Measurement of matter–antimatter differences in beauty baryon decays ARTICLES PUBLISHED ONLINE: 30 JANUARY 2017 | DOI: 10.1038/NPHYS4021 Measurement of matter–antimatter di�erences in beauty baryon decays The LHCb collaboration† Di�erences in the behaviour of matter and antimatter have been observed in K and B meson decays, but not yet in any baryon decay. Such di�erences are associated with the non-invariance of fundamental interactions under the combined charge- conjugation and parity transformations, known as CP violation. Here, using data from the LHCb experiment at the Large Hadron Collider, we search for CP-violating asymmetries in the decay angle distributions of Λ0b baryons decaying to pπ −π+π− and pπ−K+K− final states. These four-body hadronic decays are a promising place to search for sources of CP violation both within and beyond the standard model of particle physics. We find evidence for CP violation in Λ0b to pπ −π+π− decays with a statistical significance corresponding to 3.3 standard deviations including systematic uncertainties. This represents the first evidence for CP violation in the baryon sector. The asymmetry between matter and antimatter is related to theviolation of the CP symmetry (CPV), where C and P are thecharge-conjugation and parity operators. CP violation is ac- commodated in the standard model (SM) of particle physics by the Cabibbo–Kobayashi–Maskawa (CKM) mechanism that describes the transitions between up- and down-type quarks1,2, in which quark decays proceed by the emission of a virtual W boson and where the phases of the couplings change sign between quarks and antiquarks. However, the amount of CPV predicted by the CKM mechanism is not sufficient to explain our matter-dominated Universe3,4 and other sources of CPV are expected to exist. The initial discovery of CPV was in neutral K meson decays5, and more recently it has been observed in B0 (refs 6,7), B+(refs 8–11), and B0s (ref. 12) meson decays, but it has never been observed in the decays of any baryon. Decays of the Λ0b (bud) baryon to final states consisting of hadrons with no charm quarks are predicted to have non-negligible CP asymmetries in the SM, as large as 20% for certain three-body decay modes13. It is important to measure the size and nature of these CP asymmetries in as many decay modes as possible, to determine whether they are consistent with the CKM mechanism or, if not, what extensions to the SM would be required to explain them14–16. The decay processes studied in this article, Λ0b →pπ − π + π − and Λ0b →pπ −K+K−, are mediated by the weak interaction and governed mainly by two amplitudes, expected to be of similar magnitude, from different diagrams describing quark-level b→ uud transitions, as shown in Fig. 1. Throughout this paper the inclusion of charge-conjugate reactions is implied, unless otherwise indicated. CPV could arise from the interference of two amplitudes with relative phases that differ between particle and antiparticle decays, leading to differences in the Λ0b and Λ 0 b decay rates. The main source of this effect in the SM would be the large relative phase (referred to as α in the literature) between the product of the CKM matrix elements VubV∗ud and VtbV ∗ td, which are present in the different diagrams depicted in Fig. 1. Parity violation (PV) is also expected in weak interactions, but has never been observed in Λ0b decays. To search for CP-violating effects one needs to measure CP- odd observables, which can be done by studying asymmetries in the T̂ operator. This is a unitary operator that reverses both the momentum and spin three-vectors17,18, and is different from the antiunitary time-reversal operator T19,20 that also exchanges initial and final states. A non-zero CP-odd observable implies CP violation, and similar considerations apply to P-odd observables and parity violation21. Furthermore, different values of P-odd observables for a decay and its charge conjugate would imply CPV. In this paper, scalar triple products of final-state particle momenta in the Λ0b centre-of-mass frame are studied to search for P- and CP- violating effects in four-body decays. These are defined as CT̂ =pp · (ph−1 ×ph+2 ) for Λ 0 b and CT̂ =pp ·(ph+1 ×ph−2 ) for Λ 0 b, where h1 and h2 are final-state hadrons: h1=π and h2=K for Λ0b→pπ −K+K− and h1=h2=π for Λ0b→pπ − π + π −. In the latter case there is an inherent ambiguity in the choice of the pion for h1 that is resolved by taking that with the larger momentum in the Λ0b rest frame, referred to as πfast. The following asymmetries may then be defined22,23: AT̂(CT̂)= N(CT̂ >0)−N(CT̂ <0) N(CT̂ >0)+N(CT̂ <0) (1) AT̂(CT̂)= N(−CT̂ >0)−N(−CT̂ <0) N(−CT̂ >0)+N(−CT̂ <0) (2) where N and N are the numbers of Λ0b and Λ 0 b decays. These asymmetries are P-odd and T̂-odd and so change sign under P or T̂ transformations, that is, AT̂ (CT̂ ) =−AT̂ (−CT̂ ) or AT̂ (CT̂ ) = −AT̂ (−CT̂ ). The P- and CP-violating observables are defined as aT̂-oddP = 1 2 ( AT̂ +AT̂ ) , aT̂-oddCP = 1 2 ( AT̂ −AT̂ ) (3) and a significant deviation from zero would signal PV or CPV, respectively. Searches for CPV with triple-product asymmetries are particularly suited to Λ0b four-body decays to hadrons with no charm quark24 thanks to the rich resonant substructure, dominated by ∆(1232)++→pπ+ and ρ(770)0 →π+π− resonances in the Λ 0 b → pπ − π + π − final state. The observable aT̂-oddCP is sensitive to the interference of T̂-even and T̂-odd amplitudes with different CP-odd (‘weak’) phases. Unlike the overall asymmetry in the decay rate that is sensitive to the interference of T̂-even amplitudes, aT̂-oddCP does not require a non-vanishing difference † A full list of authors and a�liations appears at the end of the paper. NATURE PHYSICS | VOL 13 | APRIL 2017 | www.nature.com/naturephysics 391 © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. http://dx.doi.org/10.1038/nphys4021 www.nature.com/naturephysics ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4021 b d u u d u d u u d (s) u d (s) Vub V∗ud V∗td W− p t W− b d u d u u d u u d (s) u d (s) Vtb 0 bΛ 0 bΛ − (K−)π + (K+)π −π p − (K−)π + (K+)π −π Figure 1 | Dominant Feynman diagrams for Λ0b →pπ −π+π− and Λ0b →pπ −K+K− transitions. The two diagrams show the transitions that contribute most strongly to Λ0b →pπ − π + π − and Λ0b →pπ −K+K− decays. In both cases, a pair of π+π− (K+K−) is produced by gluon emission from the light quarks (u,d). The di�erence is in the b quark decay that happens on the left through a virtual W− boson emission (‘tree diagram’) and on the right as a virtual W− boson emission and absorption together with a gluon emission (‘loop diagram’). The magnitudes of the two amplitudes are expected to be comparable, and each is proportional to the product of the CKM matrix elements involved, which are shown in the figure. 5.2 5.4 5.6 5.8 6.0 Ev en ts /( 9 M eV /c 2 ) Ev en ts /( 9 M eV /c 2 ) 0 500 1,000 1,500 Full fit Part-rec. bkg. Comb. bkg. LHCb a b 0 200 400 Full fit Part-rec. bkg. Comb. bkg. LHCb 5.2 5.4 5.6 5.8 6.0 0 b → p − + −Λ π π π B0 → K+ − − +π π π Λ0b → pK− + −π π m(p − + −) [GeV/c2]π π π m(p −K+K−) [GeV/c2]π Λ0b → p −K+K−π B0 → K−K+K+ −π B0S → K−K+ − +π π 0 b → pK+K−K−Λ 0 b → pK− + −π πΛ Figure 2 | Reconstructed invariant mass fits used to extract the signal yields. The invariant mass distributions for (a) Λ0b →pπ − π + π − and (b) Λ 0 b →pπ −K+K− decays are shown. A fit is overlaid on top of the data points, with solid and dotted lines describing the projections of the fit results for each of the components described in the text and listed in the legend. Uncertainties on the data points are statistical only and represent one standard deviations, calculated assuming Poisson-distributed entries. in the CP-invariant (‘strong’) phase between the contributing amplitudes19,25. The observables AT̂ , AT̂ , aT̂-oddP and a T̂-odd CP are, by construction, largely insensitive to particle–antiparticle production asymmetries and detector-induced charge asymmetries26. This article describes measurements of the CP- and P-violating asymmetries introduced in equation (3) in Λ0b →pπ − π + π − and Λ 0 b →pπ −K+K− decays. The asymmetries are measured first for the entire phase space of the decay, integrating over all possible final-state configurations, and then in different regions of phase space so as to enhance sensitivity to localized CPV. The analysis is performed using proton–proton collision data collected by the LHCb detector, corresponding to 3.0 fb−1 of integrated luminosity at centre-of-mass energies of 7 and 8 TeV, and exploits the copious production ofΛ0b baryons at the LHC, which constitutes around 20% of all b hadrons produced27. Control samples of Λ0b→pK − π + π − and Λ0b →Λ + c π − decays, with Λ+c decaying to pK − π +, pπ−π+, and pK−K+ final states, are used to optimize the event selection and study systematic effects; the most abundant control sample consists of Λ0b→Λ + c (pK − π + )π − decays mediated by b→c quark transitions in which no CPV is expected28. To avoid introducing biases in the results, all aspects of the analysis, including the selection, phase space regions, and procedure used to determine the statistical significance of the results, were fixed before the data were examined. The LHCb detector29,30 is designed to collect data of b-hadron decays produced from proton–proton collisions at the Large Hadron Collider. It instruments a region around the proton beam axis, covering the polar angles between 10 and 250mrad, where approximately 24% of the b-hadron decays occur31. The detector includes a high-precision tracking system with a dipole magnet, providing measurements of the momentum and decay vertex position of particle decays. Different types of charged particles are distinguished using information from two ring-imaging Cherenkov detectors, a calorimeter and a muon system. Simulated samples of Λ 0 b signal modes and control samples are used in this analysis to verify the experimental method and to study certain systematic effects. These simulated events model the experimental conditions in detail, including the proton–proton collision, the decays of the particles, and the response of the detector. The software used is described in refs 32–38. The online event selection is performed by a trigger system that takes fast decisions about which events to record. It consists of a hardware stage, based on information from the 392 © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. NATURE PHYSICS | VOL 13 | APRIL 2017 | www.nature.com/naturephysics http://dx.doi.org/10.1038/nphys4021 www.nature.com/naturephysics NATURE PHYSICS DOI: 10.1038/NPHYS4021 ARTICLES Table 1 | Definition of binning scheme A for the decay mode Λ0b →pπ −π+π−. Phase space bin m(pπ+) m(pπ−slow) m(π +π − slow), m(π +π − fast) |Φ| 1 (1.07, 1.23) (0, π2 ) 2 (1.07, 1.23) ( π2 ,π) 3 (1.23, 1.35) (0, π2 ) 4 (1.23, 1.35) ( π2 ,π) 5 (1.35, 5.34) (1.07, 2.00) m(π+π−slow )<0.78 or m(π + π − fast )<0.78 (0, π 2 ) 6 (1.35, 5.34) (1.07, 2.00) m(π+π−slow )<0.78 or m(π + π − fast )<0.78 ( π 2 ,π) 7 (1.35, 5.34) (1.07, 2.00) m(π+π−slow )>0.78 and m(π + π − fast )>0.78 (0, π 2 ) 8 (1.35, 5.34) (1.07, 2.00) m(π+π−slow )>0.78 and m(π + π − fast )>0.78 ( π 2 ,π) 9 (1.35, 5.34) (2.00, 4.00) m(π+π−slow )<0.78 or m(π + π − fast )<0.78 (0, π 2 ) 10 (1.35, 5.34) (2.00, 4.00) m(π+π−slow )<0.78 or m(π + π − fast )<0.78 ( π 2 ,π) 11 (1.35, 5.34) (2.00, 4.00) m(π+π−slow )>0.78 and m(π + π − fast )>0.78 (0, π 2 ) 12 (1.35, 5.34) (2.00, 4.00) m(π+π−slow )>0.78 and m(π + π − fast )>0.78 ( π 2 ,π) Binning scheme A is defined to exploit interference patterns arising from the resonant structure of the decay. Bins 1–4 focus on the region dominated by the ∆(1232)++→pπ+ resonance. The other eight bins are defined to study regions where pπ− resonances are present (5–8) on either side of the ρ(770)0 →π+π− resonances (5–12). Further splitting for |Φ| lower or greater than π/2 is done to reduce potential dilution of asymmetries, as suggested in ref. 19. Masses are in units of GeV/c2 . calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. The software trigger requires Λ 0 b candidates to be consistent with a b-hadron decay topology, with tracks originating from a secondary vertex detached from the primary pp collision point. The mean Λ0b lifetime is 1.5ps (ref. 39), which corresponds to a typical flight distance of a few millimetres in the LHCb. The Λ0b→pπ −h+h− candidates are formed by combining tracks identified as protons, pions, or kaons that originate from a common vertex. The proton or antiproton identifies the candidate as a Λ0b or Λ 0 b. There are backgrounds from b-hadron decays to charm hadrons that are suppressed by reconstructing the appropriate two- or three-body invariant masses, and requiring them to differ from the known charm hadron masses by at least three times the experimental resolution. For the Λ0b→Λ + c π − control mode, only the Λ0b→ph +h−π− events with reconstructed ph+h− invariant mass between 2.23 and 2.31GeV/c2are retained. A boosted decision tree (BDT) classifier40 is constructed from a set of kinematic variables that discriminate between signal and background. The signal and background training samples used for the BDT are derived from the Λ0b →pK − π + π − control sample, since its kinematics and topology are similar to the decays under study; background in this sample is subtracted with the sPlot technique41, a statistical technique to disentangle signal and background contributions. The background training sample consists of candidates that lie far from the signal mass peak, between 5.85 and 6.40 GeV/c2. The control modes Λ0b→Λ + c (pπ + π − )π − and Λ0b→Λ + c (pK −K+)π− are used to optimize the particle identification criteria for the signal mode with the same final state. For events in which multiple candidates pass all selection criteria for a given mode, one candidate is retained at random and the rest discarded. Unbinned extended maximum likelihood fits to the pπ−π+π− and the pπ−K+K− invariant mass distributions are shown in Fig. 2. The invariant mass distribution of the Λ0b signal is modelled by a Gaussian core with power-law tails42, with the mean and the width of the Gaussian determined from the fit to data. The combinatorial background is modelled by an exponential distribution with the rate parameter extracted from data. All other parameters of the fit model are taken from simulations except the yields. Partially reconstructed Λ 0 b decays are described by an empirical function 43 convolved with a Gaussian function to account for resolution effects. The shapes of backgrounds from other b-hadron decays due to incorrectly identified particles, for example, kaons identified as pions or protons identified as kaons, are modelled using simulated events. These consist mainly of Λ0b→pK − π + π − and B0→K+π−π−π+ decays for the Λ0b→pπ − π + π − sample and of similar final states for the Λ 0 b →pπ −K+K− sample, as shown in Fig. 2. The yields of these contributions are obtained from fits to data reconstructed under the appropriate mass hypotheses for the final-state particles. The signal yields of Λ0b →pπ − π + π − and Λ0b →pπ −K+K− are 6,646±105 and 1,030±56, respectively. This is the first observation of these decay modes. Signal candidates are split into four categories according to Λ 0 b or Λ 0 b flavour and the sign of CT̂ or CT̂ to calculate the asymmetries defined in equations (1) and (2). The reconstruction efficiency for signal candidates with CT̂ > 0 is identical to that with CT̂ < 0 within the statistical uncertainties of the control sample, and likewise for CT̂ , which indicates that the detector and the reconstruction program do not bias this measurement. This check is performed both on the Λ0b→Λ + c (pK − π + )π − data control sample and on large samples of simulated events, using yields about 30 times those found in data, which are generated with no CP asymmetry. The CP asymmetry measured in the control sample is aT̂-oddCP (Λ + c π − )=(0.15±0.31)%, compatible with CP symmetry. The asymmetries AT̂ and AT̂ in the signal samples are measured with a simultaneous unbinned maximum likelihood fit to the invariant mass distributions of the different signal categories, and are found to be uncorrelated. Corresponding asymmetries for each of the background components are also measured in the fit; they are found to be consistent with zero, and do not lead to significant systematic uncertainties in the signal asymmetries. The values of aT̂-oddCP and aT̂-oddP are then calculated from AT̂ and AT̂ . In four-body particle decays, the CP asymmetries may vary over Φ 0 p +π − slowπ −fastπ Figure 3 | Definition of the Φ angle. The decay planes formed by the pπ−fast (blue) and the π−slowπ + (red) systems in the Λ0b rest frame. The momenta of the particles, represented by vectors, determine the two decay planes and the angle Φ∈[−π,π] (ref. 19) measures their relative orientation. NATURE PHYSICS | VOL 13 | APRIL 2017 | www.nature.com/naturephysics © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. 393 http://dx.doi.org/10.1038/nphys4021 www.nature.com/naturephysics ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4021 A sy m m et ri es ( % ) Phase space bin 5 10 20 0 −20 20 0 −20 A sy m m et ri es ( % ) 20 0 −20 20 0 −20 LHCb Scheme A χ2/ndf = 27.9/12 χ2/ndf = 21.1/12 ˆ aP T-odd χ2/ndf = 20.7/10ˆaP T-odd 1 2 3 LHCb Scheme B ˆ aCP T-odd χ2/ndf = 30.5/10ˆaCP T-odd | | (rad)Φ Figure 4 | Distributions of the asymmetries. The results of the fit in each region of binning schemes A and B are shown. The asymmetries aT̂-oddP and aT̂-oddCP for Λ 0 b →pπ − π + π − decays are represented by open boxes and filled circles, respectively. The error bars represent one standard deviation, calculated as the sum in quadrature of the statistical uncertainty resulting from the fit to the invariant mass distribution and the systematic uncertainties estimated as described in the main text. The values of the χ2 /ndf are quoted for the P- and CP-conserving hypotheses for each binning scheme, where ndf indicates the number of degrees of freedom. the phase space due to resonant contributions or their interference effects, possibly cancelling when integrated over the whole phase space. Therefore, the asymmetries are measured in different regions of phase space for the Λ0b →pπ − π + π − decay using two binning schemes, defined before examining the data. Scheme A, defined in Table 1, is designed to isolate regions of phase space according to their dominant resonant contributions. Scheme B exploits in more detail the interference of contributions which could be visible as a function of the angle Φ between the decay planes formed by the pπ−fast and the π − slowπ + systems, as illustrated in Fig. 3. Scheme B has ten non-overlapping bins of width π/10 in |Φ|. For every bin in each of the schemes, the Λ0b efficiencies for CT̂ > 0 and CT̂ < 0 are compared and found to be equal within uncertainties, and likewise the Λ 0 b efficiencies for CT̂ > 0 and CT̂ < 0. The analysis technique is validated on the Λ0b→Λ + c (pK − π + )π − control sample, for which the angle Φ is defined by the decay planes of the pK− and π+π− pairs, and on simulated signal events. The asymmetries measured in Λ0b →pπ − π + π − decays with these two binning schemes are shown in Fig. 4 and reported in Table 2, together with the integrated measurements. For each scheme individually, the compatibility with the CP-symmetry hypothesis is evaluated by means of a χ2 test, with χ2 =RT V−1R, where R is the array of aT̂-oddCP measurements and V is the covariance matrix, which is the sum of the statistical and systematic covariance matrices. An average systematic uncertainty, whose evaluation is discussed below, is assigned for all bins. The systematic uncertainties are assumed to be fully correlated; their contribution is small compared to the statistical uncertainties. The p-values of the CP- symmetry hypothesis are 4.9×10−2 and 7.1×10−4 for schemes A and B, respectively, corresponding to statistical significances of 2.0 and 3.4 Gaussian standard deviations (σ). A similar χ2 test is performed on aT̂-oddP measurements with p-values for the P- symmetry hypothesis of 5.8×10−3 (2.8σ) and 2.4×10−2 (2.3σ), for scheme A and B, respectively. The overall significance for CPV in Λ0b →pπ − π + π − decays from the results of schemes A and B is determined by means of a permutation test44, taking into account correlations among the results. A sample of 40,000 pseudoexperiments is generated from the data by assigning each event a random Λ0b/Λ 0 b flavour such that CP symmetry is enforced. The sign of CT̂ is unchanged if a Λ0b candidate stays Λ 0 b and reversed if the Λ0b candidate becomes Λ 0 b. The p-value of the CP-symmetry hypothesis is determined as the fraction of pseudoexperiments with χ 2 larger than that measured in data. Applying this method to the χ2 values from schemes A and B individually, the p-values obtained agree with those from the χ2 test within the uncertainty due to the limited number of pseudoexperiments. To assess a combined significance from the two schemes, the product of the two p-values measured in data is compared with the distribution of the product of the p-values of the two binning schemes from the pseudoexperiments. The fraction of pseudoexperiments whose p- value product is smaller than that seen in data determines the overall p-value of the combination of the two schemes45. An overall p-value of 9.8×10−4 (3.3σ) is obtained for the CP-symmetry hypothesis, including systematic uncertainties. For the Λ0b →pπ −K+K− decays, the smaller purity and signal yield of the sample do not permit PV and CPV to be probed with the same precision as for Λ0b→pπ − π + π −, and therefore only two regions of phase space are considered. One spans 1.43