Measurements of Partial Branching Fractions for Bbar -->X_u ell nubar and Determination of |V_{ub}|

We present partial branching fractions for inclusive charmless semileptonic B decays Bbar -->X_u ell nubar, and the determination of the CKM matrix element |V_{ub}|. The analysis is based on a sample of 383 million Y(4S) decays into B Bbar pairs collected with the BaBar detector at the PEP-II e+ e- storage rings. We select events using either the invariant mass M_X of the hadronic system, the invariant mass squared, q^2, of the lepton and neutrino pair, the kinematic variable P_+ or one of their combinations. We then determine partial branching fractions in limited regions of phase space: Delta B = (1.18 +- 0.09_{stat.} +- 0.07_{syst.} +- 0.01_{theo.}) x 10^{-3} (M_X<1.55 GeV/c^2), Delta B = (0.95 +- 0.10_{stat.} +- 0.08_{syst.} +- 0.01_{theo.}) x 10^{-3} (P_+<0.66 GeV/c), and Delta B = (0.81 +- 0.08_{stat.} +- 0.07_{syst.} +- 0.02_{theo.}) x 10^{-3} (M_X<1.7 GeV/c^2, q^2>8 GeV^2/c^4). Corresponding values of |V_{ub}| are extracted using several theoretical calculations.

PACS numbers: 13.20.He, 12.15.Hh,14.40.Nd In the Standard Model the element V ub of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1] plays a critical role in tests of the prediction of CP violation. Since the rate for charmless semileptonic decays, B → X u ℓν [2], is proportional to |V ub | 2 , and the hadronic and leptonic currents are factorizable, the best method to extract this quantity is to measure branching fractions for such decays [3]. Experimentally, the principal challenge is to separate the rare B → X u ℓν decays from the approximately 50 times larger B → X c ℓν background. Given that the u quark is much lighter than the c quark, regions of phase space can be defined where the background is suppressed. To relate the decay rate of the B meson to |V ub |, parton level calculations have to be corrected for perturbative and non-perturbative QCD effects. A variety of QCD calculations are available to determine these corrections [4][5][6].
In this letter, we present a measurement of partial branching fractions for inclusive charmless semileptonic decays, B → X u ℓν [7]. Υ (4S) → BB events are tagged by the full reconstruction of a hadronic decay of one of the B mesons (B reco ). The semileptonic decay of the second B meson (B recoil ) is identified by the presence of an electron or a muon. This technique results in a low event selection efficiency but allows the determination of the momentum, charge, and flavor of the B mesons.
We use three kinematic variables to separate B → X u ℓν decays from the dominant B → X c ℓν background: M X , the invariant mass of the hadronic system X u,c ; q 2 , the invariant mass squared of the lepton-neutrino system; and P + ≡ E X − | P X | [4,5], where E X and P X are the energy and momentum of the hadronic system X u,c calculated in the B rest frame. We measure the fraction of partial rates of charmless semileptonic decays ∆R u/sl = ∆B(B → X u ℓν)/B(B → Xℓν) in restricted phase space regions, corrected for resolution effects. The resulting partial branching fractions are used to calculate |V ub | following theoretical prescriptions.
The analysis uses a sample of 383 million Υ (4S) decays into BB pairs, corresponding to an integrated luminosity of 347.4 fb −1 , collected with the BABAR detector [8]. Charmless semileptonic B → X u ℓν decays are simulated as a combination of three-body decays (X u = π, η, η ′ , ρ, ω, . . .) [9] and decays to non-resonant hadronic final states X u [10]. The motion of the b quark inside the B meson is modeled with the shape function parametrization given in Ref. [10]. The simulation of the B → X c ℓν background uses an HQET parametrization of form factors for B → D * ℓν [11,12], and models for B → Dπℓν, D * πℓν [13], and for B → Dℓν, D * * ℓν [9]. The simulation of the hadronization is performed by Jetset7.4 [14]. We use GEANT4 [15] to simulate the detector response.
To reconstruct a large sample of hadronically decaying B mesons, B reco → D ( * ) Y ± are selected. Here, the system Y ± consists of hadrons with a total charge of ±1, composed of n 1 π ± n 2 K ± n 3 K 0 S n 4 π 0 , where n 1 + n 2 ≤ 5, n 3 ≤ 2, and n 4 ≤ 2. The kinematic consistency of B reco candidates is checked with two variables, Here √ s is the total energy in the Υ (4S) center of mass frame, and p B and E B denote the momentum and energy of the B reco candidate in the same frame. We require ∆E = 0 within three standard deviations as measured for each decay mode. For each of the B reco decay modes, the purity P is estimated using Monte Carlo (MC) simulation. P is defined as the ratio of signal over background events with m ES ≥ 5.27 GeV/c 2 . Only modes for which P exceeds 20% are used. On average, we reconstruct at least one B candidate in 0.3% (0.5%) of the B 0 B 0 (B + B − ) events. For events with more than one reconstructed B decay, the decay mode with the highest purity is selected.
We determine the number of B reco candidates from an unbinned maximum likelihood fit to the m ES distribution. The data are fit to the sum of three contributions: signal B reco decays, combinatorial background from BB events, and continuum (e + e − → qq, q = u, d, s, c) events. A Threshold function [16] is used to describe the combinatorial and continuum backgrounds. To obtain a good description of the signal m ES distribution, we adopt the modified Gaussian function used in Ref. [17], to account for energy losses of photons in the detector. Fits to the m ES distribution are shown in Fig. 1. Semileptonic decays B → Xℓν of the B recoil candidate are identified by an electron or muon with momentum, p * ℓ , defined in the B rest frame, greater than 1 GeV/c. For charged B reco candidates, we require the charge of the lepton to be consistent with a prompt semileptonic B decay. For neutral B reco candidates, both charge-flavor combinations are retained and the known average B 0 -B 0 mixing rate [18] is used to extract the prompt lepton yield. The hadronic system X in the decay B → Xℓν is reconstructed from charged tracks and energy depositions in the calorimeter that are not associated with the B reco candidate or the identified lepton. We reconstruct K 0 S by performing a mass-constrained fit to π + π − pairs with an invariant mass in the range 0.473-0.523 GeV/c 2 . The neutrino four-momentum p ν is estimated from the missing momentum four-vector p miss = p Υ (4S) −p Breco −p X −p ℓ , where all momenta are measured in the laboratory frame and p Υ (4S) refers to the Υ (4S) meson.
To select B → X u ℓν candidates we require exactly one charged lepton with p * ℓ > 1 GeV/c, charge conservation (Q X + Q ℓ + Q Breco = 0), and a missing mass consistent with zero (m 2 miss < 0.5 GeV 2 /c 4 ). These criteria suppress the dominant B → X c ℓν decays, many of which contain additional leptons or an undetected K 0 L meson. We suppress the B → D * ℓν background by reconstructing the low momentum π + from the D * + → D 0 π + decay. Since the momentum of the π + is almost collinear with the D * + momentum p D * + , we can approximate the D * + energy as E D * + ≃ m D * + × E π /145 MeV/c 2 . The neutrino mass m 2 veto = (p B −p D * + −p ℓ ) 2 is peaked at zero for background events. The requirement m 2 veto < −3 GeV 2 /c 4 reduces the B → D * ℓν background by about 36% while keeping more than 90% of signal events. We reject events with charged kaons or K 0 S in the B recoil to reduce the background from B → X c ℓν decays.
To extract the distribution in the variables M X , P + , and the combination of M X and q 2 , we perform fits to the B reco m ES distributions for subsamples of events in individual bins for each of the variables, and subsequently separate the signal from the combinatorial and continuum backgrounds for the three distributions. The resulting distributions are presented in Fig. 2. To reduce the systematic uncertainties in the derivation of the branching fractions we determine the ratios of the partial branching fractions to the total semileptonic branch-ing fraction. This is done for restricted regions of phase space, M X < 1.55 GeV/c 2 , P + < 0.66 GeV/c, and (M X < 1.7 GeV/c 2 , q 2 > 8.0 GeV 2 /c 4 ). Specifically we define this ratio as (1) where N u refers to the number of observed events, BG u to the estimated number of background events, and N out u to the signal events that migrate from outside the kinematic region into the signal region. They are determined by a χ 2 fit to the measured spectra with signal and background shapes determined from MC simulation. N sl = 181074 ± 706 and BG sl = 12185 ± 78 are the number of semileptonic events, extracted with a m ES fit, and the corresponding background, determined from simulation. The efficiency ǫ u sel denotes the fraction of selected B reco -tagged signal events with a high-energy lepton. The model-dependent efficiency ǫ u kin accounts for the loss of selected events generated in the kinematic region that migrate outside this region. The efficiency of the tag and lepton selection, ǫ t and ǫ ℓ , differ slightly for the signal and the semileptonic samples, due to differences in the lepton momentum distribution and the multiplicity of the recoiling B meson. To convert the ratio in Eq. 1 to partial branching fractions, we use the total semileptonic branching fraction, B(B → Xℓν ℓ ) = (10.75±0.15)% [18]. The resulting partial branching fractions for the three selected kinematic regions, along with parameters in Eq. 1, are listed in Table I. The statistical correlations between the M X and (M X ,q 2 ), P + analyses are 65%, 67%, 38% respectively.
We consider several sources of systematic uncertainties. Detector-related uncertainties take into account particle (e, µ, K) identification (efficiency, misidentification), charged particle tracking efficiency, photon reconstruction efficiency and K 0 L interactions. We estimate the uncertainty due to signal and background modeling. The uncertainty on the signal modeling are due to the modeling of exclusive charmless semileptonic decays and gluon splitting into ss-quark pairs. We also calculate the uncertainties due to the non-perturbative parameters and the functional form of the shape function. The background simulation depends on the B and D branching fractions and B → D * ℓν form factors; the corresponding systematic uncertainties are calculated by varying all these quantities within their experimental errors. We estimate the error due to m ES fits, coming from the uncertainty in the parameterization ansatz. Finally, we estimate the error due to MC statistics. The fractional contribution of each uncertainty is shown in Table II together with the total error.
The results of the partial branching fractions are translated into |V ub | in the context of recent QCD calculations [4][5][6], including estimates of theoretical uncertain-   ), and extracted |V ub | for the three kinematic cuts. The first uncertainty is statistical, the second systematic. For ∆B, the third uncertainty is due to the theoretical knowledge of the signal efficiency; for the |V ub | values, it comes from the the theoretical uncertainty on ∆ζ. For Ref. [4] we use the exponential parametrization of the shape function.
In summary, we have measured the branching fractions for inclusive charmless semileptonic B decays B → X u ℓν in three overlapping regions of phase space. Relying on theoretical predictions, we extract values for the CKM matrix element |V ub | from our measured ∆B.
We find that the determinations of |V ub | agree at 1 σ level in the BNLP framework for the M X and combined (M X ,q 2 ) analyses. The analysis based on P + differs from the two others at a 2.5 σ level, as indicated also by other experiments [21]. The M X analysis captures the largest portion of phase space and gives the most precise determination of |V ub |. Within their stated theoretical uncertainties, the results based on BLNP and DGE give consistent results. The result, based on the hadronic mass spectrum, supersedes our previously published measurement [3], reducing the relative uncertainty by 40%. These values are in good agreement with other inclusive |V ub | determinations and they are somewhat higher, though compatible, than the results based on exclusive charmless semileptonic decays [18]. We would like to thank the many theorists with whom we have had valuable discussions, in particular J. R. Andersen, E. Gardi, B. Lange, Z. Ligeti, M. Neubert and G. Paz. 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. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation. * Deceased † Now at Tel Aviv University, Tel Aviv, 69978, Israel ‡ Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy § Also with Università della Basilicata, Potenza, Italy ¶ Also with Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain