Measurement of the Branching Fraction and Photon Energy Moments of B->X_s gamma and A_{cp}(B->X_(s+d) gamma)

The photon spectrum in B ->X_s gamma decay, where X_s is any strange hadronic state, is studied using a data sample of 88.5 million e+e- ->Upsilon(4S) ->BBbar decays collected by the BaBar experiment at SLAC. The partial branching fraction, Delta B(B ->X_s gamma)=(3.67 +- 0.29(stat.) +- 0.34(sys.) +- 0.29(model)) times 10^-4, the first moment<E_gamma>=2.288 +- 0.025 +- 0.017 +- 0.015 GeV and the second moment<E_gamma^2>-<E_gamma>^2 =0.0328 +- 0.0040 +- 0.0023 +- 0.0036 GeV^2 are measured for the photon energy range 1.9 GeV<E_gamma<2.7 GeV. They are also measured for narrower E_gamma ranges. The moments are then fit to recent theoretical calculations to extract the Heavy Quark Expansion parameters, m_b and mu_pi^2, and to extrapolate the partial branching fraction to E_gamma>1.6 GeV. In addition, the direct CP asymmetry A_CP(B ->X_(s+d) gamma) is measured to be -0.110 +- 0.115(stat.) +- 0.017(sys.).

PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er In the Standard Model (SM) the radiative decay of the b quark, b → sγ, proceeds via a loop diagram, and is sensitive to possible new physics, with new heavy particles participating in the loop [1]. Next-to-leadingorder SM calculations for the branching fraction give B(B → X s γ) = (3.61 +0.37 −0.49 ) × 10 −4 (E γ > 1.6 GeV) [2], and calculations to higher order, which are expected to considerably decrease the uncertainty, are currently underway [3]. The shape of the photon energy spectrum, which is insensitive to non-SM physics [4], can be used to determine the Heavy Quark Expansion (HQE) parameters, m b and µ 2 π [5,6], related to the mass and momentum of the b quark within the B meson. These parameters can be used to reduce the error in the extraction of the CKM matrix elements |V cb | and |V ub | from semi-leptonic B-meson decays [7]. New physics can also significantly enhance the direct CP asymmetry for b → sγ and b → dγ decay [2], A CP = Γ(b→sγ+b→dγ)−Γ(b→sγ+b→dγ) Γ(b→sγ+b→dγ)+Γ(b→sγ+b→dγ) which is ≈ 10 −9 in the SM [8]. Measurements of this joint asymmetry complement those of A CP in b → sγ [9] to constrain new physics models.
This letter reports on a fully-inclusive analysis of B → X s γ decays collected from e + e − → Υ (4S) → BB, where the photon from the decay of one B meson is measured, but the X s is not reconstructed. This avoids incurring large uncertainties from the modeling of the X s fragmentation, but at the cost of high backgrounds which need to be strongly suppressed. The principal backgrounds are from other BB decays containing a high energy photon and from continuum qq (q = udsc) and τ + τ − events. The continuum background, including a contribution from initial state radiation (ISR), is suppressed principally by requiring a high-momentum lepton from the non-signal B decay, and also by discriminating against its more jet-like topology. The BB background to high energy photons, dominated by π 0 and η decays, is reduced by vetoing on reconstructed π 0 or η. The residual continuum background is subtracted using off-resonance data taken at a center-of-mass energy 40 MeV below that of the Υ (4S), while the remaining BB background is estimated using a Monte Carlo simulation which has been checked and corrected using data control samples. Previous inclusive measurements of B → X s γ have been presented by the CLEO [10], BELLE [11] and BABAR [12] collaborations using alternative techniques which incur different systematic uncertainties.
The results presented are based on data collected with the BABAR detector [13] at the PEP-II asymmetricenergy e + e − collider located at the Stanford Linear Accelerator Center. The on-resonance integrated luminosity is 81.5 fb −1 , corresponding to 88.5 million BB events. Additionally, 9.6 fb −1 of off-resonance data are used in the continuum background subtraction. The BABAR Monte Carlo simulation program, based on GEANT4 [14], EVTGEN [15] and JETSET [16], is used to generate samples of B + B − and B 0 B 0 (excluding signal channels), qq, τ + τ − , and signal events. The signal models used to calculate efficiencies are based on references [5] ("kinetic scheme") and [6] ("shape function scheme") and on an earlier calculation [4]("KN"). These predictions approximate the X s resonance structure with a smooth distribution in m Xs . This is reasonable except at the lowest masses where the K * (892) dominates the spectrum. Hence the portion of the m Xs spectrum below 1.1 GeV/c 2 is replaced by a Breit-Wigner K * (892) distribution. The analysis was done "blind" in the range of reconstructed photon energy E * γ from 1.9 to 2.9 GeV (asterisk denotes the Υ (4S) rest frame); that is, the onresonance data were not looked at until all selection requirements were set and the corrected backgrounds determined. The signal range is limited by high BB backgrounds at low E * γ . The event selection begins by finding at least one photon candidate with, 1.6 < E * γ < 3.4 GeV, in the event. A photon candidate is a localized electromagnetic calorimeter energy deposit with a lateral profile consistent with that of a single photon. It is required to be isolated by 25 cm from any other energy deposit and to be well contained in the calorimeter (−0.74 < cos θ γ < 0.93), where θ γ is the polar angle with respect to the beam-axis. Photons that are consistent with originating from an identifiable π 0 or η → γγ decay are vetoed. Hadronic events are selected by requiring at least three reconstructed charged particles and the normalized second Fox-Wolfram moment R * 2 to be less than 0.55. To reduce radiative Bhabha and two-photon backgrounds, the number of charged particles plus half the number of photons with energy above 0.08 GeV is required to be ≥ 4.5.
Event shape variables are used to exploit the difference in topology of isotropic BB events and jet-like continuum events. This is accomplished by the R * 2 requirement as well as a single linear discriminant formed from nineteen different variables. Eighteen of the quantities are the sum of charged and neutral energy found in 10-degree cones (from 0 to 180 degrees) centered on the photon candidate direction; the photon energy is not included. Additionally the discriminant includes R ′ 2 /R * 2 , where R ′ 2 is the normalized second Fox-Wolfram moment calculated in the frame recoiling against the photon, which for ISR events is the qq rest frame. The discriminant coefficients were determined by maximizing the separation power between simulated signal and continuum events.
Lepton tagging further reduces the backgrounds from continuum events. About 20% of B mesons decay semileptonically to either e or µ. Leptons from hadron decays in continuum events tend to be at lower momentum. Since the tag lepton comes from the recoiling B meson, it does not compromise the inclusiveness of the B → X s γ selection. The tag lepton is required to have momentum p * e > 1.25 GeV/c for electrons and p * µ > 1.5 GeV/c for muons. Additionally requiring the photon-lepton angle, cos θ * γℓ > −0.7 removes more continuum background, in which the lepton and photon candidates tend to be backto-back. Finally the presence of a relatively high-energy neutrino in semi-leptonic B decays is exploited by requiring the missing energy of the event, E * miss > 0.8 GeV/c. Virtually all of the tagging leptons arise from the decay B → X c ℓν. The rate of such events in the simulation is corrected as a function of lepton momentum [17].
The event selection is chosen to maximize the statistical significance of the expected signal using simulated signal (KN with m b =4.80 GeV/c 2 , µ 2 π = 0.30 GeV 2 ) and background events, allowing for the low statistics of the off-resonance data used for the subtraction of continuum background. After selection the low energy range, 1.6 < E * γ < 1.9 GeV, is dominated by the BB background, while the high energy range, 2.9 < E * γ < 3.4 GeV, is dominated by the continuum background; they provide control regions for the BB subtraction and continuum subtraction, respectively. The signal region lies between 1.9 GeV and 2.7 GeV. The signal efficiency (≈ 1.6% for this E * γ range) depends on E * γ and the signal model, but has negligible dependence on the details of the fragmentation of the X s .
The BB background is estimated with the simulated BB data set. It consists predominantly of photons originating from π 0 or η decays (≈ 80%). Other significant sources are n's which fake photons by annihilating in the calorimeter and electrons that are misreconstructed or lost, or that undergo hard Bremsstrahlung. The π 0 (η) background simulation is compared to data by using the same selection criteria as for B → X s γ but removing the π 0 (η) vetos. The photon energy and lepton momentum thresholds are relaxed to E * γ > 1.0 GeV, p * e > 1.0 GeV/c, p * µ > 1.1 GeV/c to gain statistics. The yields of π 0 (η) are measured in bins of E * π 0 (η) by fitting the γγ mass distributions in on-resonance data, off-resonance data and simulated BB background. Correction factors to the π 0 (η) components of the BB simulation are derived from these yields, including a small adjustment for the different efficiencies of the π 0 (η) vetoes between data and simulation. As no n control sample could be isolated, this source of BB background is corrected by comparing in data and simulation the inclusive p yields in B decay and the calorimeter response to p's, using a Λ → pπ + sample. The electron component of the BB simulation is corrected with electrons from a Bhabha data sample, taking into account the lower track multiplicity of these events compared to the signal events. Finally, the small contributions from ω and η ′ decays are corrected using inclusive B decay data. After including all corrections and systematic errors the expected background yield from the simulation in the BB control region (1.6 < E * γ < 1.9 GeV) is 1667 ± 54 events, compared to 1790 ± 64 events observed in data after continuum subtraction. Note that a small contribution in this region from the expected signal (≈ 20 to 40 events) has been neglected in this comparison. In the high energy control region 2.9 < E * γ < 3.4 GeV the expected background is 390 ± 20 events, compared to 393 ± 58 events observed in data.

Eγ (GeV) ∆B(B → Xsγ) (10 −4 )
Eγ (GeV) E 2 γ − Eγ 2 (GeV 2 ) 1.9 to 2.7 3.67 ± 0.29 ± 0.34 ± 0.29 2.288 ± 0.025 ± 0.017 ± 0.015 0.0328 ± 0.0040 ± 0.0023 ± 0.0036 2.0 to 2.7 3.41 ± 0.27 ± 0.29 ± 0.23 2.316 ± 0.016 ± 0.010 ± 0.013 0.0266 ± 0.0026 ± 0.0010 ± 0.0020 2.1 to 2.7 2.97 ± 0.24 ± 0.25 ± 0.17 2.355 ± 0.014 ± 0.007 ± 0.011 0.0191 ± 0.0019 ± 0.0006 ± 0.0015 2.2 to 2.7 2.42 ± 0.21 ± 0.20 ± 0.13 2.407 ± 0.012 ± 0.005 ± 0.008 0.0116 ± 0.0014 ± 0.0004 ± 0.0005 control regions after the BB and continuum backgrounds have been subtracted. To extract partial branching fractions (PBFs) and first and second moments from this spectrum it is necessary to first correct for efficiency. Theoretical predictions are made for the true E γ in the B meson rest frame, whereas the experimental measurements are made with reconstructed E * γ in the Υ (4S) frame. Hence it is also necessary to correct for smearing due to the asymmetric calorimeter resolution and the Doppler shift between the Υ (4S) frame and the B rest frame. The efficiency and smearing corrections depend upon the assumed signal model (underlying theory and parameter values). In a broad selection of signal models it is found that the efficiency for each E * γ range has a model-independent linear relationship to the mean E * γ in that range. Hence a nominal signal model is chosen for which the mean matches the data, and a model-dependence uncertainty is assigned to the PBFs and moments based on signal models within one (statistical and systematic) standard deviation of the measured mean E * γ . To correct for resolution smearing a small multiplicative correction to the PBF and small additive corrections to the first and second moments are computed using the nominal signal model, and an uncertainty assigned based on a conservative range of models. The model-dependence uncertainty from the smearing correction is fully correlated with the corresponding uncertainty of the efficiency correction.
The results for four energy ranges are given in Table 1 along with the statistical, systematic and model errors. The PBFs have been corrected to exclude a (4.0 ± 0.4)% [2,18] contribution from b → dγ. The systematic errors are described below and the associated correlation matrices are given in the appendix.
The most significant systematic uncertainty in the measurement of the spectrum is from the uncertainty in the corrections to the BB background simulation. It is due mostly to the statistical uncertainty on the correction factors derived from the π 0 (η) control sample. The BB corrections depend on E * γ ; the resulting correlations between the 100 MeV E * γ bins have been taken into account in the computation of the total systematic uncertainty in the PBFs and moments. For example, for 2.0 GeV < E γ < 2.7 GeV, the BB corrections contribute 5.5% to a total systematic uncertainty of 8.5% of the PBF, and 0.008 GeV and 0.0009 GeV 2 of the total systematic uncertainty of the first and second moments, respectively. Additional contributions to the PBF uncertainty (added in quadrature), all energy-independent, come from the photon selection (3.3%) due to the photon efficiency, determined with π 0 's from τ decay, and the isolation requirement, calorimeter energy scale and resolution, determined from B → K * γ decays and photons from virtual Compton scattering; efficiency of the event shape variable selection (3%), determined from a π 0 control sample; the semi-leptonic corrections (3%); lepton identification (2%) and the modeling of the X s fragmentation (1.5%). Additional uncertainties to the first and second moment, added in quadrature, come from the uncertainty in the calorimeter energy scale (0.006 GeV) and resolution (0.0004 GeV 2 ), respectively.
The parameters m b and µ 2 π , which are defined differently in the kinetic (K) and shape function (SF) schemes, can be extracted by fitting theoretical predictions to the measured moments. The first moments for E γ > 1.9 and 2.0 GeV and the second moment for E γ > 2.0 GeV are fitted, taking into account the correlations between the measured moments. As the moments are dependent on the assumed signal model due to the efficiency and resolution smearing corrections, the signal model and the model-dependence errors are adjusted based on the results of the fit and the moments are recomputed and refit. Only a few iterations are required until the result is stable. In the kinetic scheme m b(K) = 4.44 +0.08+0.12 −0.07−0.14 GeV/c 2 and µ 2 π(K) = 0.64 +0.13+0.23 −0.12−0.24 GeV 2 , with a correlation of −0.93. The first error is due to the uncertainty in the measured moments and the second error is due to uncertainty in the theoretical calculations [5]. In the shape function scheme, using the exponential shape function form [6], m b(SF ) = 4.43 +0.07 −0.08 GeV/c 2 and µ 2 π(SF ) = 0.44 +0.06 −0.07 GeV 2 , with a correlation of −0.63. If the Gaussian shape function form were used, m b(SF ) and µ 2 π(SF ) would increase by 0.13 GeV/c 2 and 0.01 GeV 2 , respectively. The spectra with the fitted parameters are compared to data in figure 1. These results (without theory error) are then used to extrapolate the measured partial branching fraction from E γ > 1.9 GeV to 1.6 GeV to allow comparisons to theoretical predictions. In the kinetic scheme B(B → X s γ, E γ > 1.6 GeV) = (3.94 ± 0.31 ± 0.36 ± 0.21) × 10 −4 and in the shape function scheme B(B → X s γ, E γ > 1.6 GeV) = (4.79 ± 0.38 ± 0.44 +0.73 −0.47 ) × 10 −4 , where the errors are statistical, systematic and model-dependence. The model-dependence is derived from the 1σ error ellipse for the m b -µ 2 π fit. The central value in the shape function scheme is reduced to 4.55 × 10 −4 if the Gaussian form is used.
Finally the sample is divided into b and b decays using the charge of the lepton tag to measure A CP (B → X s+d γ) = N + −N − N + +N − 1 1−2ω where N +(−) are the positively (negatively) tagged signal yields and 1/(1 − 2ω) is the dilution factor due to the mistag fraction ω. A requirement 2.2 < E * γ < 2.7 GeV maximizes the statistical precision of the measurement as determined from simulated data. The yields are N + = 349 ± 48 and N − = 409 ± 45. The bias on A CP due to any charge asymmetry in the detector or BB background is measured to be −0.005±0.013 using control samples of e + e − → Xγ and B → Xπ 0 , η. The mistag fraction due to mixing is 9.3±0.2% [19]. An additional 2.6 ± 0.3% mistag fraction arises from leptons from D decay, π ± faking µ ± , γ conversions, π 0 Dalitz decay, and charmonium decay. After correcting for charge bias and dilution A CP = −0.110 ± 0.115(stat.) ± 0.017(syst.), including multiplicative systematic uncertainties from the BB background subtraction (5.4%) and the dilution factor (1.0%). The model-dependence uncertainty due to differences in the B → X s γ and B → X d γ spectra is estimated to be negligible.
In conclusion, the branching fraction and the energy moments of the photon spectrum in B → X s γ are measured for E γ > 1.9 GeV. The moments are consistent with previous measurements [10,11,12] and are used to extract values of m b and µ 2 π which are consistent with those extracted from semi-leptonic B decays [20]. These measurements have been used to reduce the systematic error in the estimation of |V cb | and |V ub | [7]. The measured branching fractions are in agreement with the SM expectation and previous measurements. The measured A CP is also consistent with the SM expectation.
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