Measurement of the Decay B- -->D*0 e- nubar

Using 226 million BBbar events recorded on the Upsilon(4S) resonance with the BABAR detector at the SLAC e+e- PEPII storage rings, we reconstruct B- ->D*0 e- nubar decays using the decay chain D*0 ->D0 pi0 and D0 ->K pi. From the dependence of their differential rate on w, the dot product of the four-velocities of B and D*0, and using the form factor description by Caprini et al. with the parameters F(1) and rho_A1^2, we obtain the results rho_A1^2 = 1.16 +- 0.06 +- 0.08, F(1)|V_cb| = (35.9 +- 0.6 +- 1.4) 10^-3, and BF(B- ->D*0 e- nubar) = (5.56 +- 0.08 +- 0.41)%.

PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er The Standard Model of particle physics (SM) contains a large number of free parameters which can only be determined by experiment. Precision measurements of all of these parameters are essential for probing the validity range of the model by comparing many other precision measurements with SM calculations. One of the SM parameters, the element |V cb | of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix, is determined with semileptonic B-meson decays. Their rates Γ are given by the universality of the weak interaction (the Fermi constant G F ), by quark mixing (Γ ∝ G 2 F |V cb | 2 ), and by strong-interaction corrections calculated in heavyquark effective QCD. For the exclusive decays B 0 → D * + ℓ − ν ℓ and B − → D * 0 ℓ − ν ℓ (ℓ = e, µ), these corrections are expressed as form factors in the differential rate dΓ/dw, where w is the dot product of the four velocities of the B and the D * . The form factors depend on the three parameters ρ 2 , R 1 (1), and R 2 (1) [1]. Whereas the B 0 mode has been measured by many experiments [2], the B − mode has only been measured by two groups [3,4] with much smaller data samples. However, the B 0 experiments do not agree well in their ρ 2 results. Using the isospin symmetry dΓ( , a precision measurement of the B − mode can improve knowledge of ρ 2 and consequently of Γ and |V cb |. The aim of our analysis [5] is the determination of the differential decay fraction dB(B − → D * 0 e − ν e )/dw, where B = Γτ , with the B − lifetime τ . The neutrino in the B − → D * 0 e − ν e decay is not reconstructed. Therefore, the w value of each reconstructed event cannot be obtained, only an approximationw as defined below. Instead of unfolding dB/dw, the parametrized dB/dw expectation convolved with the w resolution from Monte Carlo (MC) simulation is fitted to the observed dB/dw distribution. The fit uses the parametrization of Caprini et al. [1] with ρ 2 ≡ ρ 2 A1 and determines the two parameters F (1) · |V cb | and ρ 2 . The decay fraction B is obtained by integrating dB/dw. Using , the parametrization is defined by the following expressions: . The values of R 1,2 (1) are not determined in this analysis; they are taken from Ref. [6]. For our analysis, we use 205 fb −1 of e + e − annihilation data recorded at √ s ≈ m(Υ (4S)) with the BABAR detector [7] at the SLAC PEP-II storage rings [8]. In addition to these on-peak data, we also use 16 fb −1 of off-peak data collected 40 MeV below the Υ (4S) resonance. We select B − → D * 0 e − ν e candidates [9] by pairing electrons with p * > 1.2 GeV/c in the e + e − rest frame (cms) with D * 0 candidates. Since the precision of our results is not statistically limited, we restrict the analysis to the sequential decay modes D 0 → K − π + , which has the smallest combinatorial background, and D * 0 → D 0 π 0 , which has a better resolution in ∆m ≡ m( Charged particles are selected if they have at least 10 hits in the drift chamber, transverse momentum p T > 0.1 GeV/c, and a polar angle between 23.5 • and 145.5 • in the laboratory frame. Electrons (kaons) are selected with tight (loose) particle identification criteria [10]. Neutral pions are reconstructed from two photons, each with energy above 30 MeV and a photon-compatible lateral shower shape in the calorimeter. The two photons must be consistent with the π 0 hypothesis (115 < m γγ < 150 MeV/c 2 ). A kinematic fit with the constraint m γγ = m π 0 improves the ∆m resolution by a factor of 3. The decay candidates have to fulfill the following additional requirements: the D * 0 -D 0 mass difference and the D 0 -candidate mass must satisfy 135 < ∆m < 153 MeV/c 2 and 1.8496 < m(K − π + ) < 1.8796 GeV/c 2 , respectively. To reject non-B-decay candidates, the second normalized Fox-Wolfram moment [11] of the event has to be smaller than 0.45. To help reject combinatorial background with a D * 0 and an e − from different B mesons in the event, the cms angle between them must be larger than 90 • .
Since there are many low-energy background photons, the selection criteria result in many events with two or more D * 0 e candidates, on average 1.75 per event. All D * 0 e candidates in the same eKπ combination form one group, called a candidate group. On average there are 1.015 candidate groups per event. When an event has more than one candidate group, we keep only the one with the best |m(Kπ) − m(D 0 )|. All candidates in one group are kept in the analysis because the simulation of low-energy photons is not perfect. This procedure ensures that correctly reconstructed candidates are selected with the same probability in data and MC simulation.
The surviving candidates are binned in ∆m, cos θ * BY , andw. The first two variables are used for signalbackground separation, and the third is used for the w dependence of the signal. The mass difference ∆m is defined above, and θ * BY is the angle between the B meson and the Y = D * 0 + e system in the cms defined by cannot be determined since the angle β * between the B and the D * 0 in the cms is unknown. However, β * is bounded by a minimum and a maximum value and we usew = [w(β * min ) + w(β * max )]/2 as an estimator for w. Both w andw range from 1.0 to 1.5, and the distribution ofw − w is nearly Gaussian with an RMS of 0.026.
The fit for V = F (1)|V cb | and ρ 2 is a binned maximumlikelihood fit with 41, 14, and 10 equidistant bins in ∆m, cos θ * BY , andw, respectively. The fit function in each w bin is the sum of the signal function Sw(V, ρ 2 ) and 23 background functions B i,w (V, ρ 2 ). Each summand is taken as the product of one-dimensional functions of ∆m and cos θ * BY . The ∆m distributions of correctly (wrongly) reconstructed D * 0 mesons are parametrized by the sum of 3 bifurcated Gaussians (product of an exponential and a power law function). The cos θ * BY distributions are modeled by modified KEYS functions [5].
The factor functions of Sw are obtained from fits to the reweighted signal MC distributions with V -, ρ 2 -, R 1 (1)-, and R 2 (1)-dependent weights on the generator level. Sw also includes the total number of produced BB pairs, all decay fractions of sequential decays, the B − lifetime, all MC reconstruction efficiencies, and efficiency corrections. The corrections for track reconstruction and charged-particle identification are obtained from control data samples and their MC expectations. The correction of the π 0 reconstruction efficiency is described below. Small corrections are also applied for deviations of the shapes of the ∆m distributions in data and MC because of track resolution differences, and for deviations in the shapes of the cos θ * BY distributions because of differences in storage-ring energy calibration and resolution.
The background functions are separately determined for the 23 background classes [5]. The large number of backgrounds is necessary in order to factorize all B i,w as B 1,i,w (∆m) × B 2,i,w (cos θ * BY ). The one-dimensional fit functions B j,i,w are again obtained from fits to MC distributions. The fit to the data has 49 free parameters; V , ρ 2 , and 47 for adjustments of ∆m shapes, cos θ * BY shapes, and background fractions. The number of e + e − → cc background events is fixed by the off-peak data.
As validation of the fit procedure, we perform our fit on five different MC subsamples whose size corresponds to that of the data sample. All five results for V and ρ 2 agree with the MC input to within one standard deviation. Applied to the data and using the input-parameter 0.827 ± 0.044 [6] values in Table I, the fit result is V = (35.9 ± 0.6) · 10 −3 and ρ 2 = 1.16 ± 0.06 with a correlation coefficient of +0.90. The result leads to B = (5.56 ± 0.08)% after integrating dB/dw. The total number of signal events is 23 499±329. A control value of χ 2 can be calculated after the fit as a goodness-of-fit measure. We find 4436.3 for 4095 degrees of freedom after rebinning in regions with low statistics. The values of χ 2 in the MC-subsample fits are of similar size indicating that the factorization assumptions for Sw and B i,w are not perfect. Since there is no bias in V or ρ 2 in the MC-subsample fits and no significant correlation between background parameters and both V and ρ 2 in the fit to the data, we conclude that the results are unbiased. Figure 1 shows the result of the fit together with the selected data. The "Signal" part of the fit function contains the correctly reconstructed B − → D * 0 e − ν e decays. The two D * * parts contain B → D * * eν decays with ("∆m peaking") and without ("∆m flat") a correctly reconstructed D * 0 intermediate state (D * * = D 1 , D * 0 , D ′ 1 , D * 2 , D * π, Dπ). Events with a correctly reconstructed D * 0 and a correctly identified electron from the same B and from two different B mesons are in the "Correlated" and "Uncorrelated" background parts, respectively. "Signal-like" are true decays B − → D * 0 e − ν e and B 0 → D * + e − ν e which are not correctly reconstructed. The background from true B → D 0 eν decays is called "D 0 eν". All other background candidates from BB events ("Combinatorial D * 0 ") are flat in the ∆m and the cos θ * BY distributions since they do not contain a correctly reconstructed D * 0 and they do not come from a charmed semileptonic decay. The last contribution, only visible at highw, comes from cc events.
To determine the systematic uncertainties listed in Table II we either rerun the fit with varied input or we rescale the fit result. The upper part of the Table gives the "internal" uncertainties which are specific to our analysis. The relative uncertainty on the efficiency to reconstruct a track is 0.8%, leading to 2.4% and 1.2% for B and V . The dependence of the tracking efficiency on the transverse momentum p T has an uncertainty which could distort the shape of thew spectrum. The uncertainties arising from the identification (ID) of charged tracks as electrons or as kaons contribute to the result as listed under "particle ID efficiency". A significant fraction of the total uncertainty comes from the precision of the π 0 reconstruction efficiency (ǫ π 0 ). It is determined from e + e − → τ + τ − events where one of the two τ leptons is either reconstructed by one track and two clusters (mainly τ → ρ(ππ 0 )ν) or by only one track without clusters (mainly τ → πν, µνν). The other τ , used as a τ -pair tag, is reconstructed in its eνν decay. From the numbers  of τ + τ − events reconstructed in each of the two channels we derive an efficiency in data and in MC, giving a correction to the simulated π 0 efficiency. The correction is obtained for momenta above 350 MeV/c and has a precision of 3%. In the lower-momentum region with all π 0 mesons from D * 0 eν decays, we use a correction factor of 0.960 ± 0.035 where the increased uncertainty covers the extrapolation into this region. Efficiency differences between τ + τ − and BB events are covered by the MC simulation as controlled by comparing the rates of reconstructed D 0 decays into K − π + and K − π + π 0 . The uncertainty in the shape of thew spectrum, i.e. its influence on ρ 2 , is estimated by fit results for different lower cuts on p π 0 ("p π 0 dependence of ǫ π 0 "). Corrections to the ∆m shape and to the cos θ * BY shape are parametrized as functions ofw, see "shape parameters" for their contributions to the systematics. Uncertainty estimates from radiative corrections are taken from the BABAR analysis of B 0 → D * ℓν decays [6] which uses the same leptonmomentum cutoff of 1.2 GeV/c.
The "external" uncertainties owing to parameters taken from other experiments are given in the lower part of Table II. For ρ 2 they are dominated by R 1 (1) and R 2 (1). For future updates, we also give in Table III the derivatives of our three results with respect to these two variables as determined from fits with varied input values. The B → D * * eν decays contribute to the uncertainties because of their less precisely known decay fractions and their uncertain ∆m shape due to low-energy photon background. Uncertainties in theirw shape are covered by 10 of the 49 fit parameters. Adding all systematic uncertainties in quadrature leads to the last line in Table II and to our final results F (1) · |V cb | = (35.9 ± 0.6 ± 1.4) · 10 −3 , The correlation coefficients between F (1) · |V cb | and ρ 2 A1 are +0.90 for statistics, +0.42 for systematics, and +0.52 in total. Using F (1) = 0.919 ± 0.033 from lattice QCD [13], we obtain |V cb | = (39.0 ± 0.6 ± 2.0) · 10 −3 in good agreement with the average from the exclusive neutral B decays B 0 → D * − ℓ + ν, (39.2 ± 0.7 ± 1.4) · 10 −3 [2], and in agreement with results from the inclusive decays B → X c ℓν, e. g. (42.0 ± 0.2 ± 0.7) · 10 −3 in Ref. [14]. Our result for ρ 2 is in the center of the range (0.5, 1.5) from the B 0 → D * − ℓ + ν experiments [2].
To conclude, this measurement is the first one for B − → D * 0 ℓ − ν ℓ decays with a data sample comparable to recent B 0 → D * + ℓ − ν ℓ experiments. The results for the decay rate and for |V cb | agree well with the B 0 mean values. Since the uncertainties in the reconstruction of low-momentum π + and π 0 are experimentally very different, the agreement of our ρ 2 result with the central value of the B 0 results provides a crucial cross check for previous |V cb | determinations in B → D * ℓν ℓ decays.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the comput-