Study of B ->X gamma Decays and Determination of |V_td/V_ts|

Using a sample of 471 million BBbar events collected with the BaBar detector, we study the sum of seven exclusive final states B->X_s(d) gamma, where X_s(d) is a strange (non-strange) hadronic system with a mass of up to 2.0GeV/c^2. After correcting for unobserved decay modes, we obtain a branching fraction for b->d gamma of (9.2 +/- 2.0(stat.) +/- 2.3(syst.))x10^-6 in this mass range, and a branching fraction for b->s gamma of (23.0 +/- 0.8(stat.) +/- 3.0(syst.))x10^-5 in the same mass range. We find BF(b->dgamma) / BF(b->sgamma) = 0.040 +/- 0.009(stat.) +/- 0.010(syst.), from which we determine |V_td/V_ts|=0.199 +/- 0.022(stat.) +/- 0.024(syst.) +/- 0.002(th.).


PACS numbers:
The decays b → dγ and b → sγ are flavor-changing neutral current processes forbidden at tree level in the * Now at Temple University, Philadelphia, Pennsylvania 19122, USA † Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy ‡ Also with Università di Roma La Sapienza, I-00185 Roma, Italy § Now at University of South Alabama, Mobile, Alabama 36688, USA ¶ Also with Università di Sassari, Sassari, Italy Standard Model (SM). The leading-order processes are one-loop electroweak penguin diagrams, for which the top quark is the dominant virtual particle. In theories beyond the SM, new virtual particles may appear in the loop, which could lead to measurable effects on experimental observables such as branching fractions and CP asymmetries [1]. In the SM the inclusive rate for b → dγ is suppressed relative to b → sγ by a factor |V td /V ts | 2 , where V td and V ts are Cabibbo-Kobayashi-Maskawa matrix elements. Measurements of |V td /V ts | using the exclusive modes B → (ρ, ω)γ and B → K * γ [4,5] are now wellestablished, with theoretical uncertainties of 7% from weak annihilation and hadronic form factors [2]. This ratio can also be obtained from the B d and B s mixing frequencies [3]. It is important to confirm the consistency of the two methods of determining |V td /V ts |, since new physics effects would enter in different ways in mixing and radiative decays. A measurement of the branching fractions of inclusive b → dγ relative to b → sγ would determine |V td /V ts | with reduced theoretical uncertainties compared to that from exclusive modes [6]. This letter supersedes of [8], and presents the first significant observation of the b → dγ transition in the hadronic mass range M (X d ) > 1.0 GeV/c 2 , resulting in a significant improvement in the determination of |V td /V ts | via the ratio of inclusive widths. Inclusive b → sγ and b → dγ rates are extrapolated from the measurements of the partial decay rates to seven exclusive final states (see Table I) in the hadronic mass ranges 0.5 < M (X d ) < 1.0 GeV/c 2 (low mass, containing the previously measured K * , ρ and ω resonances) and 1.0 < M (X d ) < 2.0 GeV/c 2 (high mass). We combine these measurements and make a model-dependent extrapolation to higher hadronic mass to obtain an inclusive branching fraction (B) for b → (s, d)γ. These measurements use the full dataset of 471 × 10 6 BB pairs collected at the Υ (4S) resonance at the PEP-II B factory with the BABAR detector [7].
High energy photons are reconstructed from an isolated energy cluster in the barrel of the calorimeter, with shape consistent with a single photon, and energy 1.15 < E * γ < 3.50 GeV, where * denotes the center-of-mass (CM) frame. We remove photons that can form a π 0 (η) candidate in association with another photon of energy greater than 30 (250) MeV if the two-photon invariant mass is in the range 110 < m γγ < 160 (520 < m γγ < 560) MeV/c 2 for the low mass region and 95 < m γγ < 155 (530 < m γγ < 565) MeV/c 2 for the high mass region.
Charged pion and kaon candidates are selected from well-reconstructed tracks. We use a pion selection algorithm to differentiate pions from kaons, with a typical selection efficiency of 95% and kaon mis-identification rate of 4%. Kaons are identified as tracks failing the pion selection criteria. We reconstruct π 0 (η) candidates from pairs of photons of minimum energy 20 MeV with an invariant mass 115 < m γγ < 150 (470 < m γγ < 620) MeV/c 2 . We require all pion, η and kaon candidates to have a momentum in the laboratory frame greater than 600 (425) MeV/c in the low (high) mass region.
The selected pion, η, kaon and high-energy photon candidates are combined to form B meson candidates consistent with one of the seven decay modes. The charged particles are combined to form a common vertex with a χ 2 probability greater than 1%. We use the kinematic variables ∆E = E * B − E * beam , where E * B is the energy of the B meson candidate and E * beam is the beam energy, and m ES = E * 2 beam − p * 2 B , where p * B is the momentum of the B candidate. We consider candidates in the range −0.3 < ∆E < 0.2 GeV and m ES > 5.22 GeV/c 2 .
Contributions from continuum processes (e + e − → qq, with q = u, d, s, c) are reduced by considering only events for which the ratio R 2 of second-to-zeroth order Fox-Wolfram moments [9] is less than 0.98. To further discriminate between the jet-like continuum background and the more spherically symmetric signal events, we compute the angle θ * T between the photon momentum and the thrust axis of the rest of the event (ROE) and require | cos(θ * T )| < 0.8. The ROE is defined as all charged tracks and neutral energy deposits that are not used to reconstruct the B candidate.
Ten other event shape variables that distinguish between signal and continuum events are combined in a neural network (NN). These include the ratio R ′ 2 , which is R 2 is calculated in the frame recoiling against the photon momentum, the B meson production angle with respect to the beam axis in the CM frame, θ * B , and the L-moments [10] of the ROE with respect to either the thrust axis of the ROE or the direction of the high energy photon. Differences in lepton, pion and kaon production between background and B decays are exploited by including several flavor-tagging variables applied to the ROE [11]. Using the NN output, we reject 99% of continuum background while preserving 25% of signal decays After all selections are applied, there remain events with more than one B candidate. In these events the candidate with the reconstructed π 0 or η mass closest to nominal is retained. Where there is no π 0 or η we retain the candidate with the highest vertex χ 2 probability.
The signal yields in the data for the sum of the seven decay modes are determined from two-dimensional extended maximum likelihood fits to the ∆E and m ES distributions. We consider the following contributions: signal, combinatorial backgrounds from continuum processes, backgrounds from other B decays, and cross-feed from mis-reconstructed B → Xγ decays. The fits to B → X d γ events contain components from misidentified b → sγ decays, and we neglect the small b → dγ background in the fits to B → X s γ events.
Each contribution is modeled by a probability density function (PDF) that is determined from Monte Carlo (MC) simulated events unless otherwise specified. For the misidentified signal cross-feed components, we use a binned two-dimensional PDF to account for correlations. All the other PDFs are products of one-dimensional func-tions of ∆E and m ES . For signal, the m ES spectrum is described by a Crystal Ball function [12], and ∆E by a Cruijff function [13]. The parameters of these functions are determined from the fit to the high-statistics B → X s γ data sample. We use these fitted values to fix the signal shape in the fits to B → X d γ events.
The remaining B backgrounds contain a small component that peaks in m ES but not ∆E, which is modeled by a Gaussian distribution in m ES . Continuum and other non-peaking backgrounds are described by an ARGUS shape [14] in m ES and a second-order polynomial in ∆E.
We perform separate fits for B → X d γ and B → X s γ in each of the hadronic mass ranges 0.5-1.0 GeV/c 2 and 1.0-2.0 GeV/c 2 . For each of the four fits, we combine the component PDFs and fit for the signal, generic B and continuum yields, the ARGUS and two polynomial shape parameters. We scale the cross-feed contributions proportionally to the fitted signal yield, re-fit and iterate until the procedure converges. Projections of m ES and ∆E from fits to data for B → X s γ and B → X d γ are shown in the high mass regions in Figure 1. Table II gives the signal yields, efficiencies (after corrections for systematic effects) and partial branching fractions (PB). We calculate PB using PB(B → Xγ) = N S /(2 ǫN BB ), where N BB is the number of BB pairs in the data sample. We have investigated a number of sources of systematic uncertainty in the measurement of the partial branching fractions, some of which are common to both B → X d γ and B → X s γ and cancel in the ratio of branching fractions (see Table III: those that do not cancel in the ratio are marked by an asterisk). Uncertainties in tracking efficiency, particle identification, γ and π 0 reconstruction, and the π 0 /η veto have been evaluated using independent control samples of data and MC simulated events, and incorporated into our analysis. Uncertainty due to the NN selection has been evaluated by comparing the efficiency of the selection in data and MC for the B → X s γ events, which are relatively free of background, assuming that potential discrepancies between data and MC are the same for the B → X d γ sample. The means and widths of the signal PDF are varied within the range allowed by the fit to the B → X s γ data, accounting for correlations. Other PDF parameters are also varied within the 1σ limits determined from the fit to MC. We vary the b → sγ background in the fit to B → X d γ by the statistical uncertainty on our measurement of those decays. The signal cross-feed originating from our measured channels is varied by the statistical uncertainty on our measurement; other signal cross-feed backgrounds by ±50%. An additional uncertainty on the efficiency arises from the fragmentation of the hadronic system among the measured final states. For B → X s γ the uncertainty is constrained by the errors on the measured data; for B → X d γ an estimate is obtained from the difference between the default phase-space fragmentation (see below) and a re-weighting using the measured data/MC differences in B → X s γ.
To obtain inclusive B(b → sγ) and B(b → dγ) we need to correct the partial B values in Table II for the fractions of missing final states. After correcting for the 50% of missing decay modes with neutral kaons, the low mass B → X s γ measurement is found to be consistent with previous measurements of the rate for B → K * γ [15]. For the low mass B → X d γ region, we correct for the small amount of non-reconstructed ω final states (for example, ω → π 0 γ), and find a partial branching fraction consistent with previous measurements of B(B → (ρ, ω)γ) [15]. We assume that non-resonant decays do not contribute in this region.
In the high mass region, the missing fractions depend on the fragmentation of the hadronic system and are expected to be different for X d and X s . In our signal MC, fragmentation is modeled by selecting an array of finalstate particles and resonances according to the phasespace probability of the final state, as implemented by JETSET [16]. We further constrain the distribution of X s final states to that observed for our seven decay modes as well as the distributions of a number of other states measured in [17]. According to this MC model we reconstruct 43% of the total width in b → dγ , and 36% in b → sγ . A further 37% of the width of b → sγ is constrained by the isospin relation between charged and neutral kaon decays. We explore the uncertainty in the correction for missing modes by considering several alternative models: replacing 50% of b → sγ and b → dγ II: Signal yields (NS), efficiencies (ǫ), partial branching fractions (PB), inclusive branching fractions (B) and the ratio of inclusive branching fractions for the measured decay modes. The first error is statistical and second is systematic (including an error from extrapolation to missing decay modes, for the inclusive B).
Conversion of the ratio of inclusive branching fractions to the ratio |V td /V ts | is done according to [6], which requires the Wolfenstein parametersρ andη as input. However, since the world average of these quantities relies on previous measurements of |V td /V ts | we instead re-express ρ andη in terms of the world average of the independent CKM angle β [15]. This procedure yields a value of |V td /V ts | = 0.199±0.022(stat.)±0.024(syst.)±0.002(th.), compatible and competitive with more model-dependent determinations from the measurement of the exclusive modes B → (ρ, ω)γ and B → K * γ [4,5].
In summary, we have measured the inclusive b → sγ and b → dγ transition rates using a sum of seven final states in the hadronic mass range up to 2.0 GeV/c 2 , making the first significant observation of the b → dγ transition in the region above 1.0 GeV/c 2 . The value of |V td /V ts | derived from these measurements has an experimental uncertainty approaching that from the measurement of exclusive decays B → (ρ, ω)γ and B → K * γ, but a significantly smaller theoretical uncertainty.

I. ACKNOWLEDGMENTS
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