Measurement of the $B^0_s\rightarrow J/\psi K^{*0}$ branching fraction and angular amplitudes

A search for the decay $B^0_s\rightarrow J/\psi K^{*0}$ with $K^{*0} \rightarrow K^-\pi^+$ is performed with 0.37 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 7 TeV collected by the LHCb experiment, finding a $\Bs \to J\psi K^-\pi^+$ peak of $114 \pm 11$ signal events. The $K^-\pi^+$ mass spectrum of the candidates in the $B^0_s$ peak is dominated by the $K^{*0}$ contribution. Subtracting the non-resonant $K^-\pi^+$ component, the branching fraction of \BsJpsiKst is $(4.4_{-0.4}^{+0.5} \pm 0.8) \times 10^{-5}$, where the first uncertainty is statistical and the second systematic. A fit to the angular distribution of the decay products yields the \Kst polarization fractions $f_L = 0.50 \pm 0.08 \pm 0.02$ and $f_{||} = 0.19^{+0.10}_{-0.08} \pm 0.02$.

Interpretations of measurements of time-dependent CP violation in B 0 s → J/ψ φ and B 0 s → J/ψ f 0 (980) decays have thus far assumed the dominance of the colour-suppressed tree-level process. However, there are contributions from higher order (penguin) processes (see Fig. 1) that cannot be calculated reliably in QCD and could be large enough to affect the measured asymmetries. It has been suggested that the penguin effects can be determined by means of an analysis of the angular distribution of B 0 s → J/ψK * (892) 0 , where the penguin diagram is not suppressed relative to the tree-level one, and SU (3) flavour symmetry arguments can be used to determine the hadronic parameters entering the B 0 s → J/ψ φ observables [1]. In this paper the K * (892) 0 meson will be written as K * 0 , while for other K * resonances the mass will be given in parentheses. Furthermore, mention of any specific mode implies the use of the charge conjugated mode as well, and K − π + pairs will be simply written as Kπ. The decay B 0 s → J/ψK * 0 has already been observed by the CDF experiment [2], which reported B(B 0 s → J/ψK * 0 ) = (8.3 ± 3.8) × 10 −5 . Under the assumption that the light quark (s,d) is a spectator of the b quark decay, the branching fraction can be approximated as with |V cd | = 0.230 ± 0.011, |V cs | = 1.023 ± 0.036 [3], and B(B 0 → J/ψK * 0 ) = (1.29 ± 0.05 ± 0.13) × 10 −3 [4]. The measurement in Ref. [4], where the Kπ S-wave contribution is subtracted, is used instead of the PDG average. In this paper, 0.37 fb −1 of data taken in 2011 are used to determine B(B 0 s → J/ψK * 0 ), to study the angular properties of the decay products of the B 0 s meson, and to measure the resonant contributions to the Kπ spectrum in the region of the K * 0 meson. The measurement of the branching fraction uses the decay B 0 → J/ψK * 0 as a normalization mode.
The LHCb detector [5] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector located around the interaction point, 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 down- stream. The combined tracking system has a momentum resolution ∆p/p that varies from 0.4 % at 5 GeV/c to 0.6 % at 100 GeV/c. Two ring-imaging Cherenkov detectors (RICH) are used to determine the identity of charged particles. The separation of pions and kaons is such that, for efficiencies of ∼ 75% the rejection power is above 99%. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by alternating layers of iron and multiwire proportional chambers.
The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage called High Level Trigger (HLT) that applies a full event reconstruction. Events with muon final states are triggered using two hardware trigger decisions: the single-muon decision (one muon candidate with transverse momentum p T > 1.5 GeV/c), and the di-muon decision (two muon candidates with p T,1 and p T,2 such that √ p T,1 p T,2 > 1.3 GeV/c). All tracks in the HLT are required to have a p T > 0.5 GeV/c. The single muon trigger decision in the HLT selects events with at least one muon track with an impact parameter IP > 0.1 mm with respect to the primary vertex and p T > 1.0 GeV/c. The di-muon trigger decision, designed to select J/ψ mesons, also requires a di-muon mass (M µµ ) 2970 < M µµ < 3210 MeV/c 2 . Simulated events are used to compute detection efficiencies and angular acceptances. For this purpose, pp collisions are generated using Pythia 6.4 [6] with a specific LHCb configuration [7]. Decays of hadronic particles are described by EvtGen [8] in which final state radiation is generated using Photos [9]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [10] as described in Ref. [11].
The selection of B 0 (s) → J/ψ ( -) K * 0 decays first requires the reconstruction of a J/ψ → µ + µ − candidate. The J/ψ vertex is required to be separated from any primary vertex (PV) by a distance-of-flight significance greater than 13. Subsequently, the muons from the J/ψ decay are combined with the K and π candidates to form a good vertex, where the di-muon mass is constrained to the J/ψ mass. A p T > 0.5 GeV/c is required for each of the four daughter tracks. Positive muon identification is required for the two tracks of the J/ψ decay, and the kaons and pions are selected using the different hadron probabilities based on combined information given by the RICH detectors. The candidate B 0 (s) momentum is required to be compatible with the flight direction as given by the vector connecting the PV with the candidate vertex. An explicit veto to remove B + → J/ψK + events is applied, as they otherwise would pollute the upper sideband of the B 0 (s) mass spectrum. Following this initial selection, several geometrical variables are combined into a single discriminant geometrical likelihood variable (GL). This multivariate method is described in Refs. [12,13]. The geometrical variables chosen to build the GL are: the B 0 (s) candidate minimum impact parameter with respect to any PV in the event, the decay time of the B 0 (s) candidate, the minimum impact parameter χ 2 of the four daughter tracks with respect to all PV in the event (defined as the difference between the χ 2 of the PV built with and without the considered track), the distance of closest approach between the J/ψ and K * 0 trajectories reconstructed from their decay products, and the p T of the B 0 (s) candidate. The GL was tuned using simulated B 0 → J/ψK * 0 signal passing the selection criteria, and background from data in the B 0 (s) mass sidebands with a value for the kaon particle identification variable in a range which does not overlap with the one used to select the data sample for the final analysis.
The Kπ mass spectrum in the B 0 → J/ψKπ channel is dominated by the K * 0 resonance but contains a non-negligible S-wave contribution, originating from K * 0 (1430) 0 and non-resonant Kπ pairs [14]. To determine B(B 0 s → J/ψK * 0 ) it is therefore important to measure the S-wave magnitude in both B 0 (s) → J/ψ Kπ channels. The Kπ spectrum is analyzed in terms of a non-resonant S-wave and several Kπ resonances parameterized using relativistic Breit-Wigner distributions with mass-dependent widths, following closely [14]. The considered waves are: a non-resonant S-wave amplitude interfering with the K * 0 (1430) 0 resonance, K * 0 for the P-wave and K * 2 (1430) 0 for the D-wave. F-wave and G-wave components are found to be negligible in the B 0 fit. In bins of the Kπ mass, a fit is made to the B 0 (s) candidate mass distribution to determine the yield. As shown in Fig. 2, a fit is then made to the B 0 and B 0 s yields as a function of the Kπ mass without any efficiency correction. The S and P-wave components dominate in the ±40 MeV/c 2 window around the K * 0 mass, where the K * 0 contribution is above 90%. A more exact determination of this contribution using this method would require Kπ mass-dependent angular acceptance corrections. For the branching fraction calculation, the fraction of K * 0 candidates is determined from a different full angular and mass fit, which is described next.
The angular and mass analysis is based on an unbinned maximum likelihood fit which handles simultaneously the mass (M J/ψ Kπ ) and the angular parameters of the B 0 (s) decays and the background. Each of these three components is is modelled as a product of probability density functions (PDF), P(M J/ψ Kπ , ψ, θ, ϕ) = P(M J/ψ Kπ ) P(ψ, θ, ϕ), with ψ the angle between the kaon momentum in the rest frame of the K * 0 and the direction of motion of the K * 0 in the rest frame of the B. The polar and azimuthal angles (θ, ϕ) describe the direction of the µ + in the coordinate system defined in the J/ψ rest frame, where the x axis is the direction of motion of the B 0 (s) meson, the z axis is normal to the plane formed by the x axis and the kaon momentum, and the y axis is chosen so that the y component of the kaon momentum is positive.
The function describing the mass distribution of both B 0 (s) signal peaks is the sum of two Crystal Ball (CB) functions [16], which are a combination of a Gaussian and a power law function to describe the radiative tail at low masses, The starting point of the radiative tail is governed by a transition point parameter α (1,2) . The mean and width of the Gaussian component are µ B and σ (1,2) . The values of the f , σ 1 , σ 2 , α 1 and α 2 parameters are constrained to be the same for the B 0 s and B 0 peaks. The difference in the means between the B 0 s and the B 0 distributions, (µ B 0 s − µ B 0 ), is fixed to the value taken from Ref. [17]. The mass PDF of the background is described by an exponential function. Assuming that direct CP violation and the B 0 (s) − B 0 (s) production asymmetry are insignificant, the differential decay rate is [1,15] where A 0 , A and A ⊥ are the decay amplitudes corresponding to longitunally and transversely polarized vector mesons. A S = |A S |e iδ S is the Kπ S-wave amplitude and (δ − δ 0 ) the relative phase between the longitudinal and parallel amplitudes. The convention δ 0 = 0 is used hereafter. The Ω differential is dΩ ≡ d cos ψ d cos θ dϕ. The polarization fractions are normalized according to which satisfy f L + f + f ⊥ = 1.
The parameters f L , f and δ describing the P-wave are left floating in the fit. The |A S | amplitude and the δ S phase depend on M Kπ , but this dependence is ignored in the fit, which is performed in a Kπ mass window of ±40 MeV/c 2 , and they are just treated also as floating parameters. A systematic uncertainty is later associated with this assumption. The angular distribution of observed events is parameterized as a product of the expression in Eq. 3 and a detector acceptance function, Acc(Ω), which describes the efficiency to trigger, reconstruct and select the events. Simulation studies have shown almost no correlation between the three one-dimensional angular acceptances Acc ψ (ψ), Acc θ (θ) and Acc ϕ (ϕ). Therefore the global acceptance factorizes as Acc(Ω) = Acc ψ (ψ) Acc θ (θ) Acc ϕ (ϕ), where Acc ψ (ψ) is parameterized as a fifth degree polynomial, Acc θ (θ) as a second degree polynomial and Acc φ (φ) as a sinusoidal function. A systematic uncertainty due to this factorization hypothesis is later evaluated. The angular distribution for the background component is determined using the upper sideband of the B 0 s mass spectrum, defined as the interval [5417, 5779] MeV/c 2 . Figure 3 shows the projection of the fit in the M J/ψ Kπ mass axis, together with the projections in the angular variables in a window of ±25 MeV/c 2 around the B 0 s mass. The number of candidates corresponding to B 0 and B 0 s decays is found to be 13,365 ± 116 and 114 ± 11, respectively.  Tables 1 and 2 summarize the measurements of the B 0 (s) → J/ψ ( -) K * 0 angular parameters, together with their statistical and systematic uncertainties. The correlation coefficient given by the fit between f L and f is ρ = −0.44 for B 0 s decays. The results for the B 0 → J/ψK * 0 decay are in good agreement with previous measurements [4,15,18,19]. Based on this agreement, the systematic uncertainties caused by the modelling of the angular acceptance were evaluated by summing in quadrature the statistical error on Table 2: Angular parameters of B 0 → J/ψK * 0 needed to compute B(B 0 s → J/ψK * 0 ). The systematic uncertainties from background modelling and the mass PDF are found to be negligible in this case. the measured B 0 → J/ψK * 0 parameters with the uncertainties on the world averages (f L = 0.570 ± 0.008 and f ⊥ = 0.219 ± 0.010) [3]. The angular analysis was repeated with two additional acceptance descriptions, one which uses a three-dimensional histogram to describe the efficiency avoiding any factorization hypothesis, and another one based on a method of normalization weights described in Ref. [20]. A very good agreement was found in the values of the polarization fractions computed with all the three methods. For the parameter |A S | 2 , uncertainties caused by the finite size of the simulation sample used for the acceptance description, as well as from the studies with several acceptance models, are included. The systematic uncertainty caused by the choice of the angular PDF for the background is shown for the B 0 s → J/ψK * 0 decay but it was found to be negligible for B 0 → J/ψK * 0 .

Parameter name
Also included in Tables 1 and 2 is the uncertainty from the assumption of a constant δ S as a function of M Kπ . This assumption can be relaxed by adding an extra free parameter to the angular PDF. This addition makes the fit unstable for the small size of the B 0 s sample, but can be used in the control channel B 0 → J/ψK * 0 . The differences found in the B 0 parameters with the two alternate parameterizations are used as systematic uncertainties. The parameters δ fit to cos(δ ) = −0.960 +0.021 −0.017 for the B 0 and to cos(δ ) = −0.93 ± 0.31 (where the error corresponds to the positive one, being symmetrized) for the B 0 s . These parameters could in principle affect the efficiency corrections, but it was found that the effect of different values of δ on the overall efficiency is negligible. A simulation study of the fit pulls has shown that the errors on f L and f of the B 0 s decays are overestimated by a small amount (∼ 10%) since they do not follow exactly a Gaussian distribution, therefore the decision was taken to quote an uncertainty which corresponds to an interval containing 68% of the generated experiments, rather than giving an error corresponding to a log-likelihood interval of 0.5. A slight bias observed in the pulls of f in B 0 s decays was accounted for by adding a systematic uncertainty corresponding to 6% of the statistical error.
The ratio of the two branching fractions is obtained from where f d (f s ) is the probability of the b quark to hadronize to B 0 (B 0 s ) mesons, ε tot s is the ratio of angular corrections, f (s) K * 0 is the ratio of K * 0 fractions and N B 0 s /N B 0 is the ratio of signal yields. The value of f d /f s has been taken from Ref. [21]. The efficiencies in the ratio ε tot B 0 /ε tot B 0 s are computed using simulation and receive two contributions: the efficiency of the offline reconstruction (including geometrical acceptance) and selection cuts, and the trigger efficiency on events that satisfy the analysis offline selection criteria. The systematic uncertainty in the efficiency ratio is negligible due to the similarity of the final states. Effects due to possible differences in the decay time acceptance between data and simulation were found to affect the efficiency ratio by less than 1 per mille. On the other hand, since the efficiency depends on the angular distribution of the decay products, correction factors λ B 0 and λ B 0 s are applied to account fractions and corresponds to the time integrated quantity, while theory predictions usually refer to the branching fraction at t = 0 [22]. In the case of B 0 s → J/ψK * 0 , the two differ by (∆Γ s /2Γ s ) 2 = (0.77 ± 0.25)%, where ∆Γ s = Γ L − Γ H , Γ s = (Γ L + Γ H )/2, and Γ L(H) is the decay width of the light (heavy) B 0 s -mass eigenstate. In conclusion, using 0.37 fb −1 of pp collisions collected by the LHCb detector at √ s = 7 TeV, a measurement of the B 0 s → J/ψK * 0 branching fraction yields B(B 0 s → J/ψK * 0 ) = 4.4 +0. 5 −0.4 ±0.8 ×10 −5 . In addition, an angular analysis of the decay products is presented, which provides the first measurement of the K * 0 polarization fractions in this decay, giving f L = 0.50 ± 0.08 ± 0.02, f = 0.19 +0. 10 −0.08 ± 0.02, and an S-wave contribution of |A S | 2 = 0.07 +0. 15 −0.07 in a ±40 MeV/c 2 window around the K * 0 mass.