Measurement of the Branching Fraction of Upsilon(4S) -->B0B0bar

We report the first measurement of the branching fraction f00 for Upsilon(4S) -->B0B0bar. The data sample consists of 81.7 fb^-1 collected at the Upsilon(4S) resonance with the BABAR detector at the PEP-II asymmetric-energy e^+e^- storage ring. Using partial reconstruction of the decay B0bar -->D^{*+} \ell^{-} \bar{\nu}_{\ell} in which only the charged lepton and the soft pion from the decay D^{*+} -->D0 pi^+ are reconstructed, we obtain f00 = 0.487 \pm 0.010(stat) \pm 0.008(sys). Our result does not depend on the branching fractions of B0bar -->D^{*+} \ell^{-} \bar{\nu}_{\ell} and D^{*+} -->D0 pi^+ decays, on the ratio of the charged and neutral B meson lifetimes, nor on the assumption of isospin symmetry.

We report the first measurement of the branching fraction f00 for Υ (4S) → B 0 B 0 . The data sample consists of 81.7 fb −1 collected at the Υ (4S) resonance with the BABAR detector at the PEP-II asymmetric-energy e + e − storage ring. Using partial reconstruction of the decay B 0 → D * + ℓ −ν ℓ in which only the charged lepton and the soft pion from the decay D * + → D 0 π + are reconstructed, we obtain f00 = 0.487 ± 0.010(stat) ± 0.008(sys). Our result does not depend on the branching fractions of B 0 → D * + ℓ −ν ℓ and D * + → D 0 π + decays, on the ratio of the charged and neutral B meson lifetimes, nor on the assumption of isospin symmetry.
PACS numbers: 14.40.Nd,13.20.He Isospin violation in the decay Υ (4S) → BB will lead to a difference between the branching fractions f 00 ≡ B(Υ (4S) → B 0 B 0 ) and f +− ≡ B(Υ (4S) → B + B − ). Predictions for the ratio R +/0 ≡ f +− /f 00 range from 1.03 to 1.25 [1]. Measurements of R +/0 [2,3,4,5,6] have been made assuming isospin symmetry in specific decay rates and resulting in an average value of 1.006±0.039 [7], consistent with isospin conservation in Υ (4S) decays to BB. To date no measurement has been made of either f 00 or f +− . In this paper we report the first direct measurement of f 00 . It is completely independent of the previous measurements of R +/0 . Independent measurements of f 00 and R +/0 can be used to constrain the Υ (4S) → non-BB fraction. The f 00 value is important for measuring absolute Υ (4S) branching fractions and for measuring V cb , the Cabibbo-Kobayashi-Maskawa matrix element.
The data sample used in this analysis consists of 81.7 fb −1 collected at the Υ (4S) resonance (on-resonance) and 9.6 fb −1 collected 40 MeV below the resonance (offresonance). The on-resonance data sample has a mean energy of 10.580 GeV and an energy rms spread of 4.6 MeV. Due to the small spread, any plausible energy dependence of f 00 has a negligible effect on the central value. A simulated sample of BB with integrated luminosity equivalent to approximately three times the data is used for background studies.
A detailed description of the BABAR detector and the algorithms used for track reconstruction and particle identification is provided elsewhere [8]. A brief summary is given here. High-momentum particles are reconstructed by matching hits in the silicon vertex tracker (SVT) with track elements in the drift chamber (DCH). Lower momentum tracks, which do not leave signals on many wires in the DCH due to the bending induced by a magnetic field, are reconstructed in the SVT alone. Electrons are identified by the ratio of the track momentum to the associated energy deposited in the calorimeter (EMC), the transverse profile of the shower, the energy loss in the drift chamber, and information from a Cherenkov detector (DIRC). Muons are identified in the instrumented flux return (IFR), composed of resistive plate chambers and layers of iron. Muon candidates are required to have a path length and hit distribution in the IFR and energy deposition in the EMC consis-tent with that expected for a minimum-ionizing particle. The BABAR detector Monte Carlo simulation is based on GEANT4 [9].
We select the decays B 0 → D * + ℓ −ν ℓ , D * + → D 0 π + (ℓ = e, µ). The inclusion of charge-conjugate reactions is implied throughout this paper. The sample of events in which at least one B 0 → D * + ℓ −ν ℓ candidate decay is found is labeled the "single-tag sample". The number of signal decays in this sample is where N BB is the total number of BB events in the data sample and ε s is the reconstruction efficiency for B 0 → D * + ℓ −ν ℓ . We determine N BB = 88.7 million events by counting the number of hadronic decays in the onresonance data and subtracting the e + e − → qq (q = u, d, s, or c quark) component using off-resonance data, as described in detail in Ref. [10]. The error in N BB is 1.1% and is dominated by systematic uncertainties. We attribute all BB pairs to Υ (4S) decays. The number of signal events in the subset in which two B 0 → D * + ℓ −ν ℓ candidates are found is labeled the "double-tag sample". The number of such events is where ε d is the efficiency to reconstruct two B 0 → D * + ℓ −ν ℓ decays in the same event. From Eq. (1) and Eq. (2), f 00 is given by where we have defined C ≡ ε d /ε 2 s . The value of C is 1 if the efficiencies for detecting each B meson are uncorrelated in double-tag events, which, given the pseudoscalar nature of B mesons and the proximity of the Υ (4S) to the BB threshold, is expected. Using the Monte Carlo simulation we determine C = 0.995 ± 0.008, where the error is due to the finite size of the simulated sample.
No attempt is made to reconstruct the D 0 , resulting in a high reconstruction efficiency.
The B 0 decay point is determined from a vertex fit of the soft-pion and lepton tracks, with the vertex constrained to the beam spot position in the x− y plane. We only use events with vertex-fit probability, P V , greater than 0.1% to optimize a signal-to-background ratio.
We select hadronic events by requiring at least four charged particle tracks reconstructed in the SVT and the DCH. To reduce non-BB background, the ratio of the second to the zeroth Fox-Wolfram moments [14], R 2 = H 2 /H 0 , is required to be less than 0.5.
To suppress leptons from charm decays, all lepton candidates are required to have momenta between 1.5 GeV/c and 2.5 GeV/c in the e + e − center-of-mass frame. Soft pion candidates are required to have center-of-mass momenta between 60 MeV/c and 200 MeV/c. As a consequence of the limited phase space available in the D * + decay, the soft pion is emitted nearly at rest in the D * + rest frame. The D * + four-momentum can therefore be computed by approximating its direction as that of the soft pion, and parameterizing its momentum as a linear function of the soft-pion momentum, with parameters obtained from a Monte Carlo simulation. The presence of an undetected neutrino is inferred from conservation of momentum and energy. The neutrino invariant mass squared is calculated as where E beam is half the center-of-mass energy and E ℓ (E D * ) and p ℓ (p D * ) are the center-of-mass energy and momentum of the lepton (the D * meson). We set p B = 0, which introduces a negligible spread in M 2 compared with the approximation of the D * momentum based on the soft pion. For signal decays that are properly reconstructed, the M 2 distribution peaks near zero. Background events, however, are spread over a wide range of M 2 values. We define a signal region (M 2 > −2 GeV 2 /c 4 ) and a sideband region (−8 < M 2 < −4 GeV 2 /c 4 ). We use the symbol M 2 s to denote M 2 for any candidate in the single-tag sample. In the double-tag sample, we randomly choose one of the two reconstructed B 0 → D * + ℓ −ν ℓ candidates as "first" and the other as "second". Their M 2 values are labeled M 2 1 and M 2 2 , respectively. We require that M 2 1 fall in the signal region. The single-tag and double-tag samples have several types of background: continuum, combinatorial BB, and peaking BB. The combinatorial BB background originates from random combinations of reconstructed leptons and soft pions. The peaking BB background is composed of B → D * πℓν ℓ decays with or without an excited charmed resonance D * * [15], where the reconstructed soft pion comes from the decay D * + → D 0 π + , leading to an accumulation of these events at high values of M 2 . The peaking BB background is suppressed by the requirement p ℓ > 1.5 GeV/c on the lepton center-of-mass momentum. Such events have an M 2 distribution that is different from the signal, allowing us to extract their contribution in the signal region.
The double-tag sample contains two additional types of background: events in which the first candidate is combinatorial background and the second is signal (called M 2 1 -combinatorial background) and events in which the first candidate is peaking background and the second is signal (called M 2 1 -peaking background). To determine N s and N d , we perform binned χ 2 fits to one-dimensional histograms of the M 2 s and M 2 2 distributions of on-resonance data events, ranging from −8 to 2 GeV 2 /c 4 . Before fitting, we subtract the continuum background contribution from the histograms. This is determined using the M 2 s and M 2 2 distributions of offresonance data, scaled to account for the ratio of onresonance to off-resonance luminosities and the centerof-mass energy dependence of the continuum production cross-section. In addition, the contributions of the M 2 1combinatorial (3%) and M 2 1 -peaking (1%) backgrounds are subtracted from the M 2 2 histogram before doing the fit. The contribution of the M 2 1 -combinatorial background is determined from sideband data. The M 2 1peaking background is determined with simulated events.
After the subtraction, the M 2 s and M 2 2 histograms are fit separately, to a function whose value for bin j of the histogram is where N t is the number of events of type t (t = signal, combinatorial, peaking) populating the histogram, and P t j is the bin j value of a discrete probability density function (PDF) obtained from simulated events of type t, normalized such that j P t j = 1. The fit determines the parameters N t by minimizing where H j is the number of entries in bin j of the data histogram being fit; σ Hj is the statistical error on H j , including uncertainties due to the background subtractions described above; and σ fj is the error on f j , determined from the errors on P t j , which are due to the finite size of the simulated sample.
The results of the fits are presented in Table I. The M 2 s and M 2 2 distributions are shown in Fig. 1. The fits yield N s = 786200 ± 1900 (Confidence Level (C.L.)= 11%) and N d = 3560 ± 70 (C.L. = 82%). Equation (3) then gives f 00 = 0.487 ± 0.010, where the error is due to data statistics.
To determine how well the simulation reproduces the M 2 s and M 2 2 distributions for the combinatorial background in the data, we study the distributions for a sample of same-charge candidates, in which the lepton and soft pion have the same electric charge. We fit the continuum-subtracted M 2 s and M 2 2 histograms of the same-charge sample using the function f ′ j = N P ′ j , where P ′ j is the bin j value of the PDF of same-charge simulated BB events, normalized such that j P ′ j = 1, and the parameter N is determined by the fit. The histograms, overlaid with the fit function, are shown in Fig. 2. The accumulated differences D ≡ j (H ′ j − f ′ j ) between the same-charge data histograms H ′ j and the fit functions are summarized in Table II. Their consistency with zero indicates that the distributions of simulated combinatorial BB background events do not lead to significant fake signal yields. Nevertheless, we evaluate a systematic uncertainty on the modeling of the combinatorial background based on the observed difference in the like-sign sample. We evaluate the absolute systematic uncertainties in f 00 due to the M 2 1 -combinatorial subtraction (0.0005), the M 2 1 -peaking background (0.0005), the value of C due to the track multiplicity dependence of the efficiency (0.0015), the finite size of the simulated sample (0.002), the same-charge sample (0.0025), the impact of a possible contribution of non-BB decays of the Υ (4S) [16] (0.0025), the peaking background composition (0.004), and the total number of BB, N BB (0.0055).
The dominant contribution to the systematic error comes from a 1.1% systematic uncertainty in N BB , due mainly to the uncertainty in the tracking efficiency. The peaking BB background is estimated from the simulated sample containing all D * * resonances and non-resonant events. We vary the ratio of the branching fraction of the resonant and the non-resonant production such that the variation of this ratio is wide enough to include poorly known decays. We repeat the analysis procedure to determine N s and N d . The uncertainties due to the lepton and soft-pion momentum spectra are negligible. We combine the uncertainties given above in quadrature to determine an absolute systematic error of 0.008 for f 00 .
In summary, we use a partial reconstruction of the decay B 0 → D * + ℓ −ν ℓ to obtain the result f 00 = 0.487 ± 0.010(stat) ± 0.008(sys), where the first error is statistical and the second is systematic. This result is the first, precise, and direct measurement of f 00 . Since this measurement is made by comparing the numbers of events with one and two reconstructed B 0 → D * + ℓ −ν ℓ decays, it does not depend on branching fractions of B 0 → D * + ℓ −ν ℓ and D * + → D 0 π + decays, on the ratio of the charged and neutral B meson lifetimes, nor on the assumption of isospin symmetry. By combining our f 00 result with the world average of R +/0 noted in the introduction, we add the errors quadratically to obtain f +− = 0.490 ± 0.023. Thus we find the fraction of Υ (4S) → non-BB to be 1 − f 00 − f +− = 0.023 ± 0.032. If f 00 + f +− = 1, our f 00 result can be averaged with R +/0 [7] to yield f 00 = 0.494±0.008, f +− = 0.506±0.008, and f +− /f 00 = 1.023 ± 0.032. This value of f +− /f 00 is in good agreement with isospin conservation in Υ (4S) → BB within errors.
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