Measurement of the CP-violating phase phi_s in the decay Bs->J/psi phi

We present a measurement of the time-dependent CP-violating asymmetry in B_s ->J/psi phi decays, using data collected with the LHCb detector at the LHC. The decay time distribution of B_s ->J/psi phi is characterized by the decay widths Gamma_H and Gamma_L of the heavy and light mass eigenstates of the B_s-B_s-bar system and by a CP-violating phase phi_s. In a sample of about 8500 B_s ->J/psi phi events isolated from 0.37 fb^-1 of pp collisions at sqrt(s)=7 TeV we measure phi_s = 0.15 +/- 0.18 (stat) +/- 0.06 (syst) rad. We also find an average B_s decay width Gamma_s == (Gamma_L + Gamma_H)/2 = 0.657 +/- 0.009 (stat) +/- 0.008 (syst) ps^-1 and a decay width difference Delta Gamma_s == Gamma_L - Gamma_H} = 0.123 +/- 0.029 (stat) +/- 0.011 (syst) ps^-1. Our measurement is insensitive to the transformation (phi_s,DeltaGamma_s -->pi - phi_s, - Delta Gamma_s.


To be submitted to Physical Review Letters
In the Standard Model (SM) CP violation arises through a single phase in the CKM quark mixing matrix [1].In neutral B meson decays to a final state which is accessible to both B and B mesons, the interference between the amplitude for the direct decay and the amplitude for decay after oscillation, leads to a time-dependent CP -violating asymmetry between the decay time distributions of B and B mesons.The decay B 0 s → J/ψ φ allows the measurement of such an asymmetry, which can be expressed in terms of the decay width difference of the heavy (H) and light (L) B 0 s mass eigenstates ∆Γ s ≡ Γ L − Γ H and a single phase φ s [2].In the SM, the decay width difference is ∆Γ SM s = 0.087 ± 0.021 ps −1 [3], while the phase is predicted to be small, [4].This value ignores a possible contribution from subleading decay amplitudes [5].Contributions from physics beyond the SM could lead to much larger values of φ s [6].
In this Letter we present measurements of φ s , ∆Γ s and the average decay width Γ s ≡ (Γ L + Γ H )/2. Previous measurements of these quantities have been reported by the CDF and DØ collaborations [7].We use an integrated luminosity of 0.37 fb −1 of pp collision data recorded at a centre-of-mass energy √ s = 7 TeV by the LHCb experiment during the first half of 2011.The LHCb detector is a forward spectrometer at the Large Hadron Collider and is described in detail in Ref. [8].
We look for B 0 s → J/ψ φ candidates in decays to J/ψ → µ + µ − and φ → K + K − .Events are selected by a trigger system consisting of a hardware trigger, which selects muon or hadron candidates with high transverse momentum with respect to the beam direction (p T ), followed by a two stage software trigger.In the first stage a simplified event reconstruction is applied.Events are required to either have two well-identified muons with invariant mass above 2.7 GeV, or at least one muon or one high-p T track with a large impact parameter to any primary vertex.In the second stage a full event reconstruction is performed and only events with a muon candidate pair with invariant mass within 120 MeV of the nominal J/ψ mass [9] are retained.We adopt units such that c = 1 and = 1.
For the final event selection muon candidates are required to have p T > 0.5 GeV.J/ψ candidates are cre-ated from pairs of oppositely charged muons that have a common vertex and an invariant mass in the range 3030 − 3150 MeV.The latter corresponds to about eight times the µ + µ − invariant mass resolution and covers part of the J/ψ radiative tail.The φ selection requires two oppositely charged particles that are identified as kaons, form a common vertex and have an invariant mass within ±12 MeV of the nominal φ mass [9].The p T of the φ candidate is required to exceed 1 GeV.The mass window covers approximately 90% of the φ → K + K − lineshape.
We select B 0 s candidates from combinations of a J/ψ and a φ with invariant mass m B in the range 5200 − 5550 MeV.The latter is computed with the invariant mass of the µ + µ − pair constrained to the nominal J/ψ mass.The decay time t of the B 0 s is obtained from a vertex fit that constrains the B 0 s → µ + µ − K + K − candidate to originate from the primary vertex [10].The χ 2 of the fit, which has 7 degrees of freedom, is required to be less than 35.In the small fraction of events with more than one candidate, only the candidate with the smallest χ 2 is kept.B 0 s candidates are required to have a decay time within the range 0.3 < t < 14.0 ps.Applying a lower bound on the decay time suppresses a large fraction of the prompt combinatorial background whilst having a small effect on the sensitivity to φ s .From a fit to the m B distribution, shown in Fig. 1, we extract a signal of 8492 ± 97 events.The B 0 s → J/ψ φ → µ + µ − K + K − decay proceeds via two intermediate spin-1 particles (i.e. with the K + K − pair in a P-wave).The final state can be CP -even or CP -odd depending upon the relative orbital angular momentum between the J/ψ and the φ.The same final state can also be produced with K + K − pairs with zero relative orbital angular momentum (S-wave) [11] .This S-wave final state is CP -odd.In order to measure φ s it is necessary to disentangle the CP -even and CP -odd components.This is achieved by analysing the distribution of the reconstructed decay angles Ω = (θ, ψ, ϕ) in the transversity basis [12,13].In the J/ψ rest frame we define a right-handed coordinate system such that the x axis is parallel to the direction of the φ momentum and the z axis is parallel to the cross-product of the K − and K + momenta.In this frame θ and ϕ are the azimuthal and polar angles of the µ + .The angle ψ is the angle between the K − momentum and the J/ψ momentum in the rest frame of the φ.
We perform an unbinned maximum likelihood fit to the invariant mass m B , the decay time t, and the three decay angles Ω.The probability density function (PDF) used in the fit consists of signal and background components which include detector resolution and acceptance effects.The PDFs are factorised into separate components for the mass and for the remaining observables.
The signal m B distribution is described by two Gaussian functions with a common mean.The mean and width of the narrow Gaussian are fit parameters.The fraction of the second Gaussian and its width relative to the narrow Gaussian are fixed to values obtained from simulated events.The m B distribution for the combinatorial background is described by an exponential function with a slope determined by the fit.Possible peaking background from decays with similar final states such as B 0 → J/ψ K * 0 is found to be negligible from studies using simulated events.
The distribution of the signal decay time and angles is described by a sum of ten terms, corresponding to the four polarization amplitudes and their interference terms.Each of these is the product of a time-dependent function and an angular function [12] The time-dependent functions h k (t) can be written as where ∆m s is the B 0 s oscillation frequency.The coefficients N k and a k , . . ., d k can be expressed in terms of φ s and four complex transversity amplitudes A i at t = 0.The label i takes the values {⊥, , 0} for the three Pwave amplitudes and S for the S-wave amplitude.In the fit we parameterize each A i (0) by its magnitude squared |A i (0)| 2 and its phase δ i , and adopt the convention δ 0 = 0 and |A i (0)| 2 = 1.For a particle produced in a B 0 s flavour eigenstate the coefficients in Eq. 2 and the angular functions f k (Ω) are then, see [13,14], given by We neglect CP violation in mixing and in the decay amplitudes.The differential decay rates for a B 0 s meson produced at time t = 0 are obtained by changing the sign of φ s , A ⊥ (0) and A S (0), or, equivalently, the sign of c k and d k in the expressions above.The PDF is invariant under the transformation (φ s , ∆Γ s , δ , δ ⊥ , δ S ) → (π − φ s , −∆Γ s , −δ , π − δ ⊥ , −δ S ) which gives rise to a two-fold ambiguity in the results.
We have verified that correlations between decay time and decay angles in the background are small enough to be ignored.Using the data in the m B sidebands, which we define as selected events with m B outside the range 5311 − 5411 MeV, we determine that the background decay time distribution can be modelled by a sum of two exponential functions.The lifetime parameters and the relative fraction are determined by the fit.The decay angle distribution is modelled using a histogram obtained from the data in the m B sidebands.The normalisation of the background with respect to the signal is determined by the fit.
The measurement of φ s requires knowledge of the flavour of the B 0 s meson at production.We exploit the following flavour specific features of the accompanying (non-signal) b-hadron decay to tag the B 0 s flavour: the charge of a muon or an electron with large transverse momentum produced by semileptonic decays, the charge of a kaon from a subsequent charmed hadron decay and the momentum-weighted charge of all tracks included in the inclusively reconstructed decay vertex.These signatures are combined using a neural network to estimate a perevent mistag probability, ω, which is calibrated with data from control channels [15].The fraction of tagged events in the signal sample is ε tag = (24.9± 0.5)%.The dilution of the CP asymmetry due to the mistag probability is D = 1 − 2ω.The effective dilution in our signal sample is D = 0.277 ± 0.006 (stat) ± 0.016 (syst), resulting in an effective tagging efficiency of ε tag D 2 = (1.91 ± 0.23)%.The uncertainty in ω is taken into account by allowing calibration parameters described in Ref. [15] to vary in the fit with Gaussian constraints given by their estimated uncertainties.Both tagged and untagged events are used in the fit.The untagged events dominate the sensitivity to the lifetimes and amplitudes.
To account for the decay time resolution, the PDF is convolved with a sum of three Gaussian functions with a common mean and different widths.Studies on simulated data have shown that selected prompt J/ψ K + K − combinations have nearly identical resolution to signal events.Consequently, we determine the parameters of the resolution model from a fit to the decay time distribution of such prompt combinations in the data, after subtracting non-J/ψ events with the sPlot method [16] using the µ + µ − invariant mass as discriminating variable.The resulting dilution is equivalent to that of a single Gaussian with a width of 50 fs.The uncertainty on the decay time resolution is estimated to be 4% by varying the selection of events and by comparing in the simulation the resolutions obtained for prompt combinations and B 0 s signal events.This uncertainty is accounted for by scaling the widths of the three Gaussians by a common factor of 1.00 ± 0.04, which is varied in the fit subject to a Gaussian constraint.In similar fashion the uncertainty on the mixing frequency is taken into account by varying it within the constraint imposed by the LHCb measurement ∆m s = 17.63 ± 0.11 (stat) ± 0.02 (syst) ps −1 [17].
The decay time distribution is affected by two acceptance effects.First, the efficiency decreases approximately linearly with decay time due to inefficiencies in the reconstruction of tracks far from the central axis of the detector.This effect is parameterized as (t) ∝ (1 − βt) where the factor β = 0.016 ps −1 is determined from simulated events.Second, a fraction of approximately 14% of the events has been selected exclusively by a trigger path that exploits large impact parameters of the decay products, leading to a drop in efficiency at small decay times.This effect is described by the empirical acceptance function (t) ∝ (at) c / [1 + (at) c ], applied only to these events.The parameters a and c are determined in the fit.As a result, the events selected with impact parameter cuts do effectively not contribute to the measurement of Γ s .
The uncertainty on the reconstructed decay angles is small and is neglected in the fit.The decay angle acceptance is determined using simulated events.The deviation from a flat acceptance is due to the LHCb forward geometry and selection requirements on the momenta of final state particles.The acceptance varies by less than 5% over the full range for all three angles.
The results of the fit for the main observables are shown in Table I.The likelihood profile for δ is not parabolic and we therefore quote the 68% confidence level (CL) range 3.0 < δ < 3.5.The correlation coefficients for the statistical uncertainties are ρ(Γ s , ∆Γ s ) = −0.30,ρ(Γ s , φ s ) = 0.12 and ρ(∆Γ s , φ s ) = −0.08. Figure 2 shows the data distribution for decay time and angles with the projections of the best fit PDF overlaid.To assess the overall agreement of the PDF with the data we calculate the goodness of fit based on the point-to-point dissimilarity test [18].The p-value obtained is 0.68. Figure 3 shows the 68%, 90% and 95% CL contours in the ∆Γ s -φ s plane.These contours are obtained from the likelihood profile after including systematic uncertainties, and correspond to decreases in the natural logarithm of the likelihood, with respect to its maximum, of 1.15, 2.30 and 3.00 respectively.s mass.The points are the data.The dashed, dotted and solid lines represent the fitted contributions from signal, background and their sum.The remaining curves correspond to different contributions to the signal, namely the CP -even P-wave (dashed with single dot), the CP -odd P-wave (dashed with double dot) and the S-wave (dashed with triple dot).
The sensitivity to φ s stems mainly from its appearance as the amplitude of the sin(∆m s t) term in Eq. 1, which is diluted by the decay time resolution and mistag probability.Systematic uncertainties from these sources and from the mixing frequency are absorbed in the statistical uncertainties as explained above.Other systematic uncertainties are determined as follows, and added in quadrature to give the values shown in Table I.
To test our understanding of the decay angle acceptance we compare the rapidity and momentum distributions of the kaons and muons of selected B 0 s candidates in data and simulated events.Only in the kaon momentum distribution do we observe a significant discrepancy.We reweight the simulated events to match the data, rederive the acceptance corrections and assign the resulting difference in the fit result as a systematic uncertainty.This is the dominant contribution to the systematic uncertainty on all parameters except Γ s .The limited size of the simulated event sample leads to a small additional uncertainty.The systematic uncertainty due to the background decay angle modelling was found to be negligible by comparing with a fit where the background was removed statistically using the sPlot method [16].
In the fit each |A i (0)| 2 is constrained to be greater than zero, while their sum is constrained to unity.This can result in a bias if one or more of the amplitudes is small.This is the case for the S-wave amplitude, which is compatible with zero within 3.2 standard deviations.The resulting biases on the |A i (0)| 2 have been determined using simulations to be less than 0.010 and are included The black square and error bar corresponds to the Standard Model prediction [3,4].
as systematic uncertainties.Finally, a systematic uncertainty of 0.008 ps −1 was assigned to the measurement of Γ s due to the uncertainty in the decay time acceptance parameter β.Other systematic uncertainties, such as those from the momentum scale and length scale of the detector, were found to be negligible.
In summary, in a sample of 0.37 fb −1 of pp collisions at √ s = 7 TeV collected with the LHCb detector we observe 8492 ± 97 B 0 s → J/ψ K + K − events with K + K − invariant mass within ± 12 MeV of the φ mass.With these data we perform the most precise measurements of φ s , ∆Γ s and Γ s in B 0 s → J/ψ φ decays, substantially improving upon previous measurements [7] and providing the first direct evidence for a non-zero value of ∆Γ s .Two solutions with equal likelihood are obtained, related by the transformation (φ s , ∆Γ s ) → (π − φ s , −∆Γ s ).The solution with positive ∆Γ s is φ s = 0.15 ± 0.18 (stat) ± 0.06 (syst) rad, Γ s = 0.657 ± 0.009 (stat) ± 0.008 (syst) ps −1 , ∆Γ s = 0.123 ± 0.029 (stat) ± 0.011 (syst) ps −1 , and is in agreement with the Standard Model prediction [3,4].Values of φ s in the range 0.52 < φ s < 2.62 and −2.93 < φ s < −0.21 are excluded at 95% confidence level.In a future publication we shall differentiate between the two solutions by exploiting the dependence of the phase difference between the P-wave and S-wave contributions on the K + K − invariant mass [14].

FIG. 1 .
FIG. 1. Invariant mass distribution for B 0s → µ + µ − K + K − candidates with the mass of the µ + µ − pair constrained to the nominal J/ψ mass.Curves for fitted contributions from signal (dashed), background (dotted) and their sum (solid) are overlaid.

FIG. 2 .
FIG.2.Projections for the decay time and transversity angle distributions for events with mB in a ± 20 MeV range around the B 0 s mass.The points are the data.The dashed, dotted and solid lines represent the fitted contributions from signal, background and their sum.The remaining curves correspond to different contributions to the signal, namely the CP -even P-wave (dashed with single dot), the CP -odd P-wave (dashed with double dot) and the S-wave (dashed with triple dot).

FIG. 3 .
FIG.3.Likelihood confidence regions in the ∆Γs-φs plane.The black square and error bar corresponds to the Standard Model prediction[3,4].

TABLE I .
Fit results for the solution with ∆Γs > 0 with statistical and systematic uncertainties.