Measurement of the $B_s^0$ meson lifetime in $D_s^+\pi^-$ decays

We present a measurement of the ratio of the Bs meson lifetime, in the flavor-specific decay to $D_s^+\pi^-$, to that of the B0 meson. The pp collision data used correspond to an integrated luminosity of 1/fb, collected with the LHCb detector, at a center-of-mass energy of 7 TeV. Combining our measured value of 1.010 +/- 0.010 +/- 0.008 for this ratio with the known lifetime, we determine the flavor-specific Bs lifetime to be tau(Bs) = 1.535 +/- 0.015 +/- 0.014 ps, where the uncertainties are statistical and systematic, respectively. This is the most precise measurement to date, and is consistent with previous measurements and theoretical predictions.

Lifetimes of b-flavored hadrons show the effects of all processes governing their weak decays. In the case of neutral mesons, the decay rates are not purely exponential, but are modified by flavor mixing and charge parity (CP ) violation. The B 0 s meson's decay width Γ s differs for the heavy and light mass eigenstates, by an amount ∆Γ s that has been measured to be significantly different from zero [1]. This gives rise to a rich phenomenology of mixing and CP violation. Precision measurement of the lifetime τ s = /Γ s is therefore an important benchmark. The ratio of B 0 s to B 0 lifetimes is well predicted in the heavy quark expansion (HQE) model [2], which is used to extract values of the quark-mixing parameters |V cb | and |V ub |, and thus lifetime measurements provide a precision test of the theory.
In this Letter we measure the lifetime of the decay ( -) B 0 s → D ± s π ∓ by summing over B 0 s and B 0 s states. Since CP violation in B 0 s mixing is negligible [3], the final state receives equal contributions from light and heavy mass eigenstates. Consequently, the decay rate is given by the sum of two exponentials and can be fitted by a single exponential with the measured flavor-specific lifetime τ fs related to the decay width. Expanding in terms of ∆Γ s /Γ s [4] The B 0 s time-dependent decay rate is measured with respect to the well-measured lifetimes of the B − and B 0 mesons, which are reconstructed in final states with similar topology and kinematic properties. 2 The LHCb detector [5] 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 siliconstrip vertex detector surrounding the pp interaction region [6], 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 [7] placed downstream of the magnet. The tracking system provides a measurement of momentum, p, with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV. The minimum distance of a track to a primary vertex, the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of p transverse to the beam, in GeV. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [8]. 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 [9].
The trigger 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 signal candidates are hardware triggered if there is at least one track having a large transverse energy deposit, then the track is required in software to have a transverse momentum p T > 1.7 GeV and an impact parameter χ 2 IP with respect to the primary vertex (PV) greater than 16, where χ 2 IP is defined as the difference in χ 2 of a given PV reconstructed with and without the considered particle included. In addition a vertex detached from the PV must be formed with either two, three or four tracks, with a scalar p T sum of the tracks that must exceed a threshold that varies with the track multiplicity.
The advantage of measuring the B 0 s lifetime using the ratio with respect to wellmeasured lifetimes is that the decay time acceptances introduced by the trigger and selection almost cancel, and only small corrections are required to the ratio of the decay time acceptances, which are taken from simulation. Thus, we reconstruct signals not only in the B 0 ) decay mode, but also in the topologically similar channels (i) ). These decay modes are selected using some common criteria. All of the tracks coming from candidate D meson decays are required to have χ 2 IP > 9. Pions arising from B meson decays have a more selective requirement χ 2 IP > 36 and they are required to be inconsistent with being identified as muons. The D candidates are required to have masses within 25 MeV of their known values [1], be reconstructed downstream of the PV, and have χ 2 IP > 4. The D vertex separation from the B vertex should satisfy χ 2 VS > 2, where χ 2 VS is the increase in χ 2 of the parent B vertex fit when the D decay products are constrained to come from the B vertex, relative to when they are allowed to come from a separate vertex.
B − and B 0 candidates are required to have χ 2 IP < 16 with respect to the PV and masses in the ranges 5100 − 5600 MeV, while for B 0 s candidates the mass range is changed to 5200 − 5700 MeV. The cosine of the angle between the B momentum and its direction of flight is required to be greater than 0.9999. All signal candidates are refitted taking both D mass and vertex constraints into account [10]. All charged particles are required to be identified as either pions or kaons. Efficiencies are evaluated with a data-driven method using large samples of D 0 → K − π + events, where the kinematic distributions of kaons and pions from the calibration sample are reweighted to match those of the B decays under study.
We eliminate B 0 [Kππ] decay candidates that result from other similar decays, the B 0 if the invariant mass of the particles forming the D + candidate, with appropriately swapped mass assignments, is compatible within 30 MeV with either of the known D + s or Λ + c masses. Similar vetoes are applied for B 0 can happen if misidentification occurs. The combined efficiencies of the particle identification requirements and the mass vetoes depend on the specific decay mode considered, ranging from 80% to 90%, while more than 95% of crossfeed backgrounds are rejected.
The B candidate mass distributions for the four decay modes considered are shown in Fig. 1, along with the results of binned maximum likelihood fits. Signal shapes are LHCb The points are the data and the superimposed curves show the fit components. The solid (blue) curve gives the total. The DK − component is not visible, but is included. parameterized using modified Gaussian functions (Cruijff) with independent tail shapes on both sides [11]. All signal parameters are allowed to vary in the fit. A residual component of B → DK − misidentified events is also included, with its yield constrained to that determined by an independent analysis where the kaon is positively identified. Partially reconstructed backgrounds, where a pion or a photon are missed in reconstruction, are modeled using a sum of parametric empirical functions convolved with resolution functions. The unique decay kinematics of each of the modes, mostly determined by the polarization amplitudes, is taken into account. The combinatorial background is parameterized by a linear term. decays, respectively. The decay time, t, is derived from a flight-length measurement between production and decay points of the B particle, given by where m is the reconstructed invariant mass, p the momentum and d the distance vector of the particle from its production to decay vertices. Prior to this determination, the PV position is refitted excluding the tracks forming the signal candidate, and the B meson is further constrained to come from the PV. The decay time distribution of the signal D T (t) can be described by an exponential function convolved with a decay time resolution function, G(t, σ), and multiplied by an acceptance function A(t): The ratio of the measured decay time distributions of B 0 s to B 0 or B − (we denote the use of either B 0 or B − modes by the symbol B x ) can be written as , respectively. Since the resolution is very similar in all the modes, and much smaller than our 0.5 ps bin width, the resolution effects cancel [12], and we are left with a ratio of two exponentials times the ratio of acceptance functions, where ∆ B 0 s Bx ≡ 1/τ B 0 s − 1/τ Bx . Acceptance functions are evaluated by simulation. The effective lifetime, τ B 0 s , can then be calculated from ∆ B 0 s Bx using the well-known B x lifetimes. The current world average values are τ B 0 = 1.519±0.007 ps and τ B − = 1.641±0.008 ps [1].
The signal yields are determined in each decay time bin by fitting the mass distribution in each bin with the same shapes as used in the full fits, with the signal shape parameters fixed to those of the full fit as they are independent of the decay time. The yields are shown in Fig. 2.
The signal yields are then corrected by the relative decay time acceptance ratio, obtained by simulation, and shown in Fig. 3. Then the efficiency-corrected yield ratios are fitted with a single exponential function to extract ∆ B 0 s Bx . Fits are performed in the 1-8 ps region. The 0-1 ps region is excluded since the ratio of acceptances varies significantly here, due to the differences between the lifetimes and track multiplicities in the D decays.
The full analysis is also applied to the control decay modes and the B − lifetime is measured relative to that of the B 0 meson. Given their well-known lifetimes, this provides a robust check on the validity of the procedure. We then measure the B 0 s /B y lifetime ratio for each of the three samples. The exponential fits for the B 0 s /B y lifetime ratios are shown in Fig. 4, with the results given in Table 1. In each case good agreement with the known values of the light B meson lifetime ratio is found, and the three values of the B 0 s lifetime are consistent.
The sources of systematic uncertainties on ∆ B 0 s Bx are summarized in Table 2. The statistical precision on the relative acceptance is the largest source of systematic uncertainty. The uncertainties due to the background description are estimated by comparing  the nominal result to that obtained when the linear background slope is allowed to float separately in each decay time bin; in addition an exponential shape is used, and the largest deviation is assigned as a systematic uncertainty. Using a different signal shape to fit the data (double Crystal Ball function [13]) leads to small changes. There is also an uncertainty due to the decay time range and binning used. These uncertainties are   where the first uncertainty is statistical, the second systematic and the third the uncertainty due to the input decay lifetimes of the B − and B 0 mesons, 0.008 ps for the B − meson and 0.007 ps for the B 0 [1]. As the results are fully correlated, that with the smallest uncertainty is chosen τ fs = 1.535 ± 0.015 ± 0.012 ± 0.007 ps.
This is the most precise measurement to date and it is consistent with previously available flavor-specific measurements [1,14], and measurements of B 0 s lifetimes in CP eigenstate modes [15]. The lifetime ratio τ fs (B 0 s )/τ (B 0 ) = 1/ 1 + τ (B 0 )∆ B 0 s B 0 is determined as 1.010 ± 0.010 ± 0.008, where we assign the uncertainty due to the B 0 lifetime as purely systematic. A rather precise prediction of Γ d /Γ s is given using the HQE model [2]. To compare with our measured lifetime ratio we apply a 0.8% correction from Eq. (1) resulting in a corrected prediction for our measured lifetime ratio of 1.009 ± 0.004, in excellent agreement with our measurement, lending credence to this 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