Measurements of B -->{pi, eta, eta'} l nu Branching Fractions and Determination of |Vub| with Semileptonically Tagged B Mesons

We report measurements of branching fractions for the decays B -->P l nu, where P are the pseudoscalar charmless mesons pi-, pi0, eta and eta', based on 348 fb-1 of data collected with the BABAR detector, using B0 and B+ mesons found in the recoil of a second B meson decaying as B -->D(*) l nu. Assuming isospin symmetry, we combine pionic branching fractions to obtain B(B0 -->pi- l+ nu) = (1.54 +/- 0.17(stat) +/- 0.09(syst)) x 10-4; we find 3.2 sigma evidence of the decay B+ -->eta l+ nu and measure its branching fraction to be (0.64 +/- 0.20 (stat) +/- 0.03 (syst)) x 10-4, and determine B(B+ -->eta' l+ nu)<0.47 x 10-4 to 90% confidence level. Using partial branching fractions for the pionic decays in ranges of the momentum transfer and a recent form factor calculation, we obtain the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub| = (4.0 +/- 0.5(stat) +/- 0.2(syst) +0.7-0.5(theory)) x 10-3.

We use a sample of 383 million BB pairs, corresponding to an integrated luminosity of 348 fb −1 recorded on the Υ(4S) resonance by the BABAR detector at the PEP-II asymmetric-energy e + e − storage rings. The BABAR detector provides neutral and charged particle reconstruction and charged particle identification, and is described in detail elsewhere [7]. We also use a detailed Monte Carlo simulation (MC) [8] to estimate signal efficiency and signal and background distributions.
We tag B mesons decaying as B → D ( * ) ℓν ℓ through the full hadronic reconstruction of D ± and D 0 mesons; D 0 mesons are reconstructed through K − π + , K − π + π + π − , K − π + π 0 and K 0 S π + π − decays, and D + mesons through K − π + π + and K 0 S π + decays; K 0 S candidates are reconstructed as K 0 S → π + π − ; and neutral pions are reconstructed as π 0 → γγ with the requirement 115 ≤ m γγ ≤ 150 MeV/c 2 . Masses of D candidates are required to be within 2.3σ of their nominal value, where the mass resolution σ ranges between 5.7 and 19.1 MeV/c 2 , depending on the decay channel; we also use a "sideband" sample of D candidates with reconstructed mass in a range (typically 4σ to 7σ) off the appropriate nominal mass. We require charged daughters of the D candidate to originate from a common vertex. We reconstruct D * + mesons as D 0 π + and D + π 0 and D * 0 mesons as D 0 π 0 and D 0 γ. The mass difference between the D * candidate and its D daughter must be within 3.7σ of its nominal value; the resolution σ of this difference ranges between 0.9 and 5.7 MeV/c 2 , depending on the decay mode.
Candidate D ( * ) mesons are paired with tracks identi-fied as leptons with absolute momentum | p ℓ | ≥ 0.8 GeV/c [9]. If a D candidate (its daughter kaon) is charged, it is required have charge opposite to (same as) that of the corresponding lepton. The Y ≡ D * ℓ system is required to have invariant mass m Y ≥ 3 GeV/c 2 and originate from a common vertex. Photons consistent with originating from bremsstrahlung from this lepton or the decay D ( * ) → Dγ(γ) are added to the Y system. Assuming that the B → Y ν decay hypothesis is correct, the angle θ BY between the directions of the (measured) Y and its parent B is described by where E B , m B and | p B | (E Y , m Y and | p Y |) are the energy, mass and absolute momentum of the B meson (Y system); for the B meson, these are inferred from initial beam energies. If the B → Y ν hypothesis is correct, we have | cos θ BY | ≤ 1 up to resolution; because cos θ BY is strongly correlated with our discriminating variable cos 2 φ B , we impose the loose requirement that | cos θ BY | ≤ 5.
To suppress background from non-BB events, we reject events for which the ratio of the second and zeroth Fox-Wolfram moments [10] is greater than 0.5. We also reject events containing lepton pairs kinematically and geometrically consistent with having originated from the decay of a J/ψ meson. We reject D ( * ) ℓ candidates for which the event contains any K 0 S → π + π − candidates not overlapping this D ( * ) ℓ system. We require exactly one additional lepton with absolute momentum | p ℓ | ≥ 0.8 GeV/c in the event. If the two leptons are an e + e − pair, we require them not to be consistent with originating from γ → e + e − conversion. This second lepton is paired with remaining tracks (assumed to be pions), neutral pions and photons in the event to form B → P ℓν ℓ candidates, where P is one of the mesons π ± , π 0 , η or η ′ . For B → π ± ℓν ℓ candidates, the lepton and pion are required to have opposite charge. B → π 0 ℓν ℓ candidates are subject to the additional requirement | p π 0 |+| p ℓ | ≥ 2.6 GeV/c, where | p π 0 | is the absolute momentum of this π 0 candidate. For B → ηℓν ℓ candidates, η mesons are reconstructed through decays to γγ, π + π − π 0 and π 0 π 0 π 0 , with invariant mass requirements 500 ≤ m γγ ≤ 570, 530 ≤ m πππ ≤ 560 MeV/c 2 . Charged pions from η → π + π − π 0 decays are required to come from a common vertex; the π 0 candidates are required to have absolute laboratory frame momentum greater than 280 MeV/c (180 MeV/c) when coming from π + π − π 0 (π 0 π 0 π 0 ) candidates. The η ′ meson in B → η ′ ℓν ℓ decays is reconstructed through its decay η ′ → ηπ + π − with the η candidate selected as above; the additional pions are required to originate from a common vertex, and the ηπ + π − system is required to have invariant mass between 920 and 970 MeV/c 2 . For B ± decays (P = π 0 ,η, η ′ ), the leptons in an event are required to have opposite charge.
We define the X as a charmless meson π ± , π 0 , η or η ′ and corresponding lepton (including photons consistent with having originated from bremsstrahlung from it); θ BX is defined analogously to θ BY ; we require | cos θ BX | ≤ 5. For each D ( * ) ℓ-P ℓ candidate, we require that there be no additional tracks in the event and, for hypothesized B 0 B 0 (B + B − ) events, at most 140 MeV (70 MeV) of neutral energy (i.e., photon candidates) not associated with the D ( * ) ℓ or P ℓ candidates. In the case that more than one D ( * ) ℓ-P ℓ pair fulfills all requirements for a given event and P mode, the candidate is chosen by smallest | cos θ BY |, then by largest absolute P momentum. Signal events containing accepted D ( * ) ℓ-P ℓ candidates have, on average, between 1.15 and 1.39 of them, depending on P .
Signal yield is extracted independently for each P ; while we implicitly allow an event to be reconstructed in multiple P modes, we find the induced pairwise statistical correlations between our measured branching fractions to be negligible. The signal yield is extracted through the quantity cos 2 φ B , where φ B is the angle between the direction of either B and the plane containing the X and Y momenta: where γ is the angle between the X and Y momenta. For correctly reconstructed signal events, we have cos 2 φ B ≤ 1 up to resolution.
For a B → P ℓν ℓ decay, q 2 is defined as the squared invariant mass of the lepton-neutrino system, and is calculated in the approximation that the B is at rest, i.e., q 2 = (m B − E P ) 2 − | p P | 2 , where E P and p P are, respectively, the energy and momentum of the P meson. The data are divided into three bins: q 2 < 8, 8 ≤ q 2 < 16 and q 2 ≥ 16 GeV 2 /c 2 , in each of which the yield is extracted separately, except in the B + → η ′ ℓ + ν ℓ mode, in which, due to a lower reconstruction efficiency, the yield is measured in a q 2 < 16 GeV 2 /c 2 bin and over the full q 2 range. The data is described as a sum of three contributions, dN/d cos 2 φ B = N sig P sig + N bg P bg + N cmb P cmb , where these N i and P i are the yield and probability density functions (PDF) of: signal ("sig"), background with correctly reconstructed D 0,± mesons ("bg") and backgrounds with combinatoric D 0,± candidates ("cmb").
filled and hollow circles represent D mass peak and sideband data, respectively. The curves are stacked fit results for "cmb" (dotted), "bg" (dashed) and "sig" (solid) PDFs, as defined in the text. The fits are performed in bins of q 2 but are here shown in the full q 2 range.
The signal PDF, P sig , is modeled as a threshold function (constant between zero and unity, vanishing elsewhere) with finite resolution and an exponential tail (four parameters). The correct D background PDF, P bg , is modeled as an exponential with a nonnegative constant term (two parameters); the combinatoric D background, P cmb , is modeled by a second order polynomial (two parameters). These eight PDF shape parameters and the P i are determined via simultaneous unbinned maximum likelihood fit (see Figure 1) of dN/d cos 2 φ B to the data, P sig to MC signal events, P bg to MC background events (with correctly identified D 0,± mesons) and P cmb to the sideband sample. The combinatoric yield N cmb is further constrained, up to statistical accuracy, by the number of events in the sideband sample. Total signal yields are found to be 150 ± 22, 134 ± 20, 55 ± 15 and 0.6 ± 3.9 events for π ± ℓν ℓ , π 0 ℓν ℓ , ηℓν ℓ and η ′ ℓν ℓ respectively.
The B → D ( * ) ℓν ℓ reconstruction efficiency is determined via an analogous cos 2 φ B study on "double tag" events, i.e., events reconstructed as BB with both B mesons decaying as B → D ( * ) ℓν ℓ . The B → P ℓν ℓ reconstruction efficiency for each q 2 bin is determined from the MC signal sample, as are bin-to-bin migrations due to the finite q 2 resolution, which are small (< 9%). Overall efficiencies, including branching fractions and reconstruction efficiency of the recoil B, are found, in units of 10 −3 , to be 1.4, 1.8, 1.1 and 0.22 for B → π ± ℓν ℓ , B → π 0 ℓν ℓ , B → ηℓν ℓ and B → η ′ ℓν ℓ respectively.
Systematic uncertainties associated with physics modeling are evaluated by determining the change in the measured branching fraction after varying independently in MC within current knowledge: B → {ρ, ω}ℓν ℓ branching fractions, B → π ±,0 ℓν ℓ branching fractions, B → η (′) ℓν ℓ branching fractions, the total B charmless semileptonic decay branching fraction, the B charmless semileptonic decay spectrum [11], B → P ℓν ℓ form factors (comparing the model by Ball and Zwicky [12] to that of Scora and Isgur [13]) and several B → Dℓν ℓ branching fractions; the largest is found to have an effect four times smaller than the statistical uncertainty. We also apply uncertainties derived from those on η and η ′ decay branching fractions.
We estimate the systematic uncertainty associated with the accuracy of BB background simulation by comparing the cos 2 φ B distributions in signal-depleted data and MC samples. From study of 37 fb −1 of e + e − collisions 40 MeV below the Υ(4S) resonance, we determine that there is no contribution from non-BB events to the signal; the precision to which this can be determined is also taken as a systemic uncertainty.
Final state radiation in B 0 → π − ℓ + ν ℓ decays is determined, from simulation, to cause q 2 bin migrations no greater than 1.2%, which is conservatively applied as a systematic uncertainty, as well as to the other branching fractions. We apply a 0.59% (1.7%) systematic uncertainty for B 0 B 0 (B + B − ) decays associated with the assumption that double tag events can be used to estimate the single tag efficiency reliably.
Extraction of |V ub | from the measured B → πℓν ℓ branching fractions ∆B proceeds through the relation |V ub | = ∆B/(τ B 0 ∆ζ), with τ B 0 = 1.530 ± 0.009 ps −1 the B 0 meson lifetime [15] and ∆ζ the calculated reduced (i.e., appropriately normalized) decay rate over the corresponding q 2 range, which depends on the decay form factor f π + . Several form factor calculations are available, including one using light-cone sum rules [12] and various lattice QCD methods [17,18,19]. Results are given in Table II. The branching fractions B(B → η (′) ℓν ℓ ) will provide additional means of determining |V ub | as accurate calculations of f η (′) + become available.