorapidities, (i.e. more close to the proton di- rection) which is not reproduced by the NLO calculation. The excess seen in the H1 data for lower muon transverse momenta is accompanied by an excess for lower jet transverse momenta while for ZEUS an excess is observed for higher jet momenta. More precise measurements are needed to clarify these different findings. 4.2. Summary of results as a function of Q2 and pT Figure 4 shows a summary of the data/theory comparison for HERA beauty results as a function of Q2. For the measurements sensitive to b quarks with pbT ∼ mb or lower (black points) there is a trend that the massive NLO QCD predictions 1,2 tend to underestimate the b production rate at very February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 6 Figure 3. H1 (top) and ZEUS (bottom) measured differential beauty cross sections in DIS, for events with a muon and an associated jet, as a function of (left) jet transverse momentum in the Breit frame, (middle) muon transverse momentum and (right) muon pseudorapidity. The data are compared to predictions from a massive scheme NLO calculation. low Q2. For the higher pT measurements (red/grey points), no clear trend is observed. Note that the estimated theoretical errors, which are typically of order 30%, are not shown. For the DIS data (Q2 > 2 GeV2) the curves from two mixed scheme NLO calculations are also shown in figure 4. These predictions from CTEQ 4 and MRST 3 are specifically provided for the F bb̄2 inclusive structure function measurements which are shown here as the triangle points and which are discussed in 4.3. While the CTEQ curve is close to the the massive scheme calculation the MRST prediction is up to a factor of two higher. The data are not yet precise enough to separate between the three different predictions. Figure 5 shows a similar compilation for all HERA measurements in photoproduction (Q2 < 1 GeV2), now as a function of the b quark pT . Some measurements agree well with the massive scheme predictions but in general the data tend to be higher than the calculations. There are indications that the data exceed the predictions more significantly towards low pT . Note, that several measurements appear in both summary figures. February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 7 1 2 3 4 5 6 7 8 10 100 Q 2 [GeV 2 ] σ b b_ / σ b b_ N L O Q C D CTEQ6HQ MRST04 QCD NLO (massive) ZEUS Prel. D*µ Correlations H1 D*µ Correlations ZEUS Prel. µµ Correlations H1 F 2 bb (low Q 2 ) Impact Par. H1 F 2 bb (high Q 2 ) Impact Par. ZEUS γp: b→eX p rel t ZEUS γp: σ vis (jjµX) p rel t H1 γp: σ vis (jjµX) p rel t ⊗ Impact Par. H1 Prel. γp: dijets Impact Par. H1 DIS: σ vis (ejµX) p rel t ⊗ Impact Par. ZEUS DIS: σ vis (ejµX) p rel t ∫∫ γp (Q2~ 0) Key Ref. Signature pT cuts Photoproduction 12 µµ low 14 D ∗ µ low 13 D ∗ µ low 15 2 jets+e medium 6 2 jets+µ medium 8 2 jets+µ medium 11 tracks high DIS 14 D ∗ µ low 10 tracks low 9 tracks low 8 1 jet+µ medium 7 1 jet+µ medium Figure 4. Ratio of beauty production cross section measurements at HERA to NLO QCD predictions in the massive scheme as a function of the photon virtuality Q2. The predictions from the mixed scheme NLO calculations by MRST and CTEQ for the DIS kinematic regime Q2 > 2 GeV2 are also presented (valid for comparison with the measurements shown as triangles). Since theoretical errors are different for each point, they are not included in this plot. 1 2 3 4 5 6 7 5 10 15 20 25 30 p T (b) [GeV] σ b b_ / σ b b_ N L O Q C D QCD NLO (massive) ZEUS Prel. D*µ Correlations H1 D*µ Correlations ZEUS Prel. µµ Correlations ZEUS γp: b→eX p rel t ZEUS γp: σ vis (jjµX) p rel t H1 γp: σ vis (jjµX) p rel t ⊗ Impact Par. H1 Prel. γp: dijets Impact Par. Figure 5. Ratio of beauty production cross section measurements in photoproduction at HERA to NLO QCD predictions in the massive scheme as a function of the transverse momentum of the b quark pT . The dashed line gives an indication of the size of the estimated theoretical uncertainties. February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 8 4.3. First measurement of structure function F bb̄ 2 Recently the first measurements 9,10 of the beauty contributions to the in- clusive deep inelastic ep scattering have been made. These analyses are based on inclusive lifetime tagging. Figure 6 shows in the left plot the results obtained for the structure function F bb̄2 as a function of Q 2 for var- ious values of Bjorken x. The data exhibit positive scaling violations, i.e. rises of F bb̄2 with Q 2 for fixed x. The data are compared to mixed scheme NLO calculations from CTEQ 4 and MRST 3. The difference between the two calculations, which reaches a factor two at the lowest Q2 and x, arises mainly from the different treatments of threshold effects by MRST and CTEQ. However, within the current experimental errors, these differ- ences cannot yet be resolved and both calculations describe the data well. The data are also compared to the mixed scheme NNLO predictions from MRST 5, which is somewhat lower than the NLO prediction from the same group, but also agrees with the data. In the right plot of figure 6 the frac- tional contribution of beauty events to deep inelastic ep scattering is shown as expressed by the ratio f bb̄ = F bb̄2 /F2 . The beauty contributions rises strongly from a few permille at small Q2 = 12 GeV2 < m2b to about 3% at the largest Q2 = 500 GeV2 ≫ m2b . This reflects the kinematic threshold behaviour, i.e. at small Q2 and x the invariant mass of the gluon-photon system barely exceeds the minimal required mass of 2mb. For comparison the corresponding fractional charm contribution is also shown, which is in the covered phase space rather flat with values of about 20-30%. 5. Outlook The ongoing data taking at HERA II will collect until summer 2007 at least five times more statistics than collected at HERA I. This together with the upgraded H1 and ZEUS detectors will improve beauty measure- ments, reaching a precision of about 10% for the total and 20% for the differential cross sections. This will allow to clarify whether the data in- deed exceed the perturbative QCD calculations where currently indicated. Improved measurements of the structure function F bb̄2 will allow to dis- tinguish between the available calculations in massive and mixed pQCD schemes whose predictions differ up to a factor two. February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 9 10 -3 10 -2 10 -1 1 10 10 2 10 10 2 10 3 x=0.0002 i=5 x=0.0005 i=4 x=0.002 i=3 x=0.005 i=2 x=0.013 i=1 x=0.032 i=0 Q 2 /GeV 2 F 2 b b_ × 8 i H1 Data H1 Data (High Q 2 ) MRST04 MRST NNLO CTEQ6HQ 10 -3 10 -2 10 -1 x = 0.0002 f q q_ H1 Data f cc _ f bb _ x = 0.0005 MRST04 f cc _ MRST04 f bb _ 10 -2 10 -1 x = 0.002 x = 0.005 10 -2 10 -1 10 10 2 10 3 x = 0.013 Q 2 / GeV 2 10 10 2 10 3 x = 0.032 Q 2 / GeV 2 H1 Data (High Q 2 ) f cc _ f bb _ Figure 6. The first results for the beauty contribution F bb̄ 2 to the inclusive structure function F2 . The left plot shows F bb̄ 2 as a function of Q2 for various x. The right plot shows the observed relative beauty contributions to the total cross section f bb̄ = F bb̄ 2 /F2 . The results for the relative charm contribution are also shown. The data are compared to different perturbative QCD calculations. References 1. S. Frixione, P. Nason and G. Ridolfi, Nucl. Phys. B 454 (1995) 3 [hep- ph/9506226]. 2. B. W. Harris and J. Smith, Nucl. Phys. B 452 (1995) 109 [hep-ph/9503484]. 3. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Eur. Phys. J. C 39 (2005) 155 [hep-ph/0411040]. 4. S. Kretzer, H. L. Lai, F. I. Olness and W. K. Tung, Phys. Rev. D 69 (2004) 114005 [hep-ph/0307022]. 5. R. S. Thorne, AIP Conf. Proc. 792 (2005) 847 [hep-ph/0506251]. 6. S. Chekanov et al. [ZEUS Collaboration], Phys. Rev. D 70 (2004) 012008 [hep-ex/0312057]. 7. S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B 599 (2004) 173 [hep- ex/0405069]. 8. A. Aktas et al. [H1 Collaboration], Eur. Phys. J. C 41 (2005) 453 [hep- ex/0502010]. 9. A. Aktas et al. [H1 Collaboration], Eur. Phys. J. C 40 (2005) 349 [hep- February 6, 2006 12:9 Proceedings Trim Size: 9in x 6in behnke 10 ex/0411046]. 10. A. Aktas et al. [H1 Collaboration], Eur. Phys. J. C 45 (2006) 23 [hep- ex/0507081]. 11. H1 Collaboration, contributed paper 405, XXII International Symposium on Lepton-Photon Interactions at High Energy, Uppsala, Sweden, 2005. 12. ZEUS Collaboration, contributed paper 269, XXII International Symposium on Lepton-Photon Interactions at High Energy, Uppsala, Sweden, 2005. 13. A. Aktas et al. [H1 Collaboration], Phys. Lett. B 621 (2005) 56 [hep- ex/0503038]. 14. S. Chekanov et al. [ZEUS Collaboration], contributed paper 575, Interna- tional Europhysics Conference on High Energy Physics (EPS 2003), Aachen, Germany, 2003. 15. J. Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C 18 (2001) 625 [hep- ex/0011081].