A Measurement of the Branching Fractions of exclusive Bbar ->D(*)(pi)l-nubar Decays in Events with a Fully Reconstructed B Meson

We report a measurement of the branching fractions for Bbar ->D(*)(pi)l-nubar decays based on 341.1 fb-1 of data collected at the Upsilon(4S) resonance with the babar detector at the PEP-II e+e- storage rings. Events are tagged by fully reconstructing one of the B mesons in a hadronic decay mode. We obtain B(B- ->D0l-nubar) = (2.33 +/- 0.09(stat.) +/- 0.09(syst.))%, B(B- ->D*0l-nubar) = (5.83 +/- 0.15(stat.) +/- 0.30(syst.))%, B(B0bar ->D+l-nubar) = (2.21 +/- 0.11(stat.) +/- 0.12(syst.))%, B(B0bar ->D*+l-nubar) = (5.49 +/- 0.16(stat.) +/- 0.25(syst.))%, B(B- ->D+pi-l-nubar) = (0.42 +/- 0.06(stat.) +/- 0.03(syst.))%, B(B- ->D*+pi-l-nubar) = (0.59 +/- 0.05(stat.) +/- 0.04(syst.))%, B(B0bar ->D0pi+l-nubar) = (0.43 +/- 0.08(stat.) +/- 0.03(syst.))%, and B(B0bar ->D*0pi+l-nubar) = (0.48 +/- 0.08(stat.) +/- 0.04(syst.))%.

PACS numbers: 13.20He, 12.38.Qk,14.40NdThe determination of the individual exclusive branching fractions of B → X c ℓ − νℓ decays [1] is important for the study of the semileptonic decays of the B meson.Improvement in the knowledge of these branching fractions is also important to reduce the systematic uncertainty in the measurements of the Cabibbo-Kobayashi-Maskawa [2] matrix elements |V cb | and |V ub |.For example, one of the leading sources of systematic uncertainty in the extraction of |V cb | from the exclusive decay B → D * ℓ − νℓ is the limited knowledge of the background due to B → D * πℓ − νℓ .Improved measurements of B → X c ℓ − νℓ decays will also benefit the accuracy of the extraction of |V ub |, as analyses are extending into kinematic regions in which these decays represent a sizable background.
Based on current measurements [3,4,5,6,7] the rate of inclusive semileptonic B decays exceeds the sum of the measured exclusive decay rates [8].While B → Dℓ − νℓ and D * ℓ − νℓ decays account for about 70% of this total, the contribution of other states, including resonant and non-resonant D ( * ) πℓ − νℓ (denoted by D * * ℓ − νℓ ), is not yet well measured and may help to explain the inclusiveexclusive discrepancy.
In this letter, we present measurements of the branching fractions for B → D ( * ) (π)ℓ − νℓ decays, separately for charged and neutral B mesons.
The analysis is based on data collected with the BABAR detector [9] at the PEP-II asymmetric-energy e + e − storage rings.The data consist of a total of 341.1 fb −1 recorded at the Υ (4S) resonance, corresponding to 378 million BB pairs.An additional 36 fb −1 off-peak data sample, taken at a center-of-mass (CM) energy 40 MeV below the Υ (4S) resonance, is used to study background from e + e − → f f (f = u, d, s, c, τ ) events (continuum production).A detailed GEANT4-based Monte Carlo (MC) simulation [10] of BB and continuum events is used to study the detector response, its acceptance, and to test the analysis techniques.The simulation models B → D ( * ) ℓ − νℓ decays using calculations based on Heavy Quark Effective Theory [11], B → D * * (→ D ( * ) π)ℓ − νℓ decays using the ISGW2 model [12], and B → D ( * ) πℓ − νℓ decays using the Goity-Roberts model [13].
We select semileptonic B decays in events containing a fully reconstructed B meson (B tag ), which allows us to constrain the kinematics, reduce the combinatorial background, and determine the charge and flavor of the signal B meson.
We first reconstruct the semileptonic B decay, selecting a lepton with momentum p * ℓ in the center-of-mass frame higher than 0.6 GeV/c.Electrons from photon conversions and π 0 Dalitz decays are removed by searching for pairs of oppositely charged tracks that form a vertex with an invariant mass compatible with a photon conversion or a π 0 Dalitz decay.Candidate D 0 mesons, having the correct charge-flavor correlation with the lepton, are reconstructed in the , and K 0 S K 0 S channels, and D + mesons in the and K 0 S π + π + π − channels.In events with multiple B → Dℓ − νℓ candidates, the candidate with the best D-ℓ vertex fit is selected.Candidate D * mesons are reconstructed by combining a D candidate with a pion or a photon in the D * + → D 0 π + , D * + → D + π 0 , D * 0 → D 0 π 0 , and D * 0 → D 0 γ channels.In events with multiple B → D * ℓ − νℓ candidates, we choose the candidate with the smallest χ 2 based on the deviations from the nominal values of the D invariant mass and the invariant mass difference between the D * and the D, using the measured resolution.
The kinematic consistency of a B tag candidate with a B meson decay is evaluated using two variables: the beam-energy substituted mass m ES = s/4 − |p * B | 2 , and the energy difference ∆E = E * B − √ s/2.Here √ s refers to the total CM energy, and p * B and E * B denote the momentum and energy of the B tag candidate in the CM frame.For correctly identified B tag decays, the m ES distribution peaks at the B meson mass, while ∆E is consistent with zero.We select a B tag candidate in the signal region defined as 5.27 GeV/c 2 < m ES < 5.29 GeV/c 2 , excluding B tag candidates with daughter particles in common with the charm meson or the lepton from the semileptonic B decay.In the case of multiple B tag candidates in an event, we select the one with the smallest |∆E| value.The B tag and the D ( * ) ℓ candidates are required to have the correct charge-flavor correlation.Mixing effects in the B 0 sample are accounted for as described in [14].Cross-feed effects, i.e., B − tag (B 0 tag ) candidates erroneously reconstructed as a neutral (charged) B, are subtracted using estimates from the simulation.
For B → D ( * ) Xℓ − νℓ decays, D(D * ) candidates are selected within 2σ (1.5-2.5σ,depending on the D * decay mode) of the D mass (D * − D mass difference), with σ typically around 8 (1-7) MeV/c 2 .We also require the cosine of the angle between the directions of the D ( * ) candidate and the lepton in the CM frame to be less than zero, to reduce background from non-B semileptonic decays.
We reconstruct B − → D ( * )+ π − ℓ − νℓ and B 0 → D ( * )0 π + ℓ − νℓ decays starting from the corresponding B → D ( * ) Xℓ − νℓ samples and selecting events with only one additional reconstructed charged track that has not been used for the reconstruction of the B tag , the signal D ( * ) , or the lepton.For the B 0 → D 0 π + ℓ − νℓ and the B 0 → D * 0 π + ℓ − νℓ decays, we additionally require the invariant mass difference M (Dπ) − M (D) to be greater than 0.18 GeV/c 2 to veto B 0 → D * + ℓ − νℓ events.To reduce the combinatorial background in the B 0 → D * 0 π + ℓ − νℓ mode, we also require the total extra energy in the event, obtained by summing the energy of all the showers in the electromagnetic calorimeter that have not been assigned to the B tag or the D ( * ) ℓ − candidates, to be less than 1 GeV.
The exclusive semileptonic B decays are identified by the missing mass squared in the event, 2 , defined in terms of the particle four-momenta in the CM frame of the reconstructed final states.For correctly reconstructed signal events, the only missing particle is the neutrino, and m 2 miss peaks at zero.Other B semileptonic decays, where one particle is not reconstructed (feeddown) or is erroneously added (feed-up) to the charm candidate, exhibit higher or lower values in m 2 miss .To obtain the B semileptonic signal yields, we perform a one-dimensional extended binned maximum likelihood fit [15] to the m 2 miss distributions.The fitted data samples are assumed to contain four different types of events: B → D ( * ) (π)ℓ − νℓ signal events, feed-down or feed-up from other B semileptonic decays, combinatoric BB and continuum background, and hadronic B decays (mainly due to hadrons misidentified as leptons).For the fit to the m 2 miss distributions of the B → D ( * ) πℓ − νℓ channel, we also include a component corresponding to other misreconstructed B → D * * (D * π)ℓ − νℓ decays.We use the MC predictions for the different B semileptonic decay m 2 miss distributions to obtain the Probability Density Functions (PDFs).The combinatoric BB and continuum background shape is also estimated by the MC simulation, and we use the off-peak data to provide the continuum background normalization.The shape of the continuum background distribution predicted by the MC simulation is consistent with that obtained from the off-peak data.
The m 2 miss distributions are compared with the results of the fits in Fig. 1 for each of the B → D ( * ) (π)ℓ − νℓ channels.The fitted signal yields and the signal efficiencies, accounting for the B tag reconstruction, are listed in Table I.
To reduce the systematic uncertainty, the exclusive B(B → D ( * ) (π)ℓ − νℓ ) branching fractions relative to the inclusive semileptonic branching fraction are measured.A sample of B → Xℓ − νℓ events is selected by identifying a charged lepton with CM momentum greater than 0.6 GeV/c and the correct charge-flavor correlation with the  B tag candidate.In the case of multiple B tag candidates in an event, we select the one reconstructed in the decay channel with the highest purity, defined as the fraction of signal events in the m ES signal region.Background components peaking in the m ES signal region include cascade B meson decays (i.e., the lepton does not come directly from the B) and hadronic decays, and are subtracted by using the corresponding MC distributions.The total yield for the inclusive B → Xℓ − νℓ decays is obtained from a maximum likelihood fit to the m ES distribution of the B tag candidates using an ARGUS function [16] for the description of the combinatorial BB and continuum background, and a Crystal Ball function [17] for the signal.Additional Crystal Ball and ARGUS functions are used to model a broad-peaking component, included in the signal definition, due to real B → Xℓ − νℓ decays for which, in the B tag reconstruction, neutral particles have not been identified or have been interchanged with the semileptonic decays.Fig. 2 shows the m ES distribution of the B tag candidates in the B − → Xℓ − νℓ and B 0 → Xℓ − νℓ sample.The fit yields 159896 ± 1361 events for the B − → Xℓ − νℓ sample and 96771 ± 968 events for the B 0 → Xℓ − νℓ sample.The relative branching fractions B(B → D ( * ) (π)ℓ − νℓ )/B(B → Xℓ − νℓ ) are obtained by correcting the signal yields for the reconstruction efficiencies (estimated from BB MC events) and normalizing to the inclusive B → Xℓ − νℓ signal yield, following the relation Here, N sig is the number of B → D ( * ) (π)ℓ − νℓ signal events for the various modes, reported in Table I together with the corresponding reconstruction efficiencies ǫ sig , N sl is the B → Xℓ − νℓ signal yield, and ǫ sl is the corresponding reconstruction efficiency including the B tag reconstruction, equal to 0.36% and 0.23% for the B − → Xℓ − νℓ and B 0 → Xℓ − νℓ decays, respectively.The absolute branching fractions B(B → D ( * ) (π)ℓ − νℓ ) are then determined using the semileptonic branching fraction B(B → Xℓ − νℓ ) = (10.78± 0.18)% and the ratio of the B 0 and the B + lifetimes τ B + /τ B 0 = 1.071 ± 0.009 [8].
Numerous sources of systematic uncertainties have been investigated.The uncertainties due to the detector simulation are established by varying, within bounds given by data control samples, the tracking efficiency of all charged tracks (resulting in 1.2-2.7%relative systematic uncertainty among the different decay modes), the calorimeter efficiency (0.5-1.8%), the lepton identification efficiency (0.4-3%), and the reconstruction efficiency for low momentum charged (1.2%) and neutral pions (1.3%).We evaluate the systematic uncertainties associated with the MC simulation of various signal and background processes: photon conversion and π 0 Dalitz decay (0.04-0.4%),B cascade decay contamination (0.6-1%), and flavor cross-feed (0.2-0.3%).We vary the B → Dℓ − νℓ and B → D * ℓ − νℓ form factors within their measured uncertainties [11] (0.4-0.8%) and we include the uncertainty on the branching fractions of the reconstructed D and D * modes (2.3-4.4%), and on the absolute branching fraction B(B → Xℓ − νℓ ) used for the normalization (1.9%).We also include a systematic uncertainty due to differences in the efficiency of the B tag selection in the exclusive selection of B → D ( * ) (π)ℓ − νℓ decays and the inclusive B → Xℓ − νℓ reconstruction (0.9-5.6%), and the extraction of the B → D ( * ) (π)ℓ − νℓ (0.4-1.8%) and B → Xℓ − νℓ (0.5-0.9%) signal yields.The complete set of systematic uncertainties is given in Ref. [18].

FIG. 2 :
FIG. 2: (Color online) mES distributions of the a) B − → Xℓ − νℓ , and b) B 0 → Xℓ − νℓ samples.The data (points with error bars) are compared to the result of the fit (solid line).The dashed lines show the broad-peaking component and the sum of the combinatorial and continuum background.