Measurement of the B+c meson lifetime using B+c→J/ψμ+νμX decays

Eur. Phys. J. C (2014) 74:2839 DOI 10.1140/epjc/s10052-014-2839-x Regular Article - Experimental Physics Measurement of the B+ cmeson lifetime using B+ c→J/ψ μ+νμX decays The LHCb Collaboration CERN, 1211 Geneva 23, Switzerland Received: 27 January 2014 / Accepted: 28 March 2014 / Published online: 1 May 2014 © CERN for the benefit of the LHCb collaboration 2014. This article is published with open access at Springerlink.com Abstract The lifetime of the B+ cmeson is measured using semileptonic decays having a J/ψ meson and a muon in the final state. The data, corresponding to an integrated luminosity of 2 fb−1, are collected by the LHCb detector in pp collisions at a centre-of-mass energy of 8 TeV. The measured lifetime is τ=509 ±8±12 fs, where the first uncertainty is statistical and the second is systematic. 1 Introduction The B+ cmeson, formed of a band a cquark, is an excellent laboratory to study QCD and weak interactions.1The B+ cmeson bound-state dynamics can be treated in a nonrelativistic expansion by QCD-inspired effective models that successfully describe the spectroscopy of quarkonia. However, B+ cproduction and decay dynamics have some distinctive features, since this meson is the only observed openflavour state formed by two heavy quarks. The decay proceeds through the weak interaction, and about 70% of the width is expected to be due to the CKM favoured c→s transition [1]. This decay process, challenging to detect, has recently been observed in the B+ c→B0 sπ+mode by the LHCb collaboration [2]. The b→ctransition offers an easier experimental signature, having a substantial probability to produce a J/ψ meson. Indeed, the B+ cmeson was discovered by the CDF collaboration [3] through the observation of the B+ c→J/ψ +νX( =μ, e)semileptonic decays, where Xdenotes any possible additional particles in the final state. The precise measurement of the B+ clifetime provides an essential test of the theoretical models describing its dynamics. Computations based on various frameworks [1,4–9]predict values ranging from 300 to 700 fs. The world average 1The inclusion of charge conjugate states is always implied throughout this paper. e-mail: [email protected] value of the B+ clifetime reported by the PDG in 2013 [10] is 452 ±33 fs. This was obtained from measurements performed at the Tevatron, using semileptonic decays [3,11,12] and the rarer B+ c→J/ψ π +decay [13]. The unprecedented B+ cproduction rate achieved at the LHC has thus far been used to measure many B+ cdecay properties, with several new decay modes observed by LHCb [2,14–18]. The current knowledge of the lifetime is one of the largest systematic uncertainties in the relative branching fraction measurements, also affecting the determination of the production cross-section [19]. This paper reports a measurement of the B+ clifetime using the semileptonic decays B+ c→J/ψ μ+νμXwith J/ψ →μ+μ−. 2 Detector and data sample The LHCb detector [20] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, designed for the study of particles containing bor cquarks. 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 with a bending power of about 4T·m, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system provides a momentum measurement with relative uncertainty that varies from 0.4% at 5 GeV/cto 0.6% at 100 GeV/c, and impact parameter resolution of 20 μm for tracks with large transverse momentum. Different types of charged hadrons are distinguished by information from two ring-imaging Cherenkov detectors [21]. 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 [22]. The trigger [23] consists of a hardware stage, based on information from the calorimeter and muon sys123 2839 Page 2 of 15 Eur. Phys. J. C (2014) 74:2839 tems, followed by a software stage, which applies a full event reconstruction. The analysis is performed on a data sample of pp collisions at a centre-of-mass energy of 8 TeV, collected during 2012 and corresponding to an integrated luminosity of 2fb−1. Simulated event samples are generated for the signal decays and the decay modes contributing to the background. In the simulation, pp collisions are generated using Pythia [24] with a specific LHCb configuration [25]. The production of B+ cmesons, which is not adequately simulated in Pythia,is performed by the dedicated generator Bcvegpy [26]usinga B+ cmass of 6276 MeV/c2and a lifetime of 450 fs. Several dynamical models are used to simulate B+ c→J/ψ μ+νμ decays, as discussed in Sect. 4. Decays of hadronic particles are described by EvtGen [27], in which final state radiation is generated using Photos [28]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [29,30] as described in Ref. [31]. 3 Analysis strategy and event selection Candidate signal decays are obtained from combinations of a dimuon compatible with a J/ψ decay and an additional candidate muon track, denoted as a bachelor muon in the following, originating from a common vertex. Since the expected signal yield is about 104candidates over a moderate background, the event selection and analysis are driven by the need to minimise systematic uncertainties. Selection variables that bias the B+ ccandidate decay time distribution are avoided, and the selection is designed not only to suppress the background contributions, but also to allow their modelling using data. Background candidates with decay time and J/ψ μ mass values comparable to the signal decays are mainly expected from b-hadron decays to aJ/ψ meson and a hadron that is misidentified as a muon. This misidentification background is modelled using data in which B+ ccandidates are selected without any bias related to the identification of the bachelor muon. The candidate events are required to pass a trigger decision based solely on the information from the J/ψ →μ+μ−candidate. To pass the hardware trigger, one or both tracks from the J/ψ decay must be identified as muons. In the first case, the muon is required to have a transverse momentum, pT, greater than 1.48 GeV/c, while in the second case, the product of the two pTvalues must be larger than 1.68 GeV2/c2. The software trigger selects dimuon candidates consistent with the decay of a J/ψ meson by applying loose criteria on the dimuon mass, vertex quality and muon identification, and requires pT>2GeV/c. An offline selection applies further kinematic criteria to enhance the signal purity. Requirements on the minimum pT are applied to the two J/ψ decay products (1.4GeV/c), the J/ψ candidate (2 GeV/c), the bachelor muon (2.5GeV/c) and the J/ψ μ combination (6 GeV/c). The momentum of the bachelor muon must be between 13 and 150 GeV/c.The J/ψ candidate mass is required to be between 3.066 and 3.131 GeV/c2, a range corresponding to about four times the mass resolution. Two sideband mass regions, 3.005–3.036 and 3.156–3.190 GeV/c2, are used to evaluate the background from track pairs misidentified as J/ψ candidates. The three muons are required to originate from a common vertex, with a χ2per degree of freedom from the fit smaller than 3.0. This restrictive requirement suppresses combinatorial background from random associations of real J/ψ and muon candidates not originating from the same vertex. The J/ψ μ mass, MJ/ψ μ , is reconstructed from a kinematic fit constraining the J/ψ mass to its known value [10], and is required to be between 3.5 and 6.25 GeV/c2. Particle identification is based on the information from the Cherenkov, calorimeter and muon detectors, combined into likelihood functions. The selection is based on the logarithm of the likelihood ratio, DLLP/P, for two given chargedparticle hypotheses Pand Pamong μ, π, Kand p.The requirement DLLμ/π >1 is applied on the two muon tracks forming the J/ψ candidate. Dedicated, more restrictive identification requirements are applied to the bachelor muon candidate, including the criterion that the track is matched with muon detector hits in all stations downstream of the calorimeters. A track fit based on a Kalman filter [32] is performed using such hits, and the resulting χ2per degree of freedom must be lower than 1.5. Vetoes against the pion (DLLμ/π >3), kaon (DLLK/π <8) and proton (DLLp/π <20) hypotheses are also applied. To avoid cases in which two candidate tracks are reconstructed from the same muon, the bachelor candidate is required not to share any hits in the muon detectors, and share less than 20% of hits in the tracking stations, with either of the two other muon candidates in the decay. Studies using simulated samples indicate that, after these requirements, the misidentified candidates are dominated by kaons and pions decaying in flight. Decays occurring in the tracker region are reduced by requiring a good match between the track segments reconstructed upstream and downstream of the magnet (χ2<15.0 with five degrees of freedom). The total selection efficiency for signal events, including the detector geometrical acceptance and the trigger, reconstruction and offline selection efficiencies, is predicted from simulation to be about 0.25%. The selected sample consists of 29756 candidates. Among the selected events, 0.6% have multiple candidates which, in most cases, are formed by the same three tracks where the muons with the same charge are exchanged. All candidates are retained, and this effect is considered as a potential source of systematic uncertainty. 123 Eur. Phys. J. C (2014) 74:2839 Page 3 of 15 2839 To study the decay time distribution, a pseudo-proper time is determined for each candidate, defined as tps =p·(v−x)M3μ |p|2,(1) where pis the three-momentum of the J/ψ μ system in the laboratory frame, and vand xare the measured positions of the B+ cdecay and production vertices, respectively. The primary pp interaction vertex (PV) associated with the production of each B+ ccandidate is chosen as the one yielding the smallest difference in χ2when fitted with and without the B+ ccandidate. The position obtained from the latter fit is used. The three-μmass M3μused in Eq. 1is computed without the constraint on the J/ψ mass, to reduce the potential bias from momentum scale miscalibration, which approximately cancels in the M3μ/|p|ratio. The B+ clifetime is determined using the variables tps and MJ/ψ μ . To infer the B+ cdecay time from the pseudo-proper time, a statistical correction based on simulation, commonly referred to as the k-factor method, is adopted. There, the average effect of the momentum of the unreconstructed decay products on the determination of the B+ cdecay time is computed as a function of MJ/ψ μ .TheB+ cmomentum can also be reconstructed for each decay, up to a two-fold ambiguity, using the measured flight direction of the B+ cmeson and the knowledge of its mass. However, due to the short B+ clifetime, the achievable resolution is poor and strongly dependent on the decay time. Therefore, this partial reconstruction is not used in the lifetime determination to avoid potentially large biases, but exploited to study systematic uncertainties arising from the assumed kinematic model of the signal. The background contributions are also modelled in the (tps,MJ/ψ μ ) plane. Models are obtained from data whenever possible, with the notable exception of combinatorial background, whose contribution is inferred from large simulated samples of inclusive b-hadron decays containing a J/ψ meson in the final state. 4 Signal model The expected (tps,MJ/ψ μ ) distribution for the signal decays depends on the simulation of the dynamics for the B+ c→ J/ψ μ+νμdecay and of the contributions from decay modes with additional particles in the final state (feed-down modes). For the B+ c→J/ψ μ+νμdecay, three different decay models are implemented in the simulation, referred to as Kiselev [33–35], Ebert [36] and ISGW2 [37]. The Kiselev model is adopted as the baseline and used to simulate more than 20 million events with the three muons in the nominal detector acceptance. Smaller samples generated with the alternative models are used for systematic studies. Figure 1 ] 2 c [GeV/ μ ψ/J M 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 PDF [arbitrary units] Kiselev Ebert ISGW2 LHCb Simulation Fig. 1 Distributions of MJ/ψ μ , without simulation of detector response, for the Kiselev (red solid line), Ebert (green short-dashed line), and ISGW2 (black long-dashed line) models compares the probability density function (PDF) for MJ/ψ μ predicted by the three models, which exhibit only small differences with each other. The simulation is used to predict the average ratio between the measured pseudo-proper time and the simulated true B+ c decay time t∗. This correction term can be factorised as k≡tps t∗=tps t∗ ps ×t∗ ps t∗≡tps t∗ ps ×k,(2) where t∗ ps is the simulated true value of the pseudo-proper time defined in Eq. 1.Thetps/t∗ ps term accounts for imperfections in the experimental reconstruction, while the k≡t∗ ps/t∗ factor includes only the kinematic effects from unobserved particles in the final state. It is found that the kinematic term dominates the average deviation from unity and the r.m.s. width of the kvariable. The k-factor distribution is empirically modelled from simulated events in bins of MJ/ψ μ . The resolution function describing t≡tps −t∗ ps is parametrised as the sum of three Gaussian functions with a common mean t0and different widths G(t)= 3  i=1 gi1 σi√2πexp −(t−t0)2 2σ2 i.(3) The parameters gi,t0and σiare determined from fits to the simulated events. A small bias t0=−1.9±0.2fsis found, and the core Gaussian term has parameters g1=0.74, σ1=27 fs. The other two Gaussian functions have parameters g2=0.24, σ2=54 fs, g3=0.02, and σ3=260 fs. These parameters are assumed not to depend on the decay time itself as indicated by the simulation. A fourth Gaussian term with the same mean and large width is added when performing the fit to simulated data to describe the small fraction of events having an incorrectly associated primary 123 2839 Page 4 of 15 Eur. Phys. J. C (2014) 74:2839 3.5 4 4.5 5 5.5 6 PDF [arbitrary units] ν + μ ψ/J ν + τ ψ/J ν + μ (2S)ψ ν + μ ) c h, c χ( LHCb Simulation (a) ] 2 c [GeV/ μ ψ/J M ] 2 c [GeV/ μ ψ/J M 4 4.5 5 5.5 6 k-factor mean 0.75 0.8 0.85 0.9 0.95 1LHCb Simulation 4 4.5 5 5.5 6 k-factor width 0.06 0.08 0.1 0.12 0.14 ν + μ ψ/J→ + c BPure Feed-down model (b) Fig. 2 Corrections to the aMJ/ψ μ and bk-factor model due to the contribution of feed-down modes after the selection. The contribution to the MJ/ψ μ distribution from B+ c→J/ψ μ+νμdecays alone is shown by the black solid curve, while the inclusion of each modelled feed-down contribution is shown by the shaded areas according to the legend. The mean and r.m.s. width of the k-factor distribution are shown as a function of MJ/ψ μ before (solid line)andafter(dashed line) the inclusion of feed-down modes vertex. This is not included in the signal model because these events are considered as a background source, which is constrained from data by exploiting the negative tail of the tps distribution. The model for the PDF of tps =kt∗+tis obtained for each MJ/ψ μ bin mby convoluting the exponential t∗distribution with the k-factor distribution hm(k)and the resolution function, resulting in fm(tps)= 3  i=1 gi +∞  −∞ dkh m(k)1 2kτ ×exp σ2 i 2k2τ2−(tps −t0) kτerfc σi kτ√2−(tps −t0) σi√2, (4) where τis the B+ clifetime and erfc is the complementary error function. The signal model must also consider feed-down modes. Their contribution is expected to bias the measured lifetime by modifying the MJ/ψ μ distribution towards lower values and, to a lesser extent, by affecting the k-factor distribution. The modes explicitly included in the model are semileptonic B+ cdecays to the higher charmonia states ψ(2S), χcJ (J=0,1,2)and hc, subsequently decaying to a J/ψ X final state, and the B+ c→J/ψ τ+ντdecay followed by τ+→μ+νμντ. Theoretical calculations give the decay widths of these decay chains relative to B+ c→J/ψ μ+νμto be 3.0% for the ψ(2S)mode [35], 3.3% for the sum of χcand hccontributions [38–41], and 4.4% for J/ψ τ+ντdecays [1]. The first two of these are subject to large uncertainties, which are considered in the systematic uncertainty. The contribution of the feed-down modes after the selection is found to be small, as shown in Fig. 2. Other possible feed-down contributions are the abundant B+ c→B0 sμ+νμdecay mode, followed by the B0 s→J/ψ X decay, and decays to J/ψ D+ (s)final states followed by the semileptonic decay of the charmed meson. These channels are studied using simulated events and found to be negligible, mainly because of the softer pTspectrum of the bachelor muon, and the long-lived intermediate particles causing the reconstructed three-muon vertex to be of poor quality. 5 Background model The main background to decays of long lived particles to three muons is expected to be due to hadrons misidentified as muons and combined with a J/ψ meson from the same vertex, hereafter referred to as misidentification background. Other sources of background, with a correctly identified bachelor muon, are either due to false J/ψ candidates (fake J/ψ background in the following), or associations of a genuine J/ψ meson and a real bachelor muon not originating from B+ cdecays. In the latter case, the two particles can both be produced at the PV (prompt background), produced at different vertices and randomly associated (combinatorial background), or produced at the same detached vertex (B→3μbackground). The yield and PDF of each contribution is modelled from data, with the exception of the last two categories, where simulation is used. The misidentification background can be accurately predicted from data as no identification requirements are imposed on the bachelor muon by the trigger. By also removing such requirements from the offline selection, a J/ψ -track 123 Eur. Phys. J. C (2014) 74:2839 Page 5 of 15 2839 sample consisting of 5.5×106candidates, dominated by J/ψ -hadron combinations, is obtained. The misidentification background is modelled by weighting each candidate in this sample by W, the probability to misidentify a hadron as a bachelor muon candidate. This is defined as the average over hadron species hof the misidentification probability Whfor the given species, each being weighted by the probability Ph for the track to be a hadron h W= h=K,π,p Ph(η, ph,I)Wh(η, ph,Nt), (5) where hcan be a kaon, a pion or a proton. The quantities Ph and Whare measured using calibration samples, as functions of the most relevant variables on which they depend. For Ph, these are the track momentum ph, its pseudorapidity η, and the impact parameter Iwith respect to the PV. The dependence on Iarises because particles produced at the collision vertex will prevail around the PV position, while bhadron decays dominate the events with a sizeable Ivalue. For Wh, the variables are ph,ηand the number of tracks in the event Nt, since the particle identification performance, notably for the Cherenkov detectors, is affected by the density of hits. The contribution from cases where the bachelor track in the J/ψ -track sample is a lepton is neglected, since its effect on the predicted background yield is small compared to the final statistical and systematic uncertainties. Calibration samples consist of selected D∗+ →π+D0(K−π+)decays for kaons and pions, and →pπ−decays for protons. The residual background to these selections, at the level of a few per cent, is subtracted using events in the sidebands of the D or mass distributions. The hadron fractions are determined in each bin from fits to the two-dimensional distribution of the particle identification variables DLLK/π and DLLp/π in the J/ψ -track sample. The discriminating power achievable with these variables is illustrated in Fig. 3. The misidentification probabilities Whare obtained by applying the muon identification criteria to the calibration samples. The result as a function of momentum, averaged over ηand Nt, is shown in Fig. 4. The approximately exponential dependence for pions is due to decays in flight, while the Cherenkov detectors provide a better identification performance for low momentum kaons. TheaveragevalueofWis found to be 0.20%, corresponding to an expected yield of 10 978±110 misidentified candidates, where the uncertainty is statistical only. The two-dimensional (tps,MJ/ψ μ ) PDF is obtained from the J/ψ -track events weighted according to Eq. 5. A yield of 1686 ±90 misidentified candidates is predicted in the detached region (defined as tps >150 fs), due to b-hadron decays. The model is validated by comparing it with the prediction from a simulated sample of events containing a B→J/ψ Xdecay, where B=B+,B0,B0 s. The yield and PDF shape are primarily π/p Bachelor track DLL -150 -100 -50 0 50 100 150 π/K Bachelor track DLL -100 -50 0 50 100 150 Kaons Pions Protons LHCb Fig. 3 Result of a fit in the (DLLp/π ,DLLK/π ) plane to determine the fractions of hadron species in the J/ψ -track sample. The colour of each bin is built as a combination of red,green and blue proportional to the fitted fractions of pions, kaons and protons, respectively ]cMomentum [GeV/ 20 40 60 80 100 120 140 160 180 200 Misid. prob. [%] -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Kaons Protons Pions LHCb Fig. 4 Probability for pions, kaons and protons to be misidentified as muons, as a function of the particle momentum due to a set of exclusive Bmeson decays, the most important ones being B0→J/ψ K∗0and B+→J/ψ K+. The fake J/ψ background is modelled using the J/ψ mass sidebands, as illustrated in Fig. 5. The expected yield is obtained by extrapolating the distribution from the sidebands assuming an exponential behaviour. The (tps,MJ/ψ μ ) distribution is found to be statistically consistent in the two sidebands. Since the two variables are found to be correlated, a two-dimensional model is used. To reduce the fluctuations due to the limited sample size, a smoothing based on kernel estimation [42] is applied to the observed two-dimensional distribution. The candidates withafakeJ/ψ and a misidentified bachelor muon are already taken into account in the misidentification background category. Their yield and PDF shape are estimated with the same technique used for the misidentification background, namely by weighting J/ψ -track events in the sideband regions according to Eq. 5, and are subtracted from the fake J/ψ model. After this correction, the fake J/ψ background yield is predicted to be 2994 ±109 candidates. 123 2839 Page 6 of 15 Eur. Phys. J. C (2014) 74:2839 ] 2 c Dimuon mass [GeV/ 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 2 cCandidates per MeV/ 0 100 200 300 400 500 600 700 800 900 LHCb Fig. 5 Dimuon mass distribution for the J/ψ candidates. The selected signal region is shown by the central light-shaded area. The sidebands used for the estimation of the fake J/ψ background are shown by the dark-shaded areas, and the function modelling such background by the solid red curve The prompt background component is important for decays close to the PV, while it is suppressed in the detached region, where most of the signal is expected. To constrain the effects of the tails of the tps distribution for prompt background events, the PV region is included in the fit, allowing the yield and shape parameters of the prompt background to be determined from data. Alternative fits with a detachment requirement are used as checks for systematic effects. The tps distribution is modelled by a Gaussian function, whose parameter values are left free to vary in the fit. The MJ/ψ μ distribution is obtained from the events in the prompt region, requiring −500 <tps <10 fs to remove the signal component, making the identification requirements for the bachelor muon more stringent to suppress the contamination from the misidentification background. Since no correlations are found between tps and MJ/ψ μ in simulated events, the twodimensional model is obtained by multiplying the PDFs of the two variables. The combinatorial background is modelled using a sample of 18 million events containing a B→J/ψ Xdecay, simulated according to the known b-quark fragmentation fractions [43] and the Bmeson branching fractions to these states, and additional simulated samples of 0 b→J/ψ  and 0 b→J/ψ pK−decays to estimate the contribution from b baryons. The measured value of the 0 bfragmentation fraction [44] is used, and the inclusive 0 b→J/ψ Xbranching fraction is assumed to equal that in Bmeson decays. The modest sample surviving the selection is used to model the tps and MJ/ψ μ distributions, neglecting their correlation. The tps distribution is parametrised with the sum of two exponential functions, while the mass distribution is modelled using the kernel estimation technique. The number of events obtained from simulation is scaled according to the measured J/ψ production cross-section from bdecays [45], the number of simulated events and the integrated luminosity of the data sample. The resulting yield is 974 ±168 candidates, where the uncertainty is statistical. Sizeable systematic uncertainties are assigned to this simulation-based estimation, as discussed in Sect. 7. Simulated samples are also used to evaluate possible irreducible backgrounds from bhadrons (different from B+ c) decaying to J/ψ μ+Xfinal states where all three muons are produced at the same vertex. The only decay mode with a non-negligible contribution is found to be B0 s→ J/ψ (μ+μ−)φ(μ+μ−), from which fewer than 20 events are expected. This B→3μbackground represents only 2% of the combinatorial background and is merged into that category in the following. Finally, the background model includes a component to describe events having an incorrectly associated PV, resulting in a faulty reconstruction of the pseudo-proper time. These events are modelled by associating the candidates with the primary vertices measured in the previous selected event. The PDF is obtained from two-dimensional kernel estimation smoothing, while the yield is left free in the fit. 6 Fit and results The B+ clifetime τis determined from a maximum likelihood unbinned fit to the (tps,MJ/ψ μ ) distribution of the selected sample, in the range −1.5<tps <8 ps and 3.5<MJ/ψ μ <6.25 GeV/c2. To avoid inadvertent experimenter bias, an unknown offset is added to the result for τ, and is removed only after the finalization of the event selection and analysis procedure. The other free parameters of the fit are the mean and width of the tps resolution function for the prompt background, and the yields for the signal, the prompt background, and the candidates with an incorrectly associated PV. The yield parameters for the other background components are Gaussian-constrained to their predicted values. The total yield is constrained to the number of events in the sample. Figure 6shows the projected distributions of the two variables, together with the signal and background contributions obtained from the fit. The fitted number of signal candidates is 8995 ±103. The B+ clifetime is determined to be τ=508.7±7.7 fs, where the uncertainty is statistical only. The total number of background candidates is 20 760 ±120, of which 2585 have tps >150 fs. In the detached region, signal decays dominate the sample, particularly for MJ/ψ μ values above 4.5 GeV/c2. The number of candidates with an incorrectly associated PV is found to be 12 ±5, corresponding to a probability of incorrect association smaller than 0.1%. The fitted mean and width of the prompt peak are −2.1±0.9 and 32.8±0.7 fs, respectively, in excellent agreement with the values obtained from simulation. The correlations between τand the other free parameters are all below 20%. Residuals 123 Eur. Phys. J. C (2014) 74:2839 Page 7 of 15 2839 [ps] ps t 01234567 Candidates per 0.2 ps 1 10 2 10 3 10 4 10 5 10 X μ ν + μ ψ/J→ + c B Combinatorial bkg. Misid. bkg. Prompt peak bkg.ψ/JFake Wrong PV bkg. Total Data LHCb (a) ] 2 c [GeV/ μ ψ/J M 3.5 4 4.5 5 5.5 6 2 c Candidates per 50 MeV/ 1 10 2 10 3 10 LHCb (b) ] 2 c [GeV/ μ ψ/J M 3.5 4 4.5 5 5.5 6 2 c Candidates per 50 MeV/ 1 10 2 10 LHCb (c) Fig. 6 Result of the two-dimensional fit of the B+ c→J/ψ μ+νμX model. Projections of the total fit function and its components are shown for athe pseudo-proper time, bthe mass of all events, and cthe mass of the detached events (tps >150 fs) from the fit are consistent with zero in the explored region of the (tps,MJ/ψ μ ) plane. A goodness-of-fit test is performed by dividing the region into 100×100 equally sized bins and computing a χ2from the bins for which the expected event yield is larger than 0.5. The resulting p-value is 0.20. The method is validated using a set of pseudo-experiments generated according to the fitted model, where the p-value distribution is found to be consistent with the expected uniform distribution in [0, 1]. Tests on pseudo-experiments also show that the fit provides unbiased estimates for the lifetime and its statistical uncertainty. Table 1 Systematic uncertainties on the B+ clifetime Source Assigned systematic (fs) B+ cproduction model 1.0 B+ cdecay model 5.0 Signal resolution model 1.3 Prompt background model 6.4 Fake J/ψ background yield 0.4 Fake J/ψ background shape 2.3 Combinatorial background yield 3.4 Combinatorial background shape 7.3 Misidentification background yield 0.8 Misidentification background shape 1.2 Length scale calibration 1.3 Momentum scale calibration 0.2 Efficiency function 2.6 Incorrect association to PV 1.8 Multiple candidates 1.0 Fit validation 0.5 Quadratic sum 12.4 7 Systematic uncertainties and checks The assigned systematic uncertainties to the B+ clifetime determination, described in the following, are summarised in Table 1. Since limited experimental information is available on semileptonic B+ cdecays, uncertainties on the assumed signal PDF are estimated by constraining generic model variations using the distributions observed in data, rather than relying on theoretical predictions. The B+ cproduction spectra obtained with the Bcvegpy generator are validated using the measured spectra in B+ c→J/ψ π +decays and found to be in good agreement. Linear deformations are applied to the rapidity and momentum spectra by reweighting the simulated events. The fit is repeated after applying the maximum deformations indicated by the comparison with the data distributions. The effect on the lifetime is found to be within ±1.0 fs. The same technique is used for the uncertainties on the B+ c→J/ψ μ+νμXdecay model. A generic model of the distribution in the J/ψ μν phase space is defined by applying the following transformation to the nominal model D(M2 J/ψ μ ,M2 μν) D(M2 J/ψ μ ,M2 μν)=D(M2 J/ψ μ ,M2 μν) ×exp(αψMJ/ψ μ +ανMμν ), (6) where M2 μν =q2is the squared mass of the μν combination. The deformation parameters αψand ανrepresent generic imperfections of the model for the decay form factors and feed-down contributions. The exponential deformation 123 2839 Page 8 of 15 Eur. Phys. J. C (2014) 74:2839 Fig. 7 Binned distributions of aMJ/ψ μ ,andb,cthe two q2 solutions for events in the detached region. The modelled contributions for misidentification background (hatched dark violet), fake J/ψ background (filled light green), combinatorial background (hatched light orange)and signal (filled dark red), are shown, stacked on each other. Markers representing data are superimposed. The background yields and PDFs are obtained with the techniques described in Sect. 5, and only the signal yield is obtained from the fit to the data ] 2 c [GeV/ μ ψ/J M 3.544.555.56 2 c Candidates per 55 MeV/ 100 200 300 400 500 Misid. bkg. bkg.ψ/JFake Combin. bkg. Signal Data LHCb (a) ] 4 /c 2 [GeV H 2 q 024681012 4 c/ 2 Candidates per 0.4 GeV 0 100 200 300 400 500 LHCb (b) ] 4 /c 2 [GeV L 2 q 024681012 4 c/ 2 Candidates per 0.4 GeV 0 100 200 300 400 500 LHCb (c) is chosen to have positive weights while keeping an approximately linear deformation in the masses for small values of the deformation parameters. Partial reconstruction of the decay, using the measured flight direction of the B+ cmeson and its known mass value, is used to determine its momentum up to a two-fold ambiguity. The agreement between the deformed model and the data is evaluated, using the signalenriched detached sample, from the distributions of MJ/ψ μ and of the two q2solutions q2 H(q2 L) obtained using the higher (lower) solution for the B+ cmomentum. The comparison for the nominal model is shown in Fig. 7. Figure 8ashowsthe results of goodness of fit tests obtained when varying the deformation parameters. The agreement is assessed by performing a χ2test on each of the three distributions. Among the models compatible with data at 90% confidence level (combined p-value >0.1), variations of the B+ c lifetime are within ±5.0 fs, which is assigned as systematic uncertainty. It can be noted, by comparing Fig. 8b with Fig. 6c, that the fit quality in the mass projection is significantly improved after applying the deformation that maximises the combined p-value. As a consistency check, the model is also varied within the uncertainties evaluated by comparing available theoretical predictions for the B+ c→J/ψ μ+νμform factors and feeddown contributions. When the signal model is built using the alternative samples of simulated B+ c→J/ψ μ+νμdecays generated with the Ebert and ISGW2 form-factor models, the lifetime changes by +2.0 fs and −1.5 fs, respectively, consistent with the model-independent evaluation. Indeed, the deformation parameters corresponding to the best approximation of the alternative models, shown in Fig. 8a, are compatible with data with a confidence level in excess of 90%. For the feed-down contributions, the relative decay widths with respect to the B+ c→J/ψ μ+νμdecay are varied according to the range of values predicted in Refs. [7,35,36,38,39,46– 49]. More conservatively, each modelled component is variedinturnby±100% in order to take into account possible smaller contributions, such as non-resonant B+ c→ J/ψμνπ0decays, which have not been modelled explicitly and whose PDF shapes are intermediate between the considered ones. The maximum variation with respect to the nominal fit is 0.3 fs. Several effects concerning the reconstruction of signal events are considered. The resolution model for the signal is varied using a quadruple Gaussian instead of the nominal triple Gaussian model. The lifetime variation is −1.3fs, which is assigned as the systematic uncertainty from this source. The number of MJ/ψ μ bins used for the k-factor parametrization is varied to evaluate the effect of the discretization. Results obtained with more than ten bins are stable within ±0.1 fs and the effect is neglected. A possible systematic bias related to the prompt background model is explored by performing fits with a minimum requirement on the tps value. The results, shown in Fig. 9a, are consistent with the expected fluctuations due to the reduced size of the sample. The lifetime variation obtained with the tps >150 fs requirement, which removes most of the prompt candidates, is +6.4 fs, corresponding to 1.5 times the expected statistical error, and is conservatively taken as the systematic uncertainty. The fitted lifetime value changes within this uncertainty when modifying the tps resolution function, using a triple Gaussian shape obtained from 123 Eur. Phys. J. C (2014) 74:2839 Page 9 of 15 2839 ] -1 GeV 2 c [ ν α -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ] -1 GeV 2 c [ ψ α -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.5 -2.7 -0.3 -4.7 -2.4 -0.2 -6.6 -4.3 -2.2 -0.0 -8.4 -6.2 -4.1 -2.0 -10.0 -7.9 -5.9 -3.9 -1.9 -11.5 -9.5 -7.5 -5.6 -3.6 -1.7 -12.8 -10.9 -9.0 -7.1 -5.3 -3.4 -1.5 -14.0 -12.3 -10.4 -8.6 -6.8 -5.0 -3.2 -1.4 -15.1 -13.4 -11.7 -9.9 -8.2 -6.4 -4.6 -2.9 -1.2 -4.6 -14.5 -12.8 -11.2 -9.5 -7.8 -6.1 -4.4 -2.7 -1.0 -17.0 -15.4 -13.8 -12.2 -10.6 -9.0 -7.4 -5.7 -4.1 -2.4 -0.8 -17.7 -16.2 -14.7 -13.2 -11.7 -10.1 -8.6 -7.0 -5.4 -3.8 -2.2 -0.7 -18.3 -16.9 -15.5 -14.0 -12.6 -11.1 -9.7 -8.2 -6.6 -5.1 -3.6 -2.0 -0.5 -18.8 -17.5 -16.2 -14.8 -13.5 -12.1 -10.6 -9.2 -7.7 -6.3 -4.8 -3.3 -1.8 -0.3 +1.9 +4.2 +6.5 +8.7 +10.9 +13.0 +15.0 +17.0 +18.8 +20.7 +22.4 +24.1 +25.7 +27.2 +1.9 +4.2 +6.4 +8.5 +6.4 +12.6 +14.6 +16.4 +18.3 +20.0 +21.7 +23.4 +24.9 +2.0 +4.1 +6.2 +8.3 +10.3 +12.2 +14.2 +16.0 +17.7 +19.5 +21.1 +22.7 +2.0 +4.1 +6.1 +8.1 +10.0 +11.9 +13.7 +15.5 +17.2 +18.9 +20.5 +0.0 +2.1 +4.1 +6.0 +7.9 +9.8 +11.6 +13.4 +15.1 +16.7 +18.4 +0.1 +2.1 +4.0 +5.9 +7.7 +9.6 +11.3 +13.0 +14.7 +16.3 +0.2 +2.1 +4.0 +5.8 +7.6 +9.3 +11.0 +12.7 +14.3 +0.3 +2.2 +4.0 +5.7 +7.4 +9.1 +10.8 +12.4 +0.4 +2.2 +3.9 +5.6 +7.3 +9.0 +10.6 +0.6 +2.3 +3.9 +5.6 +7.2 +8.8 +0.6 +2.3 +3.9 +5.6 +7.1 +0.8 +2.3 +3.9 +5.5 +0.9 +2.4 +4.0 +1.0 +2.5 +1.1 LHCb (a) ] 2 c [GeV/ μ ψ/J M 3.5 4 4.5 5 5.5 6 2 c Candidates per 50 MeV/ 1 10 2 10 LHCb (b) Fig. 8 Effect of a generic deformation of the signal model: aoffset to the lifetime value (expressed in fs) as a function of the deformation parameters; bfit projection for the MJ/ψ μ variable in the detached region after applying the deformation maximising the agreement with data (αψ=αν=0.3c2GeV−1). The colour scale on the upper plot indicates the p-value of the goodness-of-fit test on the three decay kinematic distributions. The solid blue (dashed red) lines shows the region having p-value greater than 32% for the MJ/ψ μ (q2) test only. The filled (empty) blue marker indicates the deformation parameters that fit best the Ebert (ISGW2) model. The fit components shown on the lower plot follow the legend of Fig. 6 simulation instead of the single Gaussian with free parameters used in the nominal fit, or when using the MJ/ψ μ distribution predicted using simulated events with prompt J/ψ production. For the fake J/ψ background, the expectation value of its yield is varied within its systematic uncertainty. The uncertainty on the PDF shape is studied using the two alternative models obtained using only one of the two J/ψ mass sidebands. The observed offsets are within ±2.3 fs. Since the combinatorial contribution is the only background source whose model relies on simulation, datadriven checks are performed to evaluate the uncertainty on its predicted yield. The yield of detached candidates before the bachelor muon identification requirements, which is expected to be dominated by b-hadron decays, is measured and found to differ by 35% from the value predicted by the simulation. To account for a further uncertainty related to the efficiency of the muon identification criteria, a systematic uncertainty of ±50% is assigned on the combinatorial background yield. Another check is performed by comparing the event yields in data and simulation for candidates with MJ/ψ μ values above the B+ cmass, where only combinatorial background is expected. For this check, an additional requirement pT(J/ψ) > 3GeV/cis applied on simulated data, since data are filtered with such a requirement in this mass region. The observed event yield is 221 ±14 events, and the predicted yield is 201 ±73. The pseudo-proper time and mass distributions are also found to agree. The quoted uncertainty on the yield corresponds to ±3.4 fs on τ. The uncertainty on the PDF is dominated by the shape of the tps distribution. A single exponential rather than a double exponential function is used, and the parameters of the nominal function are varied within their statistical uncertainty. The maximum variation is −7.3 fs. For the misidentification background, an alternative fit is performed allowing its yield to vary freely, instead of being Gaussian constrained to its predicted value. The exercise is repeated using only detached events. The resulting yields are found to be compatible with the expected ones, and the maximum τvariation of +0.8 fs is taken as systematic uncertainty. The accuracy of the PDF model is limited by the size of the [ps] ps t 0.5 1 1.5 2 [fs] τ 200 300 400 500 600 700 800 σ1±Expected σ2±Expected LHCb (a) ] 2 c [GeV/ μ ψ/J M 3.5 4 4.5 5 5.5 6 6.5 [fs] τ 480 500 520 540 560 580 LHCb (b) Fig. 9 Lifetime results obtained after reducing the range of the tps and MJ/ψ μ variables aremoving the events with tps lower than the threshold reported on the x-axis and, bdividing events in bins of MJ/ψ μ . The dark (light)shaded band on ashows the expected ±1(2) statistical standard deviation (σ) of the lifetime variation due to the reduced sample size. The horizontal line on bshows the lifetime result of the nominal fit 123