Precision measurement of CP violation in B0S J/ K+K- decays

The time-dependent CP asymmetry in B 0 s → J= ψ K þ K − decays is measured using pp collision data, corresponding to an integrated luminosity of 3 . 0 fb − 1 , collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96 000 B 0 s → J= ψ K þ K − decays, the CP -violating phase ϕ s is measured, as well as the decay widths Γ L and Γ H of the light and heavy mass eigenstates of the B 0 s – ¯ B 0 s system. The values obtained are ϕ s ¼ − 0 . 058 (cid:2) 0 . 049 (cid:2) 0 . 006 rad, Γ s ≡ ð Γ L þ Γ H Þ = 2 ¼ 0 . 6603 (cid:2) 0 . 0027 (cid:2) 0 . 0015 ps − 1 , and ΔΓ s ≡ Γ L − Γ H ¼ 0 . 0805 (cid:2) 0 . 0091 (cid:2) 0 . 0032 ps − 1 , where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with B 0 s → J= ψπ þ π − decays gives ϕ s ¼ − 0 . 010 (cid:2) 0 . 039 rad. All measurements are in agreement with the standard model predictions. For the first time, the phase ϕ s is measured independently for each polarization state of the K þ K − system and shows no evidence for polarization dependence.

Precision Measurement of CP Violation in B 0 S → J=Ψ K þ K − Decays R. Aaij et al. * (LHCb Collaboration) (Received 12 November 2014;published 30 January 2015) The time-dependent CP asymmetry in B 0 s → J=ψK þ K − decays is measured using pp collision data, corresponding to an integrated luminosity of 3.0 fb −1 , collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96 000 B 0 s → J=ψK þ K − decays, the CP-violating phase ϕ s is measured, as well as the decay widths Γ L and Γ H of the light and heavy mass eigenstates of the B 0 s -B 0 s system. The values obtained are ϕ s ¼−0.058AE0.049AE0.006 rad, Γ s ≡ðΓ L þΓ H Þ=2¼0.6603AE0.0027AE0.0015ps −1 , and ΔΓ s ≡Γ L −Γ H ¼0.0805AE0.0091AE0.0032ps −1 , where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with B 0 s → J=ψπ þ π − decays gives ϕ s ¼ −0.010 AE 0.039 rad. All measurements are in agreement with the standard model predictions. For the first time, the phase ϕ s is measured independently for each polarization state of the K þ K − system and shows no evidence for polarization dependence. DOI: 10.1103/PhysRevLett.114.041801 PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Ff, 12.15.Hh The CP-violating phase ϕ s arises in the interference between the amplitudes of B 0 s mesons decaying via b → ccs transitions to CP eigenstates directly and those decaying after oscillation. In the standard model (SM), ignoring subleading contributions, this phase is predicted to be −2β s , where β s ¼ arg ½−ðV ts V Ã tb Þ=ðV cs V Ã cb Þ and V ij are elements of the quark-mixing matrix [1]. Global fits to experimental data give −2β s ¼ −0.0363 AE 0.0013 rad [2]. This phase could be modified if non-SM particles were to contribute to the B 0 s -B 0 s oscillations [3,4] and a measurement of ϕ s significantly different from the SM prediction would provide unambiguous evidence for processes beyond the SM.
The LHCb Collaboration has previously reported measurements of ϕ s using B 0 s → J=ψK þ K − and B 0 s → J=ψπ þ π − decays [5,6] and determined the sign of ΔΓ s to be positive [7], which removes the twofold ambiguity in ϕ s . These measurements were based upon data, corresponding to an integrated luminosity of up to 1.0 fb −1 , collected in pp collisions at a center-of-mass energy of 7 TeV in 2011 at the LHC. The D0, CDF, ATLAS and CMS Collaborations have also measured ϕ s in B 0 s → J=ψK þ K − decays [8][9][10][11]. This Letter extends the LHCb measurements in the B 0 s → J=ψK þ K − channel by adding data corresponding to 2.0 fb −1 of integrated luminosity collected at 8 TeV in 2012 and presents the combined results for ϕ s including the analysis of B 0 s → J=ψπ þ π − decays from Ref. [12]. For the first time, the CP-violating phases are measured separately for each polarization state of the K þ K − system. Knowledge of these parameters is an important step towards the control of loop-induced effects to the decay amplitude, which could potentially be confused with non-SM contributions to B 0 s -B 0 s mixing [13]. The analysis of the B 0 s → J=ψK þ K − channel reported here is as described in Ref. [6], to which the reader is referred for details, except for the changes described below.
The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks and is described in Ref. [14]. The trigger [15] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, in which all charged particles with transverse momentum greater than 500 ð300Þ MeV=c are reconstructed for 2011 (2012) data. Further selection requirements are applied off-line, as described in Ref. [6], in order to increase the signal purity.
The B 0 s → J=ψK þ K − decay proceeds predominantly via B 0 s → J=ψϕ, in which the K þ K − pair from the ϕð1020Þ meson is in a P-wave configuration. The final state is a superposition of CP-even and CP-odd states depending upon the relative orbital angular momentum of the J=ψ and ϕ mesons. The J=ψK þ K − final state can also be produced with K þ K − pairs in a CP-odd S-wave configuration [16]. The measurement of ϕ s requires the CP-even and CP-odd components to be disentangled by analyzing the distribution of the reconstructed decay angles of the final-state particles. In this analysis, the decay angles are defined in the helicity basis, cos θ K , cos θ μ , and φ h , as described in Ref. [6].
The invariant mass distributions for K þ K − and J=ψð→ μ þ μ − ÞK þ K − candidates are shown in Figs. 1(a) and 1(b), respectively. The combinatorial background is modeled with an exponential function and the B 0 s signal shape is parameterized by a double-sided Hypatia function [17], which gives a better description of the tails compared to the sum of two Gaussian distributions used in Ref. [6]. The fitted signal yield is 95 690 AE 350. In addition to the combinatorial background, studies of the data in sidebands of the mðJ=ψK þ K − Þ spectrum show contributions from approximately 1700 B 0 → J=ψK þ π − (4800 Λ 0 b → J=ψpK − ) decays where the pion (proton) is misidentified as a kaon. These background events have complicated correlations between the angular variables and mðJ=ψK þ K − Þ. In order to avoid the need to describe explicitly such correlations in the analysis, the contributions from these backgrounds are statistically subtracted by adding to the data simulated events of these decays with negative weight. Prior to injection, the simulated events are weighted such that the distributions of the relevant variables used in the fit, and their correlations, match those of data.
The principal physics parameters of interest are Γ s , ΔΓ s , ϕ s , jλj, the B 0 s mass difference, Δm s , and the polarization amplitudes A k ¼ jA k je −iδ k , where the indices k ∈ f0; ∥; ⊥; Sg refer to the different polarization states of the K þ K − system. The sum jA ∥ j 2 þ jA 0 j 2 þ jA ⊥ j 2 equals unity and by convention δ 0 is zero. The parameter λ describes CP violation in the interference between mixing and decay and is defined by η k ðq=pÞðĀ k =A k Þ, where it is assumed to be the same for all polarization states. The complex parameters p ¼ hB 0 s jB L i and q ¼ hB 0 s jB L i describe the relation between mass and flavor eigenstates and η k is the CP eigenvalue of the polarization state k. The CP-violating phase is defined by ϕ s ≡ − arg λ. In the absence of CP violation in decay, jλj ¼ 1. CP violation in B 0 s -meson mixing is negligible, following measurements in Ref. [18]. Measurements of the above parameters are obtained from a weighted maximum likelihood fit [19] to the decay-time and angle distributions of the 7 and 8 TeV data, as described in Ref. [6].
The B 0 s decay-time distribution is distorted by the trigger selection requirements and by the track reconstruction algorithms. Corrections for both 7 and 8 TeV samples are determined from data using the methods described in Ref. [20] and are incorporated in the maximum likelihood fit by a parameterized function, in the case of the trigger, and by per-candidate weights, in the case of the track reconstruction. Both corrections are validated using a sample of 10 6 simulated B 0 s → J=ψϕ events. To account for the experimental decay-time resolution, the signal probability density function (PDF) is defined per candidate and is convolved with the sum of two Gaussian functions with a common mean, μ, and independent widths. The widths are given by the per candidate decay-time uncertainty, estimated by the kinematic fit used to calculate the decay time, multiplied by separate scale factors. The scale factors are determined from the decay-time distribution of a control sample of prompt J=ψK þ K − candidates that are selected as for signal except for decay-time requirements. The average value of the σ distribution in the sample of prompt candidates is approximately 35 fs and the effective average resolution is 46 fs.
The flavor of the B 0 s candidate at production is inferred using two independent classes of flavor tagging algorithms, the opposite-side (OS) tagger and the same-side kaon (SSK) tagger, which exploit specific features of the production of bb quark pairs in pp collisions. The OS tagger algorithm is described in Ref. [6] but is recalibrated using data sets of flavor-specific decays, yielding a tagging power of ð2.55 AE 0.14Þ%. The SSK algorithm deduces the signal production flavor by exploiting charge-flavor correlations of the kaons produced during the hadronization process of theb quark forming the signal B 0 s meson. The tagging kaon is identified using a selection based on a neural network that gives an effective tagging power of ð1.26 AE 0.17Þ%, corresponding approximately to a 40% improvement in tagging power with respect to that in Refs. [6]. The SSK algorithm is calibrated using a sample of B 0 s → D − s π þ decays [21]. For events that have both OS and SSK tagging decisions, corresponding to 26% of the tagged sample, the effective tagging power is ð1.70 AE 0.08Þ%. The combined tagging power of the three overlapping tagging categories defined above is ð3.73 AE 0.15Þ%.
Due to different mðK þ K − Þ line shapes of the Sand P-wave contributions, their interferences are suppressed by an effective coupling factor after integrating over a finite mðK þ K − Þ region. The fit is carried out in six bins of mðK þ K − Þ, as shown in Fig. 1(a), to allow measurement of the small S-wave amplitude in each bin and to minimize correction factors in the interference terms of the PDF.
The results of the fit are consistent with the measurements reported in Ref. [6] and are reported in Table I where the first uncertainty is statistical and the second, systematic. The correlation matrix is given in Ref. [22]. In contrast to Ref. [6], the value of Δm s is unconstrained in this fit, thereby providing an independent measurement of this quantity, which is consistent with the results of Ref. [23]. The projections of the decay time and angular distributions are shown in Fig. 2.
The results reported in Table I are obtained with the assumption that ϕ s and jλj are independent of the final-state polarization. This condition can be relaxed to allow the measurement of ϕ k s and jλ k j separately for each polarization, following the formalism in Ref. [24]. The results of this fit are shown in Table II, and the statistical correlation matrix is given in Ref. [22]. There is no evidence for a polarization-dependent CP violation arising in B 0 s → J=ψK þ K − decays.
A summary of systematic uncertainties is reported in Tables III and IV in the Appendix. The tagging parameters are constrained in the fit and therefore their associated systematic uncertainties contribute to the statistical uncertainty of each parameter in Table I. This contribution is 0.004 rad to the statistical uncertainty on ϕ s , 0.004 ps −1 to that of Δm s , 0.01 rad to that of δ ∥ , and is negligible for all other parameters.
The assumption that the mðJ=ψK þ K − Þ distribution is independent from the decay time and angles is tested by reevaluating the signal weights in bins of the decay time and angles and repeating the fit. The difference in fit results is assigned as a systematic uncertainty. The systematic effect from the statistical uncertainty on the signal weights is determined by recomputing them after varying the parameters of the mðJ=ψK þ K − Þ fit model within their statistical uncertainties and assigning the difference in fit results as a systematic uncertainty.
The effect due to the b-hadron background contributions is evaluated by varying the proportion of simulated background events included in the fit by one standard deviation of their measured fractions. In addition, a further systematic uncertainty is assigned as the difference between the results of the fit to weighted or nonweighted data.
A small fraction of B 0 s → J=ψK þ K − decays come from the decays of B þ c mesons [25]. The effect of ignoring this component in the fit is evaluated using simulated pseudoexperiments where a 0.8% contribution [25,26] Neglecting the B þ c component leads to a bias on Γ s of 0.0005 ps −1 , which is added as a systematic uncertainty. Other parameters are unaffected.
The decay angle resolution is found to be of the order of 20 mrad in simulated events. The result of pseudoexperiments shows that ignoring this effect in the fit only leads to small biases in the polarization amplitudes, which are assigned as systematic uncertainties.
The angular efficiency correction is determined from simulated signal events weighted as in Ref. [6] such that the kinematic distributions of the final state particles match those in the data. A systematic uncertainty is assigned as the difference between the fit results using angular corrections from weighted or nonweighted simulated events. The limited size of the simulated sample leads to an additional systematic uncertainty.
The systematic uncertainty from the decay time resolution parameters is not included in the statistical   uncertainty of each parameter and is now quoted explicitly. It is assigned as the difference of fit parameters obtained from the nominal fit and a fit where the resolution model parameters are calibrated using a sample of simulated prompt-J=ψ events.
The trigger decay-time efficiency model, described in Ref. [6], introduces a systematic uncertainty that is determined by fixing the value of each model parameter in the fit and subsequently repeating the fit with the parameter values constrained within their statistical uncertainty. The quadratic differences of the uncertainties returned by each fit are then assigned as systematic uncertainties. The systematic effect of the track reconstruction efficiency is evaluated by applying the same techniques on a large simulated sample of B 0 s → J=ψϕ decays. The differences between the generation and fitted values of each physics parameter in this sample is assigned as the systematic uncertainty. The limited size of the control sample used to determine the track reconstruction efficiency parameterization leads to an additional systematic uncertainty.
The uncertainty on the longitudinal coordinate of the LHCb vertex detector is found from survey data and leads to an uncertainty on Γ s and ΔΓ s of 0.020%, with other parameters being unaffected. The momentum scale uncertainty is at most 0.022% [23], which only affects Δm s . Different models of the S-wave line shape and mðK þ K − Þ resolution are used to evaluate the coupling factors in each of the six mðK þ K − Þ bins and the resulting variation of the fit parameters are assigned as systematic uncertainties. Possible biases of the fitting procedure are studied by generating and fitting many simulated pseudoexperiments of equivalent size to the data. The resulting biases are small, and those that are significantly different from zero are assigned as systematic uncertainties.
The systematic correlations between parameters are evaluated by assuming that parameters are fully correlated when the systematic uncertainty is determined by comparing results obtained from the nominal and a modified fit. Other sources of systematic uncertainty are assumed to have negligible parameter correlations. The combined statistical and systematic correlation matrix is given in Ref. [22].
A measurement of ϕ s and jλj by LHCb using B 0 s → J=ψπ þ π − decays of ϕ ππ s ¼ 0.070 AE 0.068 AE 0.008 rad and jλ ππ j ¼ 0.89 AE 0.05 AE 0.01, consistent with the measurement reported here, was reported in Ref. [12]. The results  from the two analyses are combined by incorporating the B 0 s → J=ψK þ K − result as a correlated Gaussian constraint in the B 0 s → J=ψπ þ π − fit, under the assumption that B 0 s → J=ψπ þ π − and B 0 s → J=ψK þ K − decays both proceed dominantly via b → ccs transitions and the ratio between loop-induced processes and tree diagrams are the same in each mode. The fit accounts for correlations between common parameters and correlations between systematic uncertainties. The combined result is ϕ s ¼ −0.010 AE 0.039 rad and jλj ¼ 0.957 AE 0.017. The correlation between the parameters is about −0.02.
In conclusion, the CP-violating phase ϕ s , and the B 0 s decay width parameters Γ s and ΔΓ s , are measured using B 0 s → J=ψK þ K − decays selected from the full LHCb data set from the first LHC operation period. The results are ϕ s ¼ −0.058 AE 0.049 AE 0.006 rad, jλj ¼ 0.964 AE 0.019AE 0.007, Γ s ¼ 0.6603 AE 0.0027 AE 0.0015 ps −1 , and ΔΓ s ¼ 0.0805 AE 0.0091 AE 0.0032 ps −1 . The parameter jλj is consistent with unity, implying no evidence for CP violation in B 0 s → J=ψK þ K − decays. For the first time, the polarizationdependent CP-violating parameters are measured and show no significant difference between the four polarization states. The measurements of ϕ s and jλj in B 0 s → J=ψK þ K − decays areconsistent withthose measured inB 0 s → J=ψπ þ π − decays, and the combined results are ϕ s ¼ −0.010 AE 0.039 rad and jλj ¼ 0.957 AE 0.017. The measurement of the CP violating phase ϕ s and ΔΓ s are the most precise to date and are in agreement with the SM predictions [2,[27][28][29], in which it is assumed that subleading contributions to the decay amplitude are negligible. Figure 3 compares this measured value of ϕ s with other independent measurements [8][9][10][11]30].
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software research and development tools provided by Yandex LLC (Russia). Individual groups or members have received support from EPLANET, Marie Skłodowska-Curie Actions, and ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom).

APPENDIX: SUMMARY OF SYSTEMATIC UNCERTAINTIES
See Tables III and IV.