Measurement of the Electron Energy Spectrum and its Moments in Inclusive B->X e nu Decays

We report a measurement of the inclusive electron energy spectrum for semileptonic decays of B mesons in a data sample of 52 million Y4S ->BBar decays collected with the BABAR detector at the PEP-II asymmetric-energy B-meson factory at SLAC. We determine the branching fraction, first, second, and third moments of the spectrum for lower cut-offs on the electron energy between 0.6 and 1.5 GeV. We measure the partial branching fraction to be Br(B ->X e nu, E_e>0.6 GeV) = (10.36 +-0.06(stat.) +-0.23(sys))%.

The operator product expansion provides corrections to the relation between the semileptonic B decay rate and the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) [1] matrix element V cb in the free-quark model [2].The corrections are expressed in terms of nonperturbative quantities that can be extracted from moments of inclusive distributions.We plan to use the precision measurements of moments of the lepton energy spectra presented here and of hadron mass distributions [3] to determine those parameters and thereby to improve the determination of |V cb | [4].
In this paper, we present a new measurement of the inclusive electron energy spectrum from semileptonic B decays, averaged over charged and neutral B mesons produced at the Υ(4S) resonance.After correcting for charmless semileptonic decays, we derive from this spectrum several moments as a function of the minimum electron energy ranging from 0.6 GeV to 1.5 GeV, where lower endpoint is set by the limits of electron identification and prevalence of background.In the B meson rest frame, we define R i (E 0 , µ) as ∞ E0 (E e − µ) i (dΓ/dE e ) dE e , and measure the first moment M 1 (E 0 ) = R 1 (E 0 , 0)/R 0 (E 0 , 0), the central moments M n (E 0 ) = R n (E 0 , M 1 (E 0 ))/R 0 (E 0 , 0) for n = 2, 3 and the partial branching fraction B(E 0 ) = τ B R 0 (E 0 , 0), where τ B is the average lifetime of charged and neutral B mesons.
The measurements presented here are based on data collected by the BABAR detector [5] at the PEP-II asymmetric e + e − storage ring; they correspond to an integrated luminosity of 47.4 fb −1 on the Υ(4S) resonance and 9.1 fb −1 at an energy 40 MeV below the resonance (off-resonance), measured in the electron-positron center of mass frame.Where background and efficiency corrections cannot be measured directly from data, we use a full simulation of the detector based on GEANT4 [6].In the following, all kinematic variables defined in the Υ(4S) rest frame will be annotated with an asterisk.
This analysis is similar to the BABAR measurement of the semileptonic branching fraction [7], including use of the same electron identification criteria, but super-sedes it by an order of magnitude in integrated luminosity.We identify BB events by observing an electron, e tag , with charge Q(e tag ) and a momentum of 1.4 < p * < 2.3 GeV/c in the Υ(4S) rest frame.These electrons make up the tagged sample that is used as normalization for the branching fraction.Each electron e sig with charge Q(e sig ) for which we require p * > 0.5 GeV/c is assigned to the unlike-sign sample if the tagged sample contains an electron with Q(e tag ) = −Q(e sig ), and to the like-sign sample if Q(e tag ) = Q(e sig ).In events without B 0 B 0 mixing, primary electrons from semileptonic B decays belong to the unlike-sign sample while secondary electrons contribute to the like-sign sample.
Multi-hadron events are selected by either requiring a track multiplicity N ch ≥ 5, or N ch = 4 plus at least two photon candidates with E γ > 80 MeV.Track pairs from converted photons are not included in N ch , but count as one photon.For further suppression of non-BB events we require the ratio of the Fox-Wolfram moments H * 2 /H * 0 to be less than 0.8.Electrons originating from the same B meson as the tagged electron typically have opposite charge and direction.To reject them we require cos α * > 1.0 − p * e ( GeV/c) and cos α * > −0.2, (1) where α * is the angle between the two electrons.This requirement also excludes electron pairs from J/ψ → e + e − decays.To suppress background contributions from J/ψ → e + e − decays to the tagged sample, we require the invariant mass M ee of the tag electron, paired with any electron of opposite charge and cos α * < −0.2, to be outside the interval 2.9 < M ee < 3.15 GeV/c 2 .Here the requirement on cos α * does not reduce the efficiency of this veto, but ensures that no signal electron satisfying Eq. 1 is excluded from the unlike-sign sample.The efficiencies of these selection criteria are estimated by Monte Carlo (MC) simulation.Continuum background is subtracted from the tagged, like-and unlike-sign samples by scaling the off-resonance yields by the ratio of on-to off-resonance integrated luminosities, corrected for the energy dependence of the continuum cross section.In the off-resonance sample, the momenta are scaled by the ratio of the on-and offresonance energies.
Electron spectra from photon conversions and Dalitz decays are extracted from data, taking into account the pair-reconstruction efficiencies from MC simulation.The relative uncertainty in these efficiencies is estimated to be 13% and 19% for conversion and Dalitz pairs, respectively.
The misidentification rates for pions, kaons, and protons are extracted from data control samples.They rise from 0.05% to 0.12% for pions and fall from 0.4% to 0.1% for kaons as p * increases from 0.5 to 2.5 GeV/c.The systematic errors are estimated from the control sample purities and from the uncertainties in the π, K and p abundances.The resulting relative uncertainties are less than 40%.
There is a small residual background in the sample of unlike-sign pairs originating from the same B meson and fulfilling the requirement on the opening angle α * from Eq. 1.It is estimated from a fit to the cos α * distribution, separately for each 50-MeV/c-wide bin in p * .The distribution is flat for signal pairs, while for background pairs it is taken from MC simulation, with a maximum at cos α * = −1 and gradually decreasing to 0 at cos α * = 1.Fig. 1 shows the electron momentum spectra and the background contributions discussed so far.Further backgrounds arise from decays of τ leptons, charmed mesons produced in b → ccs decays and J/ψ or ψ(2S) → e + e − decays with only one detected e.We also need to correct for cases where the tagged electron does not originate from a semileptonic B decay.These backgrounds are irreducible, and their contributions to the three electron samples are estimated from MC simulations, using the ISGW2 model [9] to describe semileptonic D and D s meson decays.Assuming Γ(D s → Xeν) = Γ(D → Xeν), we obtain B(D s → Xeν) = (8.05± 0.66)%.Using 0.84 ± 0.09 [10] for the measured fraction of B → D s X decays where the D s originates from fragmentation of the W Boson, and B(B → D s X) = (10.5 ± 2.6)% [11] yields B(B 0,+ → D + s → e + ) = (0.71 ± 0.20)%.Assuming equal production rates of D and D * and using B(B → DD ( * ) X) = (8.2± 1.3)% [10], we arrive at B(B 0,+ → D 0,+ → e + ) = (0.84 ± 0.21)%.To estimate the contribution of electrons from τ decays, we consider the cascades B → τ → e and B → D s → τ → e, with branching fractions taken from [11].The rates for the decays B → J/ψ → e + e − and B → ψ(2S) → e + e − are also adjusted to [11].
These irreducible background spectra are subtracted from the like-sign and unlike-sign spectra after correction for electron identification efficiency.We determine this efficiency as a function of p * and the polar angle θ * using e + e − → e + e − γ events and then use MC simulation to estimate losses in hadronic events with higher multiplicities.For p * > 0.6 GeV/c, the average efficiency is 91% with an uncertainty of 1.5% estimated from the size of the MC correction.A summary of the yields is given in Table I.To account for B 0 B 0 mixing, we determine the number of primary electrons in the i-th p * bin from the like-sign and unlike-sign pairs as where χ 0 = 0.186 ± 0.004 [11] is the B 0 B 0 mixing parameter and f 0 = B(Υ(4S) → B 0 B 0 ) = 0.490 ± 0.018 [11].
The parameter ǫ i α * is the efficiency of the additional requirement for the unlike-sign sample as defined in Eq. 1.
The spectrum obtained from Eq. 2 is corrected for the effects of bremsstrahlung in the detector material using MC simulation.Since this correction significantly impacts the first moments, 3% for E 0 = 0.6 GeV and 0.5% for E 0 = 1.5 GeV, we have verified that the detector material is simulated to better than 3%.Fig. 2 shows the resulting spectrum of primary electrons.Charmless semileptonic B → X u eν decays are modeled as in [12] by a combination of semileptonic decays with resonant and non-resonant hadronic systems.Using B(B → X u eν) = (2.2 ± 0.5) × 10 −3 [12] to correct for this background, we determine the moments Mn = k p n k N k b→c / k N k b→c where k runs over all bins above the energy E 0 and p k are the bin centers for n = 1 and the bin centers shifted by M1 for n = 2, 3.These moments are then transformed into E e moments M n by correcting for the movement of the B mesons in the center-of-mass frame.Further biases due to the event selection criteria and binning are estimated from MC simulation.The spectra and moments presented are those of B → X c eν(γ) decays with any number of photons.The moments as a function of E 0 are shown in Fig. 3 and Table II lists the principal systematic errors for E 0 = 0.6 and 1.5 GeV.Without subtraction of B → X u eν decays, we measure M b→x 1 (1.5 GeV) = (1779.0± 1.9 ± 0.7) MeV, which is consistent with a recent measurement by CLEO [13].Measurements with E 0 = 0 GeV have been performed by DELPHI [14].
We determine the partial branching fraction as ( k N k b→c,u )/(N tag ǫ evt ǫ cuts ), where k runs over all bins with E e > E 0 , N tag = (3616.8± 3.5(stat.)± 21.8(syst.))×10 3 is the background-corrected number of tag elec-trons, ǫ evt = (98.9± 0.5)% refers to the relative efficiency for selecting two-electron events compared to events with a single e tag , and ǫ cuts = (82.8± 0.3)% is the acceptance for the signal electron for E 0 = 0.6 GeV.The result, B(B → Xeν(γ), E e > 0.6 GeV) = (10.36± 0.06(stat.)± 0.23(syst.))%,is consistent with our previous measurement [7], with the overall error improved by 25%.The partial branching fraction can be extrapolated to E 0 = 0 as part of a combined fit of the Heavy Quark Effective Theory (HQET) parameters to the full set of moments [4].
Current theoretical predictions on the lepton energy moments do not incorporate photon emission.Therefore we use PHOTOS [15] to simulate QED radiation and correct the moments for its impact.We verify that radiation that is not included in PHOTOS, e.g.additional hard photons, have no significant effect on the moments.The radiatively corrected moments and the estimated PHOTOS uncertainty [16] are given in Table II.The complete listing of all moments and the full correlation matrix, with and without PHOTOS corrections can be found in Tables III-V.For fitting purposes, a set of tables and matrices with a precision of 5 significant digits can be obtained from the authors.
In summary, we report a measurement of the electron energy spectrum of the inclusive decay B → Xeν and its branching fraction for electron energies above 0.6 GeV, which supersedes our previous result [7].We have also derived branching fractions, first, second, and third moments of electron energy spectrum from B → X c eν decays for cut-off energies from 0.6 to 1.5 GeV.This set of moments combined with hadron mass moments [3] will be used for a significantly improved determination of HQET parameters and of |V cb | [4].
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR.The collaborating institutions wish to thank SLAC for its support and kind hospitality.

FIG. 1 :
FIG. 1: Measured momentum spectrum (points) and estimated backgrounds (histograms) for electron candidates in (a) the unlike-sign sample, and (b) the like-sign sample.

TABLE II :
Results and breakdown of the systematic errors for B = τB ∞ E 0 (dΓ/dEe) dEe , and the moments M1, M2, and M3 for B → Xceν in the B-meson rest frame for two values of E0.