Measurement of the Bs effective lifetime in the J/psi f0(980) final state

The effective lifetime of the Bs meson in the decay mode Bs->J/\psi f0(980) is measured using 1.0/fb of data collected in pp collisions at sqrt(s) = 7 TeV with the LHCb detector. The result is 1.700 +/- 0.040 +/- 0.026 ps where the first uncertainty is statistical and the second systematic. As the final state is CP-odd, and CP violation in this mode is measured to be small, the lifetime measurement can be translated into a measurement of the decay width of the heavy Bs mass eigenstate, \Gamma_H = (0.588 +/- 0.014 +/- 0.009)/ps.

The decay " B 0 s ! J=c f 0 ð980Þ, f 0 ð980Þ ! þ À , discovered by LHCb [1] at close to the predicted rate [2], is important for CP violation [3] and lifetime studies. In this Letter, we make a precise determination of the lifetime. The J=c f 0 ð980Þ final state is CP-odd, and in the absence of CP violation, can be produced only by the decay of the heavy (H), and not by the light (L), " B 0 s mass eigenstate [4]. As the measured CP violation in this final state is small [5], a measurement of the effective lifetime, J=c f 0 , can be translated into a measurement of the decay width, À H . This helps to determine the decay width difference, ÁÀ s ¼ À L À À H , a number of considerable interest for studies of physics beyond the standard model (SM) [6]. Furthermore, this measurement can be used as a constraint in the fit that determines the mixing-induced CP-violating phase in " B 0 s decays, s , using the J=c and J=c f 0 ð980Þ final states, and thus improve the accuracy of the s determination [5,7]. In the SM, if subleading penguin contributions are neglected, s ¼ À2 arg½ where the V ij are the Cabibbo-Kobayashi-Maskawa matrix elements, which has a value of À0:036 þ0:0016 À0:0015 rad [8]. Note that the LHCb measurement of s [5] corresponds to a limit on cos s greater than 0.99 at 95% confidence level, consistent with the SM prediction.
The decay time evolution for the sum of B 0 s and " B 0 s decays, via the b ! c " cs tree amplitude, to a CP-odd final state, f À , is given by [9] ÀðB 0 where N is a time-independent normalization factor and À s is the average decay width. We measure the effective lifetime by describing the decay time distribution with a single exponential function Our procedure involves measuring the lifetime with respect to the well-measured " B 0 lifetime, in the decay mode " B 0 ! J=c " K Ã0 , " K Ã0 ! K À þ (the inclusion of charge conjugate modes is implied throughout this Letter). In this ratio, the systematic uncertainties largely cancel.
The data sample consists of 1:0 fb À1 of integrated luminosity collected with the LHCb detector [10] in pp collisions at the LHC with 7 TeV center-of-mass energy. The detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < < 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. Charged hadrons are identified using two ring-imaging Cherenkov (RICH) detectors. Muons are identified by a muon system composed of 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 that applies a full event reconstruction. The simulated events used in this analysis are generated using PYTHIA 6.4 [11] with a specific LHCb configuration [12], where decays of hadronic particles are described by EVTGEN [13], and the LHCb detector simulation [14] based on GEANT4 [15].
The selection criteria we use for this analysis are the same as those used to measure s in " B 0 s ! J=c þ À decays [16]. Events are triggered by a J=c ! þ À decay, requiring two identified muons with opposite charge, transverse momentum greater than 500 MeV (we work in units where c ¼ @ ¼ 1), invariant mass within 120 MeV of the J=c mass [17], and form a vertex with a fit 2 less than 16. J=c þ À candidates are first selected by pairing an opposite sign pion combination with a J=c candidate that has a dimuon invariant mass from À48 MeV to þ43 MeV from the J=c mass [17]. The pions are required to be identified positively in the RICH detector, have a minimum distance of approach with respect to the primary vertex (impact parameter) of greater than 9 standard deviation significance, have a transverse momentum greater than 250 MeV, and fit to a common vertex with the J=c with a 2 less than 16. Furthermore, the J=c þ À candidate must have a vertex with a fit 2 less than 10, flight distance from production to decay vertex greater than 1.5 mm, and the angle between the combined momentum vector of the decay products and the vector formed from the positions of the primary and the " B 0 s decay vertices (pointing angle) is required to be consistent with zero. Events satisfying this preselection are then further filtered using requirements determined using a boosted decision tree (BDT) [18]. The BDT uses nine variables to differentiate signal from background: the identification quality of each muon, the probability that each pion comes from the primary vertex, the transverse momentum of each pion, the " B 0 s vertex fit quality, flight distance from production to decay vertex, and pointing angle. It is trained with simulated " B 0 s ! J=c f 0 ð980Þ signal events and two background samples from data, the first with like-sign pions with J=c AE AE mass within AE50 MeV of the " B 0 s mass and the second from the " B 0 s upper mass sideband with J=c þ À mass between 200 and 250 MeV above the " B 0 s mass. As the effective " B 0 s ! J=c f 0 ð980Þ lifetime is measured relative to that of the decay " B 0 ! J=c " K Ã0 , we use the same trigger, preselection, and BDT to select J=c K À þ events, except for the hadron identification that is applied independently of the BDT. The selected þ À and K À þ invariant mass distributions, for candidates with J=c þ À (J=c K À þ ) mass within AE20 MeV of the respective B mass peaks are shown in Fig. 1. The background distributions shown are determined by fitting the J=c þ À (J=c K À þ ) mass distribution in bins of þ À (K À þ ) mass. Further selections of AE90 MeV around the f 0 ð980Þ mass and AE100 MeV around the " K Ã0 mass are applied. The f 0 ð980Þ selection results in a " B 0 s ! J=c f 0 ð980Þ sample that is greater than 99.4% CP-odd at 95% confidence level [19].
The analysis exploits the fact that the kinematic properties of the " B 0 s ! J=c f 0 ð980Þ decay are very similar to those of the " B 0 ! J=c " K Ã0 decay. We can select B mesons in either channel using identical kinematic constraints and hence the decay time acceptance introduced by the trigger, reconstruction, and selection requirements should almost cancel in the ratio of the decay time distributions. Therefore, we can determine the " B 0 s ! J=c f 0 ð980Þ lifetime, J=c f 0 , relative to the " B 0 ! J=c " K Ã0 lifetime, J=c " K Ã0 , from the variation of the ratio of the B meson yields with decay time  We test the cancellation of acceptance effects using simulated " B 0 s ! J=c f 0 ð980Þ and " B 0 ! J=c " K Ã0 events. Both the acceptances themselves and also the ratio exhibit the same behavior. Because of the selection requirements, they are equal to 0 at t ¼ 0, after which there is a sharp increase, followed by a slow variation for t greater then 1 ps. Based on this, we only use events with t greater than 1 ps in the analysis. To good approximation, the acceptance ratio is linear between 1 and 7 ps, with a slope of a ¼ 0:0125 AE 0:0036 ps À1 (see Fig. 2). We use this slope as a correction to Eq. (3) when fitting the measured decay time ratio Differences between the decay time resolutions of the decay modes could affect the decay time ratio. To measure the decay time resolution, we use prompt events containing a J=c meson. Such events are found using a dimuon trigger, plus two opposite-charged tracks with similar selection criteria as for J=c þ À (J=c K À þ ) events, apart from any decay time biasing requirements such as impact parameters and B flight distance, additionally including that the J=c þ À (J=c K À þ ) mass be within AE20 MeV of the " B 0 s ð " B 0 Þ mass. To describe the decay time distribution of these events, we use a triple Gaussian function with a common mean, and two long-lived components, modeled by exponential functions convolved with the triple Gaussian function. The events are dominated by zero lifetime background with the long-lived components comprising less than 5% of the events. We find the average effective decay time resolution for " B 0 s ! J=c f 0 ð980Þ and " B 0 ! J=c " K Ã0 decays to be 41:0 AE 0:9 fs and 44:1 AE 0:2 fs respectively, where the uncertainties are statistical only. This difference was found not to bias the decay time ratio using simulated experiments.
In order to determine the " B 0 s ! J=c f 0 ð980Þ lifetime, we determine the yield of B mesons for both decay modes using unbinned maximum likelihood fits to the B mass distributions in 15 bins of decay time of equal width between 1 and 7 ps. We perform a 2 fit to the ratio of the yields as a function of decay time and determine the relative lifetime according to Eq. (4). We obtain the signal and peaking background shape parameters by fitting the time-integrated data set. In each decay time bin, we use these shapes and determine the combinatorial background parameters from the upper mass sidebands, B 0 ! J=c " K Ã0 . In (b) the error bars are smaller than the points. K Ã0 Þ < 5550 MeV. With this approach, the combinatorial backgrounds are reevaluated in each bin and we make no assumptions on the shape of the background decay time distributions. This method was tested with high statistics simulated experiments and found to be unbiased.
The time-integrated fits to the J=c f 0 ð980Þ and the J=c " K Ã0 mass spectra are shown in Fig. 3. The signal distributions are described by the sum of two crystal ball functions [20] with common means and resolutions for the Gaussian core, but different parameters describing the tails fðm; ; ; n l;r ; l;r Þ ¼ 8 > > > > > > < > > > > > > : n l j l j n l exp Àj l j 2 2 n l j l j À j l j À jmÀj Àn l ; if mÀ À l ; n r j r j n r exp Àj r j 2 2 n r j r j À j r j À jmÀj Àn r ; if mÀ ! r ; exp ÀðmÀÞ 2 2 2 ; otherwise; (5) where is the mean and the width of the core, while n l;r are the exponent of the left and right tails, and l;r are the left and right transition points between the core and tails. The left-hand tail accounts for final state radiation and interactions with matter, while the righthand tail describes non-Gaussian detector effects only seen with increased statistics. The combinatorial backgrounds are described by exponential functions. All parameters are determined from data. There are 4040 AE 75 " B 0 s ! J=c f 0 ð980Þ and 131 920 AE 400 " B 0 ! J=c " K Ã0 signal decays. The decay time distributions, determined using fits to the invariant mass distributions in bins of decay time as described above, are shown in Fig. 4. These are made by placing the fitted signal yields at the average " B 0 ! J=c " K Ã0 decay time within the bin rather than at the center of the decay time bin. This procedure corrects for the exponential decrease of the decay time distributions across the bin. The subsequent decay time ratio distribution is shown in Fig. 5, and the fitted reciprocal lifetime difference is Á J=c f 0 ¼ À0:070 AE 0:014 ps À1 , where the uncertainty is statistical only. Taking J=c " K Ã0 to be the mean " B 0 lifetime 1:519 AE 0:007 ps [17], we determine J=c f 0 ¼ 1:700 AE 0:040 ps.
Sources of systematic uncertainty on the " B 0 s ! J=c f 0 ð980Þ lifetime are investigated and listed in Table I. We first investigate our assumptions about the signal and combinatorial background mass shapes. The relative change of the determined " B 0 s ! J=c f 0 ð980Þ lifetime between fits with double crystal ball functions and double Gaussian functions for the signal models is 0.001 ps, and between fits with exponential functions and straight lines for the combinatorial background models is 0.010 ps. The different particle identification criteria used to select " B 0 s ! J=c f 0 ð980Þ ! þ À þ À and " B 0 ! J=c " K Ã0 ! þ À K À þ decays could affect the acceptance cancellation between the modes. In order to investigate this effect, we loosen and tighten the particle identification selection for the kaon, modifying the " B 0 ! J=c " K Ã0 signal yield by þ2% and À20%, respectively, and repeat the analysis. The larger difference with respect to the default selection, 0.007 ps, is assigned as a systematic uncertainty. We also assign half of the relative change between the fit without the acceptance correction and the default fit, 0.018 ps, as a systematic uncertainty. Potential statistical biases of our method were evaluated with simulated experiments using similar sample sizes to those in data. An average bias of 0.012 ps is seen and included as a systematic uncertainty.  The observed bias vanishes in simulated experiments with large sample sizes. As a cross-check, the analysis is performed with various decay time bin widths and fit ranges, and consistent results are obtained. The possible CP-even component, limited to be less than 0.6% at 95% confidence level [19], introduces a 0.001 ps systematic uncertainty. Using the Particle Data Group value for the " B 0 lifetime [17] as input requires the propagation of its error as a systematic uncertainty. All the contributions are added in quadrature and yield a total systematic uncertainty on the lifetime of 0.026 ps (1.5%). Thus the effective lifetime of the J=c f 0 ð980Þ final state in " B 0 s decays, when describing the decay time distribution as a single exponential, is J=c f 0 ¼ 1:700 AE 0:040 AE 0:026 ps: Given that s is measured to be small, and the decay is given by a pure b ! c " cs tree amplitude, we may interpret the inverse of the " B 0 s ! J=c f 0 ð980Þ effective lifetime as a measurement of À H with an additional source of systematic uncertainty due to a possible nonzero value of s . For cos s ¼ 0:99, À s ¼ 0:6580 ps À1 and ÁÀ s ¼ 0:116 ps À1 [5], J=c f 0 changes by 0.002 ps. This is added in quadrature to the systematic uncertainties on J=c f 0 to obtain the final systematic uncertainty on À H .
In summary, the effective lifetime of the " B 0 s meson in the CP-odd J=c f 0 ð980Þ final state has been measured with respect to the well-measured " B 0 lifetime in the final state J=c " K Ã0 . The analysis exploits the kinematic similarities between the " B 0 s ! J=c f 0 ð980Þ and " B 0 ! J=c " K Ã0 decays to determine an effective lifetime of where the uncertainties are statistical and systematic, respectively. This result is consistent with, and more precise than, the previous measurement of 1:70 þ0:12 À0:11 AE 0:03 ps from CDF [21]. Interpreting this as the lifetime of the heavy " B 0 s eigenstate, we obtain À H ¼ 0:588 AE 0:014 AE 0:009 ps À1 : This value of À H is consistent with the value 0:600 AE 0:013 ps À1 , calculated from the values of À s and ÁÀ s in Ref. [5]. 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 CERN and at the LHCb institutes, and acknowledge support from the national agencies: CAPES, CNPq, FAPERJ, and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF, and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN, XuntaGal, and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowledge the support received from the ERC under FP7 and the Region Auvergne.