Measurement of $CP$ violation in $B^0 \rightarrow J/\psi K^0_S$ decays

Measurements are presented of the $CP$ violation observables $S$ and $C$ in the decays of $B^0$ and $\overline{B}{}^0$ mesons to the $J/\psi K^0_S$ final state. The data sample corresponds to an integrated luminosity of $3.0\,\text{fb}^{-1}$ collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$ and $8\,\text{TeV}$. The analysis of the time evolution of $41500$ $B^0$ and $\overline{B}{}^0$ decays yields $S = 0.731 \pm 0.035 \, \text{(stat)} \pm 0.020 \,\text{(syst)}$ and $C = -0.038 \pm 0.032 \, \text{(stat)} \pm 0.005\,\text{(syst)}$. In the Standard Model, $S$ equals $\sin(2\beta)$ to a good level of precision. The values are consistent with the current world averages and with the Standard Model expectations.

The violation of charge-parity (CP) conservation in processes involving B mesons was first observed in the "golden mode" B 0 → J=ψK 0 S by the BABAR and Belle experiments at the asymmetric e þ e − colliders PEP-II and KEKB [1,2]. Since then, measurements of CP violation in this decay mode have reached a precision at the level of 10 −2 [3,4]. Thus, these measurements play an important role in constraining and testing the quark-flavor sector of the standard model [5,6], which relates CP-violating observables to a single irreducible phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [7,8]. As the J=ψK 0 S final state is common to both the B 0 and thē B 0 meson decays, the interference between the amplitudes for the direct decay and for the decay after B 0 -B 0 oscillation results in a decay-time dependent CP asymmetry between the time-dependent decay rates of B 0 andB 0 mesons AðtÞ ≡ ΓðB 0 ðtÞ → J=ψK 0 S Þ − ΓðB 0 ðtÞ → J=ψK 0 S Þ ΓðB 0 ðtÞ → J=ψK 0 S Þ þ ΓðB 0 ðtÞ → J=ψK 0 S Þ Here, B 0 ðtÞ andB 0 ðtÞ indicate the flavor of the B meson at production, while t indicates the decay time. The parameters Δm and ΔΓ are the mass and the decay width differences between the heavy and light mass eigenstates of the B 0 -B 0 system, and S, C, and A ΔΓ are CP observables. As ΔΓ is negligible for the B 0 -B 0 system [9], the timedependent asymmetry simplifies to AðtÞ ¼ S sinðΔmtÞ− C cosðΔmtÞ.
The B 0 → J=ψK 0 S decay is dominated by ab → ccs transition, and CP violation in the decay is expected to be negligible at the current level of experimental precision, giving C ≈ 0. (Mention of a particular decay mode implies the inclusion of charge-conjugate states except when the measurement of CP violation is involved.) This allows us to identify S with sinð2βÞ, where β ≡ arg½−ðV cd V Ã cb Þ=ðV td V Ã tb Þ is one of the angles of the CKM triangle. Other measurements that constrain this triangle predict sinð2βÞ as 0.771AE 0.017 0.041 [10], giving a small discrepancy with respect to the average of direct measurements, 0.682 AE 0.019 [9], where the most precise input comes from a CP violation measurement in B 0 → J=ψK 0 S decays by the Belle experiment, S ¼ 0.670 AE 0.029ðstatÞ AE 0.013ðsystÞ [4]. To clarify the CKM picture, both better experimental precision and improved understanding of higher-order contributions to the decay amplitudes are required [11,12].
The analysis presented in this Letter supersedes a previous measurement by LHCb [13], which was performed on data corresponding to an integrated luminosity of 1.0 fb −1 at a center-of-mass energy of 7 TeV. By adding data corresponding to 2 fb −1 at 8 TeV and using an optimized selection and additional "flavor tagging" algorithms to identify the quark content of the B meson at production, we increase the statistical power of the analysis by almost a factor 6.
The LHCb detector [14,15] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photon, electron, and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter, and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The online event selection system (trigger) [16] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage.
The analysis is performed with B 0 → J=ψK 0 S candidates reconstructed in the J=ψ → μ þ μ − and K 0 S → π þ π − final states. Two oppositely charged particles, identified as muons with high momentum and high transverse momentum, are required to originate from a common space point (vertex) and to have an invariant mass in a range AE60 MeV=c 2 around the known J=ψ mass [17]. Since the B 0 meson has a lifetime of 1.5 ps and has high momentum, the resulting J=ψ candidate is required to be significantly separated from all reconstructed pp collision points [primary vertices (PVs)], of which there are on average 2.4 per event. The K 0 S candidates are formed from two oppositely charged, high-momentum pion candidates with a clear separation from any PV in the event. Candidates decaying early enough for the final-state pions to be reconstructed in the vertex detector are characterized as long candidates and are required to have an invariant mass within AE15 MeV=c 2 of the known K 0 S mass [17]. The K 0 S candidates that decay later, such that track segments of the pions cannot be formed in the vertex detector, are called downstream candidates; these have a poorer momentum resolution than the long candidates, and thus the corresponding π þ π − pairs are required to have an invariant mass within AE55 MeV=c 2 of the known K 0 S mass. A good vertex fit quality and sufficient separation from the B 0 decay vertex are required for the K 0 S candidate's decay vertex. To reduce background contributions from Λ 0 b → J=ψΛ decays, the π þ (π − ) candidate has to fulfill particle identification requirements if the invariant mass under a pπ − (π þp ) mass hypothesis is compatible with the Λ mass.
The B 0 candidates are reconstructed from J=ψ and K 0 S candidates that form a good quality vertex. Multiple PVs and, in a small fraction of events, multiple B 0 → J=ψK 0 S candidates, lead to multiple (B 0 ; PV) pairs per event. For each pair, the decay time t is obtained from a fit to the full decay chain while constraining the production vertex of the B 0 candidate to the respective PV [18]. The reconstructed B 0 candidate mass m is obtained from a similar fit with the μ þ μ − and π þ π − invariant masses constrained to the known J=ψ and K 0 S masses. The latter fit must satisfy loose requirements on its quality, and resulting candidates are only retained if 5230 < m < 5330 MeV=c 2 and 0.3 < t < 18.3 ps. The fit uncertainty σ t on the decay time is required to be smaller than 200 fs, which is well above the average resolution of 55 fs (65 fs) for candidates with long (downstream) K 0 S daughters. The quantity σ t is used later in the analysis as an estimate of the per-candidate decay-time resolution. In events where more than one (B 0 ; PV) pair satisfies all selection requirements, one is chosen at random.
Various simulated data samples are used in the analysis. In the simulation, pp collisions are generated using PYTHIA [19] with a specific LHCb configuration [20]. Decays of hadronic particles are described by EVTGEN [21]. The interaction of the generated particles with the detector, and its response, are implemented using the GEANT4 toolkit [22] as described in Ref. [23].
Tagging algorithms are used to infer the initial flavor of the B meson candidate, i.e., whether it contained a b or ab quark at production. Each algorithm provides a decision d on the flavor of the B meson candidate (tag), and an estimate η of the probability for that decision to be incorrect (mistag probability). The knowledge of the B meson production flavor is essential for this analysis, and so only candidates for which the tagging algorithms yield a decision are considered.
One class of flavor tagging algorithms, the opposite-side (OS) tagger, exploits the dominant production mechanism of b hadrons, i.e., the production of bb quark pairs, by reconstructing the b hadron produced in association with the signal B meson. The OS tagger uses the charge of the electron or muon from semileptonic b decays, the charge of the kaon from the b → c → s decay chain, and the inclusive charge of particles associated with the secondary vertex reconstructed from the b hadron decay products; further details are described in Ref. [24].
A major improvement in this analysis over Ref. [13] is the inclusion of the same-side pion (SSπ) tagger, which deduces the production flavor by exploiting pions produced in the fragmentation of the b quark that produced the signal B meson or in the decay of excited B mesons into the signal B meson [25,26]. Tagging pion candidates are selected requiring charged, high momentum, and high transverse-momentum particles that are consistent with originating from the associated PV. Pions are identified using information from the particle identification detectors, and the difference between the invariant mass of the B and the Bπ AE pair is required to be less than 1.2 GeV=c 2 . Additionally, the flight directions of the pion and the B candidate must be compatible. If multiple pion candidates pass the selection, the one with the highest transverse momentum is used. The mistag probability is obtained using a neural network that is trained on simulated events and whose inputs are global event properties and kinematic and geometric information on the pion and B signal candidates.
The tagging calibration is performed in control samples of B mesons whose final state determines the B flavor at decay time, by determining a linear correction ωðηÞ that relates the estimated mistag probability η with the mistag probability ω observed in the control sample. To account for asymmetries in the detection efficiency of charged particles, which can lead to different mistag probabilities for B 0 andB 0 mesons, an additional linear correction function ΔωðηÞ is determined. Asymmetries in the efficiency of the algorithms in determining a decision are found to be negligible.
The B þ → J=ψK þ decay is used to determine the flavor tagging calibration for the OS tagger. A consistency check of the calibration is performed in a control sample of B 0 → J=ψK Ã0 decays, showing a good correspondence of the calibration between B þ and B 0 decays. As the quarks that accompany the b quark in B þ and B 0 mesons differ, the SSπ tagger calibration is performed with B 0 → J=ψK Ã0 decays [27]. Systematic uncertainties are assigned for the uncertainties associated with the calibration method and for the validity of the calibration in the signal decay mode. A summary of the calibration results is given in Ref. [28].
The effective tagging efficiency is the product of the probability for reaching a tagging decision, ε tag ¼ ð36.54 AE 0.14Þ%, and the square of the effective dilution D ≡ 1 − 2ω ¼ ð28.75 AE 0.24Þ%, which corresponds to an effective mistag probability of ω ¼ ð35.62 AE 0.12Þ%. Compared to the previous LHCb analysis [13] the effective tagging efficiency ε eff ¼ ε tag D 2 increases from 2.38% to 3.02%, mainly due to the inclusion of the SSπ tagger.
The values of the CP violation observables S and C are estimated by maximizing the likelihood of a probability density function (PDF) describing the unbinned distributions of the following observables: the reconstructed mass m, the decay time t and its uncertainty estimate σ t , the OS and SSπ flavor tag decisions d OS and d SSπ , and the corresponding per-candidate mistag probability estimates η OS and η SSπ . The fit is performed simultaneously in 24 independent subsamples, chosen according to data-taking conditions (7 TeV,8 TeV), K 0 S type (downstream, long), flavor tagging algorithm (OS only, SSπ only, OS and SSπ), and two trigger requirements. In each category the data distribution is modeled using a sum of two individual PDFs, one for the B 0 signal and one for the combinatorial background.
The reconstructed mass of the signal component is parametrized with a double-sided HYPATIA PDF [29] with tail parameters determined from simulation. An exponential function is used to model the background component, with independent parameters for the downstream and long K 0 S subsamples. The fit to the mass distributions yields 41560 AE 270 tagged B 0 → J=ψK 0 S signal decays. The mass distribution and projections of the PDFs are shown in Fig. 1(a).
The decay-time resolution is modeled by a sum of three Gaussian functions with common mean, but different widths, which are convolved with the PDFs describing the decay-time distributions. Two of the widths are given by the per-candidate resolution estimate σ t , each calibrated with independent linear calibration functions. The third Gaussian describes the resolution for candidates associated with a wrong PV. The scale and width parameters are obtained in a fit to the decay-time distribution of a control sample of B 0 candidates formed from prompt J=ψ and K 0 S mesons. The parameters are determined separately for candidates formed from downstream and long K 0 S candidates.
Trigger, reconstruction, and selection criteria distort the measured B 0 decay-time distribution, leading to a decaytime dependent efficiency. Effects of the trigger requirements, which distort the decay-time distribution at low decay times, are determined using data and following the strategy used in Ref. [30]. The misreconstruction of tracks leads to inefficiencies at large decay times. To account for this effect, an additional decay-time dependent efficiency of the form e −β t t is used, where β t is obtained from simulation. The PDF of true decay times t 0 is given by where the tag decision d takes the value þ1 (−1) for a tagged B 0 (B 0 ) candidate and d 0 takes the value þ1 (−1) for the B 0 (B 0 ) component of the signal distribution, τ is the B 0 meson lifetime, and represents the calibration of the tagging response from the tagging algorithm j ¼ fOS; SSπg. The production asymmetry A P ≡ ½σðB 0 Þ − σðB 0 Þ=½σðB 0 Þ þ σðB 0 Þ, where σ denotes the production cross section inside the LHCb acceptance, is obtained using a measurement in 7 TeV pp collisions [31]. Considering differences between the 7 and 8 TeV data-taking conditions, the production asymmetries are determined as A 7 TeV P ¼ −0.0108AE 0.0052ðstatÞ AE 0.0014ðsystÞ and A 8 TeV . The background decay-time distribution is parametrized by a sum of exponential functions, convolved with the resolution model used for the signal. This parametrization does not depend on the tag decision and mistag probability estimates. The number of required exponential functions varies across subsamples. The decay-time distribution and projections of the PDFs are shown in 1(b). The distributions of the percandidate resolution estimate σ t and the per-candidate mistag probabilities, η OS and η SSπ , are modeled by empirical functions. Independent parameterizations are chosen for the signal and background components.
The likelihood is a function of 83 free parameters, including S and C, and 48 yield parameters for the signal and the background components in 24 individual subsamples. Eleven parameters are external inputs, including the production asymmetry, the flavor tagging calibration parameters, and the mass difference Δm [17]. These are constrained in the fit within their statistical uncertainties, taking their correlations into account. The likelihood fit yields S ¼ 0.729 AE 0.035 and C ¼ −0.033 AE 0.032 with a correlation coefficient of ρðS; CÞ ¼ 0.483. Figure 2 shows the decay time-dependent signal-yield asymmetry. An additional fit with fixed C ¼ 0 yields S ¼ 0.746AE 0.030. Corrections of þ0.002 for S and −0.005 for C are applied to account for CP violation in K 0 −K 0 mixing and for the difference in the nuclear cross sections in material between K 0 andK 0 states [34]. The correction is negligible for the result for S with C ¼ 0.
Various sources of systematic uncertainties on the CP observables are examined, in particular from mismodeling PDFs and from systematic uncertainties on the input parameters. In each study, a large set of pseudoexperiments is simulated using a PDF modified such as to include the systematic effect of interest; the relevant distributions from these pseudoexperiments are then fitted with the nominal PDF. Significant average deviations of the fit results from the input values are used as estimates of systematic uncertainties. The largest systematic uncertainty on S, AE0.018, accounts for possible tag asymmetries in the background; for C the largest uncertainty, AE0.0034, results from the systematic uncertainty on Δm. Systematic uncertainties on the flavor tagging calibration account for the second largest systematic uncertainty on S, AE0.006, and on C, AE0.0024. The third largest uncertainty on S, AE0.005, arises from assuming ΔΓ ¼ 0 and is evaluated by generating pseudoexperiments with ΔΓ set to the value of its current uncertainty, 0.007 ps −1 [9], and then neglecting it in the fit. Remaining uncertainties due to neglecting correlations between the reconstructed mass and decay time of the candidates, mismodeling of the decay-time resolution and efficiency, the systematic uncertainty of the production asymmetry, and the uncertainty on the length scale of the vertex detector are small and are given in Ref. [28]. Adding all contributions in quadrature results in total systematic uncertainties of AE0.020 on S and AE0.005 on C.
Several consistency checks are performed by splitting the data set according to different data-taking conditions, tagging algorithms, and different reconstruction and trigger requirements. All results show good agreement with the nominal results.
In conclusion, a measurement of CP violation in the interference between the direct decay and the decay after collisions at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb −1 . The CP observables S and C, which allow the determination of the CKM angle β, are measured to be S ¼ 0.731 AE 0.035ðstatÞ AE 0.020ðsystÞ; with a statistical correlation coefficient ρðS; CÞ ¼ 0.483. When C is fixed to zero the measurement yields S ¼ sinð2βÞ ¼ 0.746 AE 0.030ðstatÞ. This measurement supersedes the previous LHCb result obtained with 1.0 fb −1 [13], and represents the most precise timedependent CP violation measurement at a hadron collider to date. Furthermore, the result has a similar precision to, and is in good agreement with, previous measurements performed at the Belle and BABAR experiments at the KEKB and PEP-II colliders [3,4]. This result is in excellent agreement with the expectations from other CKM related measurements and, after averaging with other results, improves the consistency of the CKM sector of the standard model.
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,