Measurement of the $B^{0}_{s}$ Lifetime Using Semileptonic Decays

We report a measurement of the $B^0_{s}$ lifetime in the semileptonic decay channel $B^0_{s}\to D^-_s \mu^{+}\nu X$ (and its charge conjugate), using approximately 0.4 fb$^{-1}$ of data collected with the D0 detector during 2002 -- 2004. We have reconstructed 5176 $D^-_s \mu^{+}$ signal events, where the $D_s^-$ is identified via the decay $D_s^-\to \phi\pi^-$, followed by $\phi\to K^+ K^-$. Using these events, we have measured the $B^0_s$ lifetime to be $\tau(B^0_{s}) = 1.398 \pm 0.044$ $({stat}) ^{+0.028}_{-0.025}$ $({syst}) {ps}$. This is the most precise measurement of the $B_s^0$ lifetime to date.

L. Mundim, 3 Y.D. Mutaf,73 E. Nagy,15 M. Naimuddin,28 M. Narain,63 N.A. Naumann,35 H.A. Neal,65  Measurements of the lifetimes of different b hadrons allow tests of the mechanism of heavy hadron decay. The spectator model predicts that all hadrons with the same heavy flavor content have identical lifetimes. However, observed charm and bottom hadron lifetimes suggest that non-spectator effects, such as interference between contributing amplitudes, are not negligible in heavy hadron decays. This implies that a mechanism beyond the simple spectator model is required. An effective theory called the Heavy Quark Expansion (HQE) [1] includes such effects and predicts lifetime differences among the different bottom hadrons. In particular, a difference of the order of 1% is predicted between B 0 and B 0 s mesons. The measurement of the flavor-specific B 0 s lifetime using semileptonic decays is also useful in determining the decay width difference between the light and heavy mass eigenstates of the B 0 s meson, which is an equal mixture of CP eigenstates that correspond to mass eigenstates in the absence of CP violation in the B 0 s system. In this Letter, we present a high-statistics measurement of the B 0 s lifetime, using a large sample of semileptonic B 0 s decays collected in pp collisions at √ s = 1.96 TeV with the D0 detector at the Fermilab Tevatron Collider in 2002 -2004. The data correspond to approximately 0.4 fb −1 of integrated luminosity. B 0 s mesons were identified through their semileptonic decay B 0 s → D − s µ + νX [13], where the D − s meson decays via D − s → φπ − , followed by φ → K + K − . The D0 detector is described in detail elsewhere [2]. The detector components most important to this analysis are the central tracking and muon systems. The D0 central-tracking system consists of a silicon microstrip tracker (SMT) and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet, with designs optimized for tracking and vertexing at pseudorapidities |η| < 3 and |η| < 2.5, respectively (where η = −ln[tan(θ/2)]). A liquid-argon and uranium calorimeter has a central section covering pseudorapidities up to ≈ 1.1, and two end calorimeters that extend the coverage to |η| ≈ 4.2 [3]. The muon system is located outside the calorimeters and has pseudorapidity coverage |η| < 2. It consists of a layer of tracking detectors and scintillation trigger counters in front of 1.8 T toroids, followed by two similar layers after the toroids [4].
Events with semileptonic B-meson decays were selected using inclusive single-muon triggers in a three-level trigger system. The triggers used did not impose any impact parameter criterion and were shown to not bias the lifetime measurement. Off-line, muons were identified by extrapolation of the muon track segments, formed by the hits in the muon system, to the tracks found in the central tracking system. Each muon was required to have a momentum p > 3 GeV/c and a transverse momentum The primary vertex of each pp interaction was defined by all available well-reconstructed tracks [5] and constrained by the mean beam-spot position. The latter was updated every few hours. The resolution of the reconstructed primary vertex was typically 20 µm in the transverse plane and 40 µm in the beam direction.
To reconstruct D − s → φπ − decays, tracks with p T > 1.0 GeV/c were assigned the kaon mass and oppositely charged pairs were combined to form a φ candidate. Each φ candidate was required to have a mass in the range 1.008 -1.032 GeV/c 2 , compatible with the reconstructed φ mass at D0. The φ candidate was then combined with another track of p T > 0.7 GeV/c. For the "right-sign" combinations, we required the charge of the track to be opposite to that of the muon and assigned the pion mass to this track. All selected tracks were required to have at least one SMT hit and one CFT hit. The three tracks selected were combined to form a common vertex (the D − s vertex) with a confidence level greater than 0.1%. The D − s candidate was required to have p T > 3.5 GeV/c. The secondary vertex, where the B 0 s decays to a muon and a D − s meson, was obtained by finding the intersection of the trajectory of the muon track and the flight path of the D − s candidate. The confidence level of that vertex had to be greater that 0.01%. The reconstructed D − s decay vertex was required to be displaced from the primary vertex in the direction of the D − s momentum. The helicity angle, Φ, defined as the angle between the directions of the K − and D − s in the φ rest frame, has a distribution proportional to cos 2 Φ. A cut of | cos Φ| > 0.4 was applied to further reduce combinatorial background, which was found to have a flat distribution. In order to suppress the physics background originating from D ( * ) D ( * ) processes [14], we required that the transverse momentum of the muon with respect to the D − s meson, p T rel , exceed 2 GeV/c. The D − s µ + invariant mass was also restricted to 3.4 − 5.0 GeV/c 2 , to be consistent with a B-meson candidate. Since the number of tracks near the B 0 s candidate tends to be small, we required the was taken over all charged particles in the cone (∆φ) 2 + (∆η) 2 < 0.5, with ∆φ and ∆η being the azimuthal angle and the pseudorapidity with respect to the (µ + D − s ) direction. The muon, kaon, and pion tracks were not included in the sum.
The lifetime of the B 0 s , τ , is related to the decay length in the transverse plane, L xy , by L xy = cτ p T /m, where p T is the transverse momentum of the B 0 s and m is its invariant mass. L xy is defined as the displacement of the B 0 s vertex from the primary vertex pro- jected onto the transverse momentum of the D − s µ + system. Since the B 0 s meson is not fully reconstructed, The quantity used to extract the B 0 s lifetime is called the pseudo-proper decay length (PPDL). The correction factor K was applied statistically when extracting cτ (B 0 s ) from the PPDL in the lifetime fit.
In the cases with more than one B 0 s candidate per event, we chose the one with the highest vertex confidence level. We also required the PPDL uncertainty to be less than 500 µm. The resulting invariant mass distribution of the D − s candidates is shown in Fig. 1. The distribution for "right-sign" D − s µ + candidates was fitted using a Gaussian, to describe the signal, and a second-order polynomial, to describe the combinatorial background. A second Gaussian was included for the Cabibbo-suppressed D − → φπ − decay. The best fit result is shown in the same figure. The fit yields a signal of 5176 ± 242 (stat) ± 314 (syst) D − s candidates and a mass of 1958.8 ± 0.9 MeV/c 2 . The width of the D − s Gaussian is 22.6 ± 1.0 MeV/c 2 . The systematic uncertainty comes from the fit. For the D − meson, the fit yields 1551 events. Figure 1 also shows the invariant mass distribution of the "wrongsign" candidates. The observed shift in the D − s mass is consistent with known issues associated with the calibration of the D0 track momenta. The contribution to the mass region from reflected states was found to be negligible. Studies confirmed that this mass shift introduces no significant residual bias in the lifetime determination.
MC samples were generated using Pythia [6] for the production and hadronization phase, and EvtGen [7] for decaying the b and c hadrons. Branching ratios from the PDG have been used when available. Detector acceptance and smearing were taken into account using the full D0 detector simulation based on geant [8]. Generated MC signal samples include contributions from D − s µ + ν, D * − s µ + ν, D * − s0 µ + ν, D ′ − s1 µ + ν, and D ( * )− s τ + ν. Apart from the background due to combinatorial processes such as a prompt muon and an identified D − s meson, there are several real physics processes that produce a muon and a D − s meson, where neither comes from the semileptonic decay of the B 0 s meson. These "right-sign" D − s µ + combinations are included in the signal sample and are defined as "physics backgrounds." Prompt D − s mesons from cc production at the interaction point can combine with high-p T muons generated either via direct production or in charm decays. These cc background events are expected to have very short lifetimes and thus could introduce a significant bias in the B 0 s lifetime measurement. Backgrounds that originate fromB mesons and provide the D − s µ + final state, but not via the semileptonic decay B 0 s → D − s µ + νX, are called non-B 0 s backgrounds. This kind of background is expected to have a relatively long lifetime, thus its effect on the B 0 s lifetime fit is smaller than that of the charm background. There are three sources of such events: where the charm meson accompanying the D ( * )− s , which decays to φπ − , decays semileptonically. The momentum of the muon coming from the decay of the D ( * ) is softer than that for the signal, since it comes from the decay of a secondary charm hadron. This implies that the contribution of these modes to the signal sample is reduced by the kinematic cuts. We found the fractional contribution of the backgrounds to the signal region to be (10.0 ± 7.0)% for cc background and (11.3 +5.3 −3.6 )% for non-B 0 s backgrounds. The lifetime of the B 0 s was found using a fit to the PPDL distribution. We defined a signal sample using the D − s mass distribution in the region from 1913.6 MeV/c 2 to 2004.0 MeV/c 2 , corresponding to ±2σ from the fitted mean mass. The PPDL distribution of the combinatorial background events contained in the signal sample was defined using "right-sign" events from the D − s sidebands (1755.3 -1800.5 MeV/c 2 and 2117. 1 -2162.3 MeV/c 2 ) and "wrong-sign" events between 1755.3 and 2162.3 MeV/c 2 . The combinatorial background due to random track combinations was modeled by the sideband sample events. This assumption is supported by the mass distribution of the "wrong-sign" combinations where no enhancement is visible in the D − s mass region. The PPDL distribution obtained from the signal sample was fitted using an unbinned maximum log-likelihood method. Both the B 0 s lifetime and the background shape were determined in a simultaneous fit to the signal and background samples. The likelihood function L is given by where N S , N B are the number of events in the signal and background samples and f sig is the ratio of D − s signal events obtained from the D − s mass distribution fit to the total number of events in the signal sample. To constrain f sig , we factored in an additional likelihood term using the number of D − s signal events observed from the invariant mass distribution, and its uncertainty, C sig .
Since the current world average width difference between the light and heavy mass eigenstates (∆Γ s ) of the B 0 s system is small [10] compared with the current precision of the data, we used for the signal probability distribution function (PDF), F i sig , a normalized single exponential decay function convoluted with a Gaussian resolution function. The K-factor correction was also convoluted with the exponential decay function. Since a priori, we do not know the decay length uncertainty, which we estimated on an event-by-event basis, an overall global scale factor, s, was introduced as a free parameter in the B 0 s lifetime fit. The events from non-B 0 s background were taken into account in the fit by including similar PDFs to those in the signal but using fixed parameters according to the world-average values [9]. A different K-factor distribution was also used for each process. To take into account the cc background, we used a Gaussian distribution with fixed parameters. These contributions were evaluated and parametrized using MC methods following a similar procedure as for the signal evaluation.
The combinatorial background sample, F i bck , was parametrized using a Gaussian distribution function for the resolution plus several exponential decays: two for the negative values in the PPDL distribution (one short and one long component) and two for the positive values of the distribution. Figure 2 shows the PPDL distribution of the D − s µ + signal sample with the fit result superimposed (dashed curve). The dotted curve represents the sum of the background probability function over the events in the signal sample. The B 0 s signal is represented by the filled area. To test the resolutions, pulls, fitting, and selection criteria, we performed detailed studies using MC samples and found no significant bias in our analysis procedure. In order to study the stability of the B 0 s lifetime measurement, we split the data sample into two parts according to different kinematic and geometric parameters, compared the fitted results, and found the lifetimes consistent within their uncertainties. We also varied the selection criteria and mass fit ranges, and did not observe any significant shifts. We performed an extensive study of our fitting procedure, looking for any possible bias using MC ensembles with statistics of the size of our dataset and distributions as those in data. These samples were fitted, and the mean and width of the distributions of extracted parameters were found to be consistent with the fits to data. One final check of the procedure involved performing a similar lifetime fit to a control sample defined by the Cabibbo-suppressed decay D − → φπ − , (see Fig. 1). We found that 89.1% of the sample comes from B 0 → D − µ + X, and the B 0 lifetime to be 1.541 ± 0.093 ps, where the uncertainty is statistical only. This result is in good agreement with the world average B 0 lifetime [9,10]. We considered and evaluated various sources of systematic uncertainties. The major contributions come from the determination of the combinatorial background, the model for the resolution, and the physics background. To determine the systematics due to the uncertainty on the combinatorial background, we tested other assumptions on the background samples: we used just the events in the sidebands, just the events in the wrong-sign combinations, and removed either the right sideband or the left sideband samples. We also modified the definitions of those samples, changing the mass window sizes and positions. The largest difference in cτ observed in these variations of background modeling was 4.3 µm, which was taken to be the systematic uncertainty due to this source. The effect of uncertainty in the resolution of the decay length was studied using an alternative global scale factor, s. We repeated the lifetime fit with fixed values of s obtained from MC samples and from a different lifetime analysis [11]. Using a variation of the resolution scale by a factor of two beyond these bounds, we found a 3.7 µm variation in cτ . The uncertainty from the physics background was evaluated by varying the branching fractions of the different processes as well as the shapes of the lifetime templates, as given by their known lifetime values [9]. The variations were within one standard deviation in each case. Assuming no correlation between them, we added the effects of all the variations in quadrature and found a total contribution of +2.9 −4.2 µm. Using a similar procedure, we evaluated the uncertainty coming from the determination of the cc background and found a difference of +2.3 −0.8 µm. To evaluate the uncertainty associated with the K factor determination, we modified the kinematics of the event using a different decay model, a different p T spectrum for the b quark, and a different p T spectrum for the muon. We also varied the amount of each component, according to their uncertainty, of the B 0 s → D − s µ + X signal. In each case, the K factor was re-evaluated and the fit repeated. We added all K factor variation effects in quadrature and found a total uncertainty of +3.6 −2.1 µm. There are two requirements in our selection method that could potentially change the final result by altering the shape of the PPDL distribution: p T rel > 2 GeV/c and the positive displacement from the primary vertex of the reconstructed D − s decay vertex. Using MC methods, we evaluated their effects by removing them one at a time. The largest variation observed was +3.0 −0.3 µm, and the selection efficiency is flat as a function of proper decay time. The effect of a possible misalignment of the SMT system was tested in Ref. [11]. We repeated the study using MC signal samples and observed the same shift of cτ = 2 µm, which was taken as a systematic uncertainty due to possible misalignment. The total systematic uncertainty from all of these sources added in quadrature is +8.4 −7.6 µm.
In summary, using an integrated luminosity of approximately 0.4 fb −1 , we have measured the B 0 s lifetime in the decay channel D − s µ + νX to be τ (B 0 s ) = 1.398 ± 0.044 (stat) +0.028 −0.025 (syst) ps. Note that this measurement takes ∆Γ s equal to zero. The extraction of the average lifetimeτ s for ∆Γ s = 0 is straight forward [10]. The result is in good agreement with previous experiments as well as the current world average value for all flavor-specific decays, τ (B 0 s ) = 1.442 ± 0.066 ps [10,12]. Our B 0 s lifetime measurement is the most precise to date and exceeds the precision of the current world average measurement τ (B 0 s ) P DG = 1.461 ± 0.057 ps [9], where semileptonic and hadronic decays were combined. This measurement is approximately 2.5σ away from the B 0 lifetime, more than the 1% predicted by HQE.