Resonances and CP violation in B0s and B¯0s→J/ψK+K− decays in the mass region above the ϕ(1020)

JHEP08(2017)037 Published for SISSA by Springer Received:April 27, 2017 Revised:June 29, 2017 Accepted:July 25, 2017 Published:August 9, 2017 Resonances and CP violation in B0 sand B0 s→J/ψK+K−decays in the mass region above the φ(1020) The LHCb collaboration E-mail: [email protected] Abstract: The decays of B0 sand B0 smesons into the J/ψK+K−final state are studied in the K+K−mass region above the φ(1020) meson in order to determine the resonant substructure and measure the CP-violating phase, φs, the decay width, Γs, and the width difference between light and heavy mass eigenstates, ∆Γs. A decay-time dependent amplitude analysis is employed. The data sample corresponds to an integrated luminosity of 3 fb−1produced in 7 and 8 TeV pp collisions at the LHC, collected by the LHCb experiment. The measurement determines φs= 119 ±107 ±34 mrad. A combination with previous LHCb measurements using similar decays into the J/ψπ+π−and J/ψφ(1020) final states gives φs= 1 ±37 mrad, consistent with the Standard Model prediction. Keywords: B physics, CP violation, Spectroscopy, Hadron-Hadron scattering (experiments) ArXiv ePrint: 1704.08217 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP08(2017)037 JHEP08(2017)037 Contents 1 Introduction 1 2 Decay rates for B0 sand B0 s→J/ψ K+K−3 3 Detector and simulation 4 4 Event selection and signal yield extraction 5 5 Detector resolution and efficiency 6 6 Flavour tagging 8 7 Resonance contributions 9 8 Maximum likelihood fit 10 9 Systematic uncertainties 12 10 Conclusions 17 A Angular moments 19 The LHCb collaboration 23 1 Introduction Measurements of CP violation through the interference of B0 smixing and decay amplitudes are particularly sensitive to the presence of unseen particles or forces. The Standard Model (SM) prediction of the CP-violating phase in quark-level b→ccs transitions is very small, φSM s≡ −2arg −VtsV∗ tb VcsV∗ cb =−36.5+1.3 −1.2mrad [1]. Although subleading corrections from penguin amplitudes are ignored in this estimate, the interpretation of the current measurements is not affected, since those subleading terms are known to be small [2–4] compared to the experimental precision. Initial measurements of φswere performed at the Tevatron [5,6], followed by LHCb measurements using both B0 sand B0 sdecays1into J/ψπ+π−and J/ψ K+K−, with K+K−invariant masses2mKK <1.05 GeV, from 3 fb−1 of integrated luminosity. The measurements were found to be consistent with the SM value [7,8], as are more recent and somewhat less accurate results from the CMS [9] and 1Whenever a flavour-specific decay is mentioned it also implies use of the charge-conjugate decay except when dealing with CP-violating quantities or other explicitly mentioned cases. 2Natural units are used where ~=c=1. – 1 – JHEP08(2017)037 ATLAS [10] collaborations using J/ψφ(1020) final states.3The average of all of the above mentioned measurements is φs=−30 ±33 mrad [13].4 Previously, using a data sample corresponding to 1 fb−1integrated luminosity, the LHCb collaboration studied the resonant structures in the B0 s→J/ψK+K−decay [14] revealing a rich resonance spectrum in the K+K−mass distribution. In addition to the φ(1020) meson, there are significant contributions from the f0 2(1525) resonance [15] and nonresonant S-wave, which are large enough to allow further studies of CP violation. This paper presents the first measurement of φsusing B0 s→J/ψK+K−decays, where J/ψ → µ+µ−with mKK above the φ(1020) region, using data corresponding to an integrated luminosity of 3 fb−1, obtained from pp collisions at the LHC. One third of the data was collected at a centre-of-mass energy of 7 TeV, and the remainder at 8 TeV. An amplitude analysis as a function of the B0 sproper decay time [16] is performed to determine the CP- violating phase φs, by measuring simultaneously the CP-even and CP-odd decay amplitudes for each contributing resonance (and nonresonant S-wave), allowing the improvement of the φsaccuracy and, in addition, further studies of the resonance composition in the decay. These B0 s→J/ψK+K−decays are separated into two K+K−mass intervals. Those with mKK <1.05 GeV are called low-mass and correspond to the region of the φ(1020) resonance, while those with mKK >1.05 GeV are called high-mass. The high-mass region has not been analyzed for CP violation before, allowing the measurement of CP violation in several decay modes, including a vector-tensor final state, J/ψ f0 2(1525). In the SM the phase φsis expected to be the same in all such modes. One important difference from the previous low-mass analysis [7] is that modelling of the mKK distribution is included to distinguish different resonance and nonresonance contributions. In the previous low mass CP-violation analysis only the φ(1020) resonance and an S-wave amplitude were considered. This analysis follows very closely the analyses of CP violation in B0 s→J/ψπ+π−decays [8] and in B0→J/ψ π+π−decays [3], and only significant changes with respect to those measurements are described in this paper. The analysis strategy is to fit the CP -even and CP-odd components in the decay width probability density functions that describe the interfering amplitudes in the particle and antiparticle decays. These fits are done as functions of the B0 sproper decay time and in a four-dimensional phase space including the three helicity angles characterizing the decay and mKK . Flavour tagging, described below, allows us to distinguish between initial B0 sand B0 sstates. This paper is organized as follows. Section 2describes the B0 sproper-time dependent decay widths. Section 3gives a description of the detector and the associated simulations. Section 4contains the event selection procedure and the extracted signal yields. Section 5 shows the measurement of the proper-time resolution and efficiencies for the final state in the four-dimensional phase space. Section 6summarizes the identification of the initial flavour of the state, a process called flavour tagging. Section 7gives the masses and widths of resonant states that decay into K+K−, and the description of a model-independent S-wave parameterization. Section 8describes the unbinned likelihood fit procedure used 3The final states D+ sD− s[11] and ψ(2S)φ(1020) [12] are also used by LHCb, but the precisions are not comparable due to lower statistics. 4See also updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/. – 2 – JHEP08(2017)037 to determine the physics parameters, and presents the results of the fit, while section 9 discusses the systematic uncertainties. Finally, the results are summarized and combined with other measurements in section 10. 2 Decay rates for B0 sand B0 s→J/ψ K+K− The total decay amplitude for a B0 s(B0 s) meson at decay time equal to zero is taken to be the sum over individual K+K−resonant transversity amplitudes [17], and one nonresonant amplitude, with each component labelled as Ai(Ai). Because of the spin-1 J/ψ in the final state, the three possible polarizations of the J/ψ generate longitudinal (0), parallel (k) and perpendicular (⊥) transversity amplitudes. When the K+K−forms a spin-0 state the final system only has a longitudinal component. Each of these amplitudes is a pure CP eigenstate. By introducing the parameter λi≡q p Ai Ai, relating CP violation in the interference between mixing and decay associated with the state i, the total amplitudes A and Acan be expressed as the sums of the individual B0 samplitudes, A=PAiand A= Pq pAi=PλiAi=Pηi|λi|e−iφi sAi. The quantities qand prelate the mass to the flavour eigenstates [18]. For each transversity state ithe CP-violating phase φi s≡ −arg(ηiλi) [19], with ηibeing the CP eigenvalue of the state. Assuming that any possible CP violation in the decay is the same for all amplitudes, then λ≡ηiλiand φs≡ −arg(λ) are common. The decay rates into the J/ψK+K−final state are5 Γ(t)∝e−Γst|A|2+|A|2 2cosh ∆Γst 2+|A|2−|A|2 2cos(∆mst) − Re(A∗A) sinh ∆Γst 2−Im(A∗A) sin(∆mst),(2.1) Γ(t)∝e−Γst|A|2+|A|2 2cosh ∆Γst 2−|A|2−|A|2 2cos(∆mst) − Re(A∗A) sinh ∆Γst 2+Im(A∗A) sin(∆mst),(2.2) where ∆Γs≡ΓL−ΓHis the decay width difference between the light and the heavy mass eigenstates, ∆ms≡mH−mLis the mass difference, and Γs≡(ΓL+ ΓH)/2 is the average width. The sensitivity to the phase φsis driven by the terms containing A∗A. For J/ψ decays to µ+µ−final states, these amplitudes are themselves functions of four variables: the K+K−invariant mass mKK, and three angular variables Ω ≡ (cos θKK,cos θJ/ψ , χ), defined in the helicity basis. These consist of the angle θKK between the K+direction in the K+K−rest frame with respect to the K+K−direction in the B0 srest frame, the angle θJ/ψ between the µ+direction in the J/ψ rest frame with respect to the J/ψ direction in the B0 srest frame, and the angle χbetween the J/ψ and K+K−decay planes in the B0 srest frame [16,19]. These angles are shown pictorially in figure 1. These definitions are the same for B0 sand B0 s, namely, using µ+and K+to define the angles for both B0 sand B0 sdecays. The explicit forms of |A(mKK,Ω)|2,|A(mKK,Ω)|2, and A∗(mKK,Ω)A(mKK,Ω) in eqs. (2.1) and (2.2) are given in ref. [16]. 5|p/q|= 1 is used. The latest LHCb measurement determined |p/q|2= 1.0039 ±0.0033 [20]. – 3 – JHEP08(2017)037 θJ/ψ µ+µ− K+K− θKK y χ x z K− µ− µ+ B0 s K+ Figure 1. Definition of the helicity angles. 3 Detector and simulation The LHCb detector [21,22] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor 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 with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV. The primary vertex (PV) is constructed from reconstructed tracks that arise from a common origin [23]. The minimum distance of a track to a PV, the impact parameter (IP), is measured with a resolution of (15 + 29/pT)µm, where pTis the component of the momentum transverse to the beam, in GeV. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov (RICH) detectors. Photons, electrons and hadrons 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 is performed by a trigger, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. The software trigger is composed of two stages, the first of which performs a partial reconstruction and requires either a pair of well-reconstructed, oppositely charged muons having an invariant mass above 2.7 GeV, or a single well-reconstructed muon with high pTand large IP. The second stage applies a full event reconstruction and for this analysis requires two opposite-sign muons to form a good-quality vertex that is well separated from all of the PVs, and to have an invariant mass within ±120 MeV of the known J/ψ mass [24]. In the simulation, pp collisions are generated using Pythia 8 [25,26]. Decays of hadronic particles are described by EvtGen [27], in which final-state radiation is generated using Photos [28]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [29,30] as described in ref. [31]. The simulation covers the full K+K−mass range. – 4 – JHEP08(2017)037 4 Event selection and signal yield extraction AB0 scandidate is reconstructed by combining a J/ψ →µ+µ−candidate with two kaons of opposite charge. The offline selection uses a loose preselection, followed by a multivariate classifier based on a Gradient Boosted Decision Tree (BDTG) [32]. In the preselection, the J/ψ candidates are formed from two oppositely charged particles with pTgreater than 550 MeV, identified as muons and consistent with originating from a common vertex but inconsistent with originating from any PV. The invariant mass of the µ+µ−pair is required to be within [−48,+43] MeV of the known J/ψ mass [24], corresponding to a window of about ±3 times the mass resolution. The asymmetry in the cut values is due to the radiative tail. The two muons are subsequently kinematically constrained to the known J/ψ mass. Kaon candidates are required to be positively identified in the RICH detectors, to have pTgreater than 250 MeV, and the scalar sum of the two transverse momenta, pT(K+) + pT(K−), must be larger than 900 MeV. The four tracks from a B0 scandidate decay must originate from a common vertex with a good fit χ2and have a decay time greater than 0.3 ps. Each B0 scandidate is assigned to a PV for which it has the smallest χ2 IP, defined as the difference in the χ2of the vertex fit for a given PV reconstructed with and without the considered particle. The angle between the momentum vector of the B0 sdecay candidates and the vector formed from the positions of the PV and the decay vertex (pointing angle) is required to be less than 2.5◦. Events are filtered with a BDTG to further suppress the combinatorial background. The BDTG uses six variables: pT(K+) + pT(K−); the vertex-fit χ2, pointing angle, χ2 IP, and pTof the B0 scandidates; and the smaller of the DLL(µ−π) for the two muons, where DLL(µ−π) is the difference in the logarithms of the likelihood values from the particle identification systems [33] for the muon and pion hypotheses. The BDTG is trained on a simulated sample of 0.7 million reconstructed B0 s→J/ψK+K−signal events, with the final-state particles generated uniformly in phase space assuming unpolarized J/ψ →µ+µ− decays, and a background data sample from the sideband 5516 < m(J/ψK+K−)< 5616 MeV. Separate samples are used to train and test the BDTG. The BDTG and particle identification (PID) requirements for the kaons are chosen to maximize the signal significance multiplied by the square root of the purity, S/√S+B×pS/(S+B), for candidates with mKK >1.05 GeV, where Sand Bare the numbers of signal and background candidate combinations, respectively. This figure of merit optimizes the total uncertainty including both statistical and background systematic errors. In addition to the expected combinatorial background, studies of the data in sidebands of the m(J/ψ K+K−) spectrum show contributions from approximately 8700 (430) B0→J/ψK−π+and 10 700 (800) Λ0 b→J/ψpK−decays at mKK greater (less) than 1.05 GeV, where the π+in the former or pin the latter is misidentified as a K+. In order to avoid dealing with correlations between the angular variables and m(J/ψK+K−), the contributions from these reflection backgrounds are statistically subtracted by adding to the data simulated events of these decays with negative weights. These weights are chosen so that the distributions of the relevant variables used in the overall fit (see below) describe the background distributions both in normalization and shapes. The simulation uses amplitude models derived from data for B0→J/ψK−π+[34] and Λ0 b→J/ψpK−decays [35]. – 5 – JHEP08(2017)037 ) [MeV] − K + Kψm(J/ 5300 5350 5400 5450 Combinations / (2 MeV) 0 1000 2000 3000 4000 5000 6000 7000 LHCb < 1.05 GeV KK (a) m ) [MeV] − K + Kψm(J/ 5300 5350 5400 5450 Combinations / (2 MeV) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 LHCb > 1.05 GeV KK (b) m Figure 2. Fits to invariant mass distributions of J/ψ K+K−combinations after subtraction of the two reflection backgrounds for (a) mKK <1.05 GeV and (b) mKK >1.05 GeV. Total fits are shown by solid (blue) lines, the signal by dashed (black) lines, and the combinatorial background by darkened regions. Note that the combinatorial background in (a) is too small to be easily visible. The invariant mass of the selected J/ψK+K−combinations, separated into samples for mKK below or above 1.05 GeV, are shown in figure 2, where the expected reflection backgrounds are subtracted using simulation. The combinatorial background is modelled with an exponential function and the B0 ssignal shape is parameterized by a double-sided Hypatia function [36], where the signal radiative tail parameters are fixed to values obtained from simulation. In total, 53 440 ±240 and 33 200±240 signal candidates are found for the low and high mKK intervals, respectively. Figure 3shows the Dalitz plot distribution of m2 K+K−versus m2 J/ψ K+for B0 s→J/ψK+K−candidates within ±15 MeV of the B0 smass peak. Clear resonant contributions from φ(1020) and f0 2(1525) mesons are seen, but no exotic J/ψK+resonance is observed. 5 Detector resolution and efficiency The resolution on the decay time is determined with the same method as described in ref. [7] by using a large sample of prompt J/ψ K+K−combinations produced directly in the pp interactions. These events are selected using J/ψ →µ+µ−decays via a prescaled trigger that does not impose any requirements on the separation of the J/ψ from the PV. The J/ψ candidates are combined with two oppositely charged tracks that are identified as kaons, using a similar selection as for the signal decay, without a decay-time requirement. The resolution function, T(t−ˆ t|δt), where ˆ tis the true decay time, is a sum of three Gaussian functions with a common mean, and separate widths. To implement the resolution model each of the three widths are given by Si·(δt+σ0 t), where Siis scale factor for the ith Gaussian, δtis an estimated per-candidate decay-time error and σ0 tis a constant parameter. The parameters of the resolution model are determined by using a maximum likelihood fit to the unbinned decay time and δtdistributions of the prompt J/ψ K+K−combinations, using a δfunction to represent the prompt component summed with two exponential functions for long-lived backgrounds; these are convolved with the resolution function. Taking into account the δt distribution of the B0 ssignal, the average effective resolution is found to be 44.7 fs. – 6 – JHEP08(2017)037 ] 2 [GeV + KψJ/ 2 m 15 20 ] 2 [GeV − K + K 2 m 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 LHCb Figure 3. Invariant mass squared of K+K−versus J/ψ K+for B0 s→J/ψ K+K−candidates within ±15 MeV of the B0 smass peak. The high intensity φ(1020) resonance band is shown with a line (light green). The reconstruction efficiency is not constant as a function of decay time due to displacement requirements made on the J/ψ candidates in the trigger and offline selections. The efficiency is determined using the control channel B0→J/ψ K∗(892)0, with K∗(892)0→K+π−, which is known to have a purely exponential decay-time distribution with τB0= 1.520 ±0.004 ps [24]. The selection efficiency is calculated as εB0 s data(t) = εB0 data(t)×εB0 s sim(t) εB0 sim(t),(5.1) where εB0 data(t) is the efficiency of the control channel and εB0 s sim(t)/εB0 sim(t) is the ratio of efficiencies of the simulated signal and control mode after the full trigger and selection chain has been applied. This correction accounts for the small differences in the kinematics between the signal and control mode. The details of the method are explained in ref. [8]. The decay-time efficiencies for the two mKK intervals are shown in figure 4. The efficiency as a function of the B0 s→J/ψK+K−helicity angles and the K+K− invariant mass is not uniform due to the forward geometry of the LHCb detector and the requirements imposed on the final-state particle momenta. The four-dimensional efficiency, ε(mKK,Ω), is determined using simulated events that are subjected to the same trigger and selection criteria as the data. The efficiency is parameterized by (mKK,Ω) = X a,b,c,d abcdPa(cos θKK )Ybc(θJ/ψ , χ)Pd2mKK −mmin KK mmax KK −mmin KK −1,(5.2) – 7 – JHEP08(2017)037 Decay time [ps] 0 5 10 Efficiency (a.u.) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 LHCb < 1.05 GeV KK (a) m Decay time [ps] 0 5 10 Efficiency (a.u.) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 LHCb > 1.05 GeV KK (b) m Figure 4. Scaled decay-time efficiency εB0 s data(t) in arbitrary units (a.u.) for (a) the φ(1020) region and (b) the high-mass region. where Paand Pdare Legendre polynomials, Ybc are spherical harmonics, and mmin KK = 2mK+and mmax KK =mB0 s−mJ/ψ are the minimum and maximum allowed values for mKK, respectively. The Ybc are complex functions. To ensure that the efficiency function is real, we set abcd =−ab(−c)d. The values of abcd are determined by summing over the fully simulated phase-space events abcd =1 PiwiX i wi 2a+ 1 2 2d+ 1 2Pa(cos θKK,i)Y∗ bc(θJ/ψ,i, χi)Pd 2mKK,i −mmin KK mmax KK −mmin KK −1!1 gi , (5.3) where the weights wiaccount for corrections of PID and tracking efficiencies, and gi= Pi RPi Bis the value of the phase-space probability density for event iwith PRbeing the momentum of either of the two hadrons in the dihadron rest frame and PBthe momentum of the J/ψ in the B0 srest frame. This approach allows the description of multidimensional correlations without assuming factorization. In practice, the sum is over a finite number of terms (a≤10, b≤8, −2≤c≤2, d≤8) and only coefficients with a statistical significance larger than three standard deviations (σ) from zero are retained. The number of events in the simulated signal sample is about 20 times of that observed in data. Since a symmetric K+and K−efficiency is used, aand b+cmust be even numbers. Projections of the efficiency integrated over other variables are shown in figure 5. The modelling functions describe well the simulated data. Since χ2 IP is not used as a variable in the selection for the two hadrons, the efficiency is quite uniform over all the four variables varying only by about ±10%. (A dedicated simulation of J/ψφ(1020) decays is used to determine the efficiency in the region of mKK <1.05 GeV, in order to have a large enough sample for an accurate determination.) 6 Flavour tagging The B0 scandidate flavour at production is determined using two independent classes of flavour-tagging algorithms, the opposite-side (OS) tagger [37] and the same-side kaon (SSK) tagger [38], which exploit specific features of the production of bb quark pairs in pp collisions, and their subsequent hadronisation. Each tagging algorithm provides a tag decision and – 8 – JHEP08(2017)037 Yields / (15 MeV) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 LHCb [GeV] K + K m 1 1.5 2 5− 0 5 − data Fit (1020)φ S-wave (1525) 2 f' (1680)φ (1270) 2 f (1750) 2 f (1950) 2 f Figure 7. Fit projection of mKK . The points represent the data; the resonances φ(1020), f0 2(1525), φ(1680) are shown by magenta, brown, and cyan long-dashed curves, respectively; the S-wave component is depicted by green long-dashed curves; the other f2resonances are described by black solid curves; and the total fit by a blue solid curve. At the bottom the differences between the data and the fit divided by the uncertainty in the data are shown. Source ∆ΓsΓs|λ|M0Γ0φs ×10−3[ ps−1] [ ps−1] [ GeV ] [ GeV ] [rad] Resonance modelling 6.9 1.9 5.5 1.1 3.6 23.6 Efficiency (mKK, Ω) 3.0 0.9 0.5 0.1 0.7 3.4 Efficiency t2.2 2.8 0.0 0.0 0.0 0.0 τB01.4 2.0 0.0 0.0 0.0 0.0 tresolution 0.3 0.2 0.2 0.0 0.0 1.1 Fit bias 5.0 1.1 - - - - AP0.1 0.3 1.4 0.0 0.0 4.0 Tagging 1.2 0.3 0.8 0.0 0.0 11.2 Background 0.5 0.8 0.4 0.1 0.1 1.5 sWeights1.1 0.1 0.5 0.1 0.4 21.4 B+ c- 0.5 - - - - Total syst. 9.6 4.3 5.7 1.1 3.7 34.2 Stat. 17.7 5.5 18.0 1.3 3.0 106.6 Table 5. Absolute systematic uncertainties for the physics parameters determined from the high mKK region compared to the corresponding statistical uncertainty. Here M0and Γ0refer to the uncertainties on the f0 2(1525) resonance mass and width. – 15 – JHEP08(2017)037 Source φ(1020) S-wave f0 2(1525) φ(1680) f2(1270) f2(1750) f2(1950) Res. modelling 0.99 0.57 0.73 0.27 0.21 0.21 0.13 Efficiency 0.58 0.06 0.48 0.12 0.04 0.03 0.01 Background 0.06 0.01 0.06 0.02 0.02 0.01 0.00 sWeights0.11 0.02 0.16 0.05 0.02 0.05 0.04 Total syst. 1.15 0.57 0.89 0.30 0.21 0.21 0.14 Statistical 0.62 0.12 0.67 0.32 0.27 +0.23 −0.16 +0.15 −0.10 Table 6. Combined systematic and statistical uncertainties in the fit fractions using an absolute scale where the numbers are in units of %. “Res. modelling” refers to resonance modelling. for B0 sdecays. The former is estimated by repeating the fit to the data 100 times. In each fit, the efficiency parameters are resampled according to the corresponding covariance matrix determined from simulation. For the latter, the efficiency used by the nominal fit is obtained by weighting the distributions of pand pTof the kaon pair and B0 smeson to match the data. Such weighting is removed to assign the corresponding systematic uncertainty. The uncertainties due to the B0lifetime and decay time efficiency determination are estimated. Each source is evaluated by adding to the nominal fit an external correlated multidimensional Gaussian constraint, either given by the fit to the B0→J/ψK∗0sample with varying τB0= 1.520±0.004 ps [24], or given by the fit to simulation for the decay time efficiency correction, i.e. εB0 s sim(t)/εB0 sim(t) in eq. (5.1). A systematic uncertainty is given by the difference in quadrature of the statistical uncertainties for each physics parameter between the nominal fit and the alternative fit with each of these constraints. The uncertainties due to the decay time acceptance are found to be negligible for the fit fraction results. The sample of prompt J/ψ mesons combined with two kaon candidates is used to calibrate the per-candidate decay-time error. This method is validated by simulation. Since the detached selection, pointing angle and BDTG requirements cannot be applied to the calibration sample, the simulations show that the calibration overestimates the resolution for B0 sdecays after final selection by about 4.5%. Therefore, a 5% variation of the widths, and the uncertainty of the mean value are used to estimate uncertainty of the time resolution modelling. The average angular resolution is 6 mrad for all three decay angles. This is small enough to have only negligible effects on the analysis. A large number of pseudoexperiments is used to validate the fitter and check potential biases in the fit outputs. Biases on Γsand ∆Γs, 20% of their statistical uncertainties, are taken as systematic uncertainties. Calibration parameters of the flavour-tagging algorithm and the B0 s–B0 sproduction asymmetry AP= (1.09 ±2.69)% [44] are fixed. The systematic uncertainties due to the calibration of the tagging parameters or the value of APare given by the difference in quadrature between the statistical uncertainty for each physics parameter between the nominal fit and an alternative fit where the tagging parameters or APare Gaussian-constrained by the corresponding uncertainties. Background sources are tested by varying the decay-time acceptance of the injected reflection backgrounds, changing these background yields by 5%, and also varying the Λ0 blifetime. – 16 – JHEP08(2017)037 Γs∆Γsφs|λ| Γs+1.00 +0.54 +0.02 −0.03 ∆Γs+1.00 +0.04 −0.06 φs+1.00 −0.14 |λ|+1.00 Table 7. The correlation matrix from the high-mass region fit, taking into account both statistical and systematic uncertainties. Γs∆Γsφs|λ| Γs+1.00 −0.13 −0.01 0.00 ∆Γs+1.00 −0.05 0.00 φs+1.00 −0.04 |λ|+1.00 Table 8. The correlation matrix taking into account both statistical and systematic uncertainties for the combination of the three measurements B0 s→J/ψ K+K−for mKK >1.05 GeV, mKK < 1.05 GeV, and J/ψπ+π−. To evaluate the uncertainty of the sPlot method that requires the fit observables being uncorrelated with the variable m(J/ψK+K−) used to obtain the sWeights, two variations are performed to obtain new sWeights, and the fit is repeated. The first consists of changing the number of |cos θJ/ψ |bins. In the nominal fit, the sWeights are determined by separate fits in four |cos θJ/ψ |bins for the event candidates, as significant variations of signal invariant mass resolution are seen as a function of the variable. In another variation of the analysis starting with the nominal number of |cos θJ/ψ |bins the decay time dependence is explored, since the combinatorial background may have a possible variation as a function of m(J/ψK+K−). Here the decay time is further divided into three intervals. The larger change on the physics parameter of interest is taken as a systematic uncertainty. About 0.8% of the signal sample is expected from the decays of B+ cmesons [48]. Neglecting the B+ ccontribution in the nominal fit leads to a negligible bias of 0.0005 ps−1 for Γs[7]. The correlation matrix with both statistical and systematic uncertainties is shown in table 7. 10 Conclusions We have studied B0 sand B0 sdecays into the J/ψ K+K−final state using a time-dependent amplitude analysis. In the mKK >1.05 GeV region we determine φs= 119 ±107 ±34 mrad, |λ|= 0.994 ±0.018 ±0.006, Γs= 0.650 ±0.006 ±0.004 ps−1, ∆Γs= 0.066 ±0.018 ±0.010 ps−1. – 17 – JHEP08(2017)037 Many resonances and a S-wave structure have been found. Besides the φ(1020) meson these include the f2(1270), the f0 2(1525), the φ(1680), the f2(1750), and the f2(1950) mesons. The presence of the f2(1640) resonance is not confirmed. The measured CP- violating parameters of the individual resonances are consistent. The f0 2(1525) mass and width are determined as 1522.2±1.3±1.1 MeV and 78.0±3.0±3.7 MeV, respectively. The fit fractions of the resonances in B0 s→J/ψK+K−are also determined, and shown in table 3. These results supersede our previous measurements [14]. The combination with the previous results from B0 sdecays in the φ(1020) region [7] gives φs=−25 ±45 ±8 mrad, |λ|= 0.978 ±0.013 ±0.003, Γs= 0.6588 ±0.0022 ±0.0015 ps−1, ∆Γs= 0.0813 ±0.0073 ±0.0036 ps−1. The two results are consistent within 1.1σ. A further combination is performed by including the φsand |λ|measurements from B0 sand B0 sdecays into J/ψ π+π−[8], which results in φs= 1±37 mrad and |λ|= 0.973±0.013, where Γsand ∆Γsare unchanged. The correlation matrix is shown in table 8. The measurement of the CP-violating phase φsis in agreement with the SM prediction −36.5+1.3 −1.2mrad [1]. These new combined results supersede our combination reported in ref. [7]. Acknowledgments 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, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.A.). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (U.S.A.). We are indebted to the communities behind the multiple open source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany), EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union), Conseil G´en´eral de Haute-Savoie, Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom). – 18 – JHEP08(2017)037 ) [GeV] − K + m(K 1 1.02 1.04 Combinations/ (1 MeV) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 > 0 0 <Y LHCb ) [GeV] − K + m(K 1 1.02 1.04 Combinations/ (1 MeV) 0 100 200 300 400 500 > 0 2 <Y LHCb ) [GeV] − K + m(K 1 1.02 1.04 Combinations/ (1 MeV) 40− 20− 0 20 40 60 > 0 4 <Y LHCb Figure 8. The K+K−mass dependence of the spherical harmonic moments of cos θKK in the region of the φ(1020) resonance after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. ) [GeV] - K + m(K 1.5 2 Combinations/ (20 MeV) 0 100 200 300 400 500 600 > 0 0 <Y LHCb ) [GeV] - K + m(K 1.5 2 Combinations/ (20 MeV) 50− 0 50 100 150 200 > 0 2 <Y LHCb ) [GeV] - K + m(K 1.5 2 Combinations/ (20 MeV) 20− 0 20 40 60 80 100 120 > 0 4 <Y LHCb Figure 9. The K+K−mass dependence of the spherical harmonic moments of cos θKK above the φ(1020) resonance region after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. A Angular moments We define the moments hY0 `i, as the efficiency-corrected and background-subtracted K+K− invariant mass distributions, weighted by the `th spherical harmonic functions of the cosine of the helicity angle θKK. The moment distributions provide an additional way of visualizing the presence of different resonances and their interferences, similar to a partial wave analysis. Figures 8and 9show the distributions of the even angular moments for the events around ±30 MeV of φ(1020) mass peak and those above the φ(1020), respectively. The general interpretation of the even moments is that hY0 0iis the efficiency-corrected and background-subtracted event distribution, hY0 2ireflects the sum of P-wave, D-wave and the interference of S-wave and D-wave amplitudes, and hY0 4ithe D-wave. The average of B0 sand B0 sdecays cancels the interference terms that involve P-wave amplitudes. This causes the odd moments to sum to zero. The fit results reproduce the moment distributions relatively well. For the region near the φ(1020), the p-values are 3%, 3%, 48% for the `=0, 2, 4 moments, respectively. For the high mass region, the p-values are 37%, 0.2% 0.5% for the `=0, 2, 4 moments, respectively. Open Access. 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Poli Lener19, A. Poluektov50,36, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce40, A. Popov37, D. Popov11,40, B. Popovici30, S. Poslavskii37, C. Potterat2, E. Price48, J. Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig Navarro42, G. Punzi24,p, C. Qian63, W. Qian50, R. Quagliani7,48, B. Rachwal28, J.H. Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F. Ratnikov35, G. Raven44, F. Redi55, S. Reichert10, A.C. dos Reis1, C. Remon Alepuz69, V. Renaudin7, S. Ricciardi51, S. Richards48, M. Rihl40, K. Rinnert54, V. Rives Molina38, P. Robbe7, A.B. Rodrigues1, E. Rodrigues59, J.A. Rodriguez Lopez66, – 24 –