Branching Fraction Measurements of B+ ->rho+ gamma, B0 ->rho0 gamma, and B0 ->omega gamma

We present a study of the decays B+ ->rho+ gamma, B0 ->rho0 gamma, and B0 ->omega gamma. The analysis is based on data containing 347 million BBbar events recorded with the BaBar detector at the PEP-II asymmetric B factory. We measure the branching fractions BR(B+ ->rho+ gamma) = (1.10 +0.37/-0.33 +/- 0.09) x 10-6 and BR(B0 ->rho0 gamma) = (0.79 +0.22/-0.20 +/- 0.06) x 10-6, and set a 90% C.L. upper limit BR(B0 ->omega gamma)<0.78 x 10-6. We also measure the isospin-averaged branching fraction BR(B->rho/omega gamma) = (1.25 +0.25/-0.24 +/- 0.09) x 10-6, from which we determine |Vtd/Vts| = 0.200 +0.021/-0.020 +/- 0.015, where the first uncertainty is experimental and the second is theoretical.

PACS numbers: 12.15.Hh,14.40.Nd In the Standard Model, the decays B + → ρ + γ, B 0 → ρ 0 γ, and B 0 → ωγ [1] arise mainly from b → dγ penguin diagrams containing a virtual top quark in the loop. By relating the three individual decay rates by isospin symmetry and using the measured ratio between the charged and neutral B meson lifetimes τ B + /τ B 0 , an isospin-averaged branching fraction is defined: Recent calculations predict B[B → (ρ/ω)γ] to be in the range of (0.9-1.8) × 10 −6 [2,3], where most of the uncertainty is due to the calculation of the form factor. These predictions could be modified by processes beyond the Standard Model [4].
While the exclusive decay rates have a large uncertainty due to non-perturbative long-distance QCD effects, some of this uncertainty cancels in the ratio of B[B → (ρ/ω)γ] to B → K * γ branching fractions. Since the dominant diagram involves a virtual top quark, this ratio is related to the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V td /V ts | [2,5] via (1) The coefficient ζ is the ratio of the form factors for the decays B → ργ and B → K * γ and ∆R accounts for different dynamics in the decay (e.g. annihilation diagrams can contribute to B + → ρ + γ). Physics beyond the Standard Model could affect these decays, creating inconsistencies between the measurement of |V td /V ts | obtained from this analysis and that obtained from the ratio of B 0 and B 0 s mixing frequencies [6]. Previous searches by BABAR [7] and CLEO [8] found no evidence for the decays B → ργ and B → ωγ. An observation of the decay B 0 → ρ 0 γ was recently reported by the Belle collaboration [9]. This letter reports on a study of the decays B + → ρ + γ, B 0 → ρ 0 γ, and B 0 → ωγ based on a data sample containing 347 million BB events, corresponding to an integrated luminosity of 316 fb −1 , collected with the BABAR detector [10] at the PEP-II asymmetric-energy e + e − storage ring. These results supersede the previous BABAR measurements [7].
The dominant source of background is continuum events (e + e − → qq, with q = u, d, s, c) that contain a high-energy photon from π 0 or η decays. Other backgrounds include photons from initial-state radiation (ISR) processes, decays of B → K * γ (K * → Kπ), decays of B → (ρ/ω)π 0 or B → (ρ/ω)η and combinatorial background from higher-multiplicity b → sγ decays. For each signal decay mode, selection requirements have been optimized for maximum statistical sensitivity with assumed signal branching fractions of 1.0 × 10 −6 and 0.5 × 10 −6 for the charged and neutral modes, respectively.
The photon from a signal B decay is identified as a well-isolated energy deposit in the electromagnetic calorimeter with energy 1.5 < E * γ < 3.5 GeV in the center of mass (CM) frame. The energy deposit must not be associated with any charged track and must meet several other requirements designed to eliminate background from hadronic showers and charged particles [12]. In order to veto photons from π 0 and η decays, we associate each high-energy photon candidate γ with each of the other photons γ ′ in the event. We reject the candidates that are consistent with originating from π 0 or η decays based on a likelihood ratio constructed from the energy of the second photon γ ′ and the invariant mass of the pair m γγ ′ . We also combine the high-energy photon candidate with photon conversions to e + e − pairs, and reject the photon if the invariant mass is consistent with a π 0 or η.
Charged-pion candidates are selected from wellreconstructed tracks with a minimum momentum transverse to the beam direction of 100 MeV/c. A stringent π ± selection algorithm [7] is applied to reduce background from charged kaons produced in b → sγ decays. The algorithm combines the information provided by the ringimaging Cherenkov detector with the measurement of energy loss in the tracking system.
Photon candidates with energy greater than 50 MeV in the laboratory frame are combined into pairs to form π 0 candidates. For B 0 → ωγ (B + → ρ + γ) decays, the invariant mass of the pair is required to satisfy 122 < m γγ < 150 MeV/c 2 (117 < m γγ < 148 MeV/c 2 ). We also require that the cosine of the opening angle between the daughter photons in the laboratory frame be greater than 0.413 (0.789).
The identified pions are combined into vector meson candidates by requiring 633 < m π + π − < 957 MeV/c 2 , 636 < m π + π 0 < 932 MeV/c 2 , and 764 < m π + π − π 0 < 795 MeV/c 2 for ρ 0 , ρ + , and ω, respectively. The charged pion pairs must originate from a common vertex. The separation along the beam axis between this vertex and the one obtained by combining the other charged particles in the event is required to be less than 4 mm and to be measured with a precision better than 0.4 mm.
The photon and ρ/ω candidates are combined to form the B meson candidates. We define ∆E is the CM energy of the B meson candidate and E * beam is the CM beam energy. We also define the beamenergy-substituted mass m ES ≡ E * 2 beam − p * 2 B , where p * B is the CM momentum of the B candidate. Signal events are expected to have a ∆E distribution centered near zero with a resolution of about 50 MeV, and an m ES distribution centered at the mass of the B meson, with a resolution of 3 MeV/c 2 . We consider candidates in the ranges −0.3 < ∆E < 0.3 GeV and m ES > 5.22 GeV/c 2 , which include sidebands that allow the combinatorial background yields to be extracted from a fit to the data.
In signal events the vector meson is transversely polarized, while in background events from B → ρ(π 0 /η) and B → ω(π 0 /η) it is longitudinally polarized. To reject this background, we calculate the vector meson helicity angle, θ H , and require | cos θ H | < 0.75. The helicity angle is defined as the angle between the B momentum vector and the π − track calculated in the ρ rest frame in the case of a ρ meson, or the angle between the B momentum vector and the normal to the ω decay plane for an ω meson.
Contributions from continuum background processes are reduced by considering only events for which the ratio R 2 of second-to-zeroth Fox-Wolfram moments [13] calculated using the momenta of all charged and neutral particles in the event is less than 0.7. A neural network combining the variables described below further suppresses continuum background. The quantity R ′ 2 , defined as R 2 in the frame recoiling against the photon momentum, is used to reject ISR events. To discriminate between the jet-like continuum background and the more spherically-symmetric signal events, we compute the angle between the photon and the thrust axis of the rest of the event (ROE) in the CM frame. The ROE is defined by all charged tracks and neutral energy deposits in the calorimeter that are not used to reconstruct the B candidate. We also calculate the moments L i ≡ j p * j ·| cos θ * j | i / j p * j , where p * j and θ * j are the momentum and angle with respect to an axis, respectively, for each particle j in the ROE. We use L 1 , L 2 , and L 3 with respect to the thrust axis of the ROE, as well as with respect to the photon direction. In addition, we calculate the B meson production angle θ * B with respect to the beam axis in the CM frame. Differences in lepton and kaon production between background and B decays are exploited by using flavor-tagging variables [14]. The significance of the separation along the beam axis of the B meson candidate and ROE vertices is included as well. The purity of the selected sample is enhanced by a cut on the output of the neural network that retains 63%, 74%, and 71% of the signal events in the modes B + → ρ + γ, B 0 → ρ 0 γ, and B 0 → ωγ, respectively.
The expected average candidate multiplicity in the selected signal events is 1.01 for B 0 → ρ 0 γ and 1.07 for both B + → ρ + γ and B 0 → ωγ. In events with multiple candidates, the one with the reconstructed vector meson mass closest to the nominal mass is retained. This criteria was chosen because the mass of the vector meson was found to be uncorrelated with the variables used in the fit. Applying all the selection criteria described above, we find efficiencies [15] of 11.0% for B + → ρ + γ, 14.1% for B 0 → ρ 0 γ, and 7.9% for B 0 → ωγ.
The signal content of the data is determined by a multidimensional unbinned maximum likelihood fit, which is constructed individually for each of the three signal decay modes. All fits use ∆E, m ES , cos θ H , and the neural network output N . In order to facilitate the parametrization of the probability density function (PDF) used in the fit, the transformation N N = tanh −1 (c 1 · N − c 2 ), in which the c i are are mode-dependent constants, is made. For decays B 0 → ωγ (ω → π + π − π 0 ), the cosine of the angle between the π + and π 0 momenta in the π + π − rest frame (Dalitz angle) is added as a fifth observable.
In the fit we consider several hypotheses for the origin of the events: signal, continuum background, B → K * γ decays, and other B backgrounds. The likelihood function for a signal mode k (= ρ + γ, ρ 0 γ, ωγ) is defined as (2) where N hyp is the number of event hypotheses, n i is the yield of each hypothesis, and N k is the number of candidate events observed in data. Since the correlations among the observables are found to be small in simulated event samples, we define the PDF P i ( x j ; α i ) for the i-th event hypothesis as the product of individual PDFs for each fit observable x j given the set of parameters α i . Each PDF is determined from a one-dimensional fit to a dedicated sample of simulated events. The ∆E PDF is corrected for the observed difference between data and simulation by using samples of B → K * γ decays. widths on the left and right of the peak, and α L,R are a measure of the tails on the left and right of the peak, respectively. Various functional forms are used to describe the continuum and B background components. We measure the signal yield n sig by maximizing the likelihood function in Eq. (2). In the fit, the continuum background yield is allowed to float, as is the overall yield of the B background, with the exception of the B + → K * + γ (K * + → K + π 0 ) yield in the B + → ρ + γ mode, which is fixed. The relative yields among the different B backgrounds are fixed to the values obtained using known branching fractions [11] and selection efficiencies determined from simulated events. Figure 1 shows the data points and the projections of the fit results for ∆E and m ES separately for each decay mode. The signal yields are reported in Table I. The significance is computed as √ 2∆ log L, where ∆ log L is the log-likelihood difference between the best fit and the null-signal hypothesis. Table II gives an overview of the contributions to the systematic uncertainties. These are associated with the signal reconstruction efficiency and the modeling of signal and BB background in the Monte Carlo simulation. The latter contributes to the uncertainties on the signal yields.
The systematic error affecting the signal efficiency includes uncertainties on tracking, particle identification, γ and π 0 reconstruction, π 0 /η veto and the neural network selection. The uncertainties on the π 0 /η veto and neural network selection are determined from a control sample of B → Dπ decays, with D → Kπ or D → Kππ. To estimate the uncertainty related to the modeling of the signal and B background in the Monte Carlo, we vary the parameters of the PDFs that are fixed in the fit within their errors. The uncertainty related to the choice of a specific functional form for the shape of the N N distribution is evaluated by using a binned PDF as an alternative description. All relative and absolute normalizations of B background components that are fixed in the fit are varied within their errors. For all these variations, the corresponding change in the fitted signal yield is taken as a systematic uncertainty.
The branching fractions are calculated from the measured signal yields assuming B(Υ (4S) → B 0 B 0 ) = B(Υ (4S) → B + B − ) = 0.5. The results are listed in Table I. For B 0 → ωγ, we also compute the 90% confidence level (C.L.) upper limit B(B 0 → ωγ) < 0.78 × 10 −6 using a Bayesian technique. We determine the branching fraction upper limit B l such that B l 0 L dB/ ∞ 0 L dB = 0.90, assuming a flat prior in the branching fraction and taking into account the systematic uncertainty.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and