Measurement of B Decays to phi K gamma

We search for the decays B- ->phi K- gamma and B0bar ->phi K0bar gamma in a data sample of 228 million BBbar pairs collected at the Upsilon(4S) resonance with the BaBar detector. We measure the branching fraction B(B- ->phi K- gamma) = (3.5 +/- 0.6 +/- 0.4) x 10^-6 and set an upper limit B(B0bar ->phi K0bar gamma)<2.7 x 10^-6 at the 90% confidence level. We also measure the direct CP asymmetry in B- ->phi K- gamma, A_CP = (-26 +/- 14 +/- 5)%. The uncertainties are statistical and systematic, respectively.

Measurements of the branching fractions and CP asymmetries of b → sγ decays provide a sensitive probe of the standard model (SM), in which these decays are forbidden at tree level but allowed through electroweak penguin processes.They are sensitive to the possible effects of physics beyond the SM manifesting as new virtual particles contributing to loops.These additional contributions to the decay amplitudes could affect branching fractions and CP violation [1].The SM theoretical prediction [2] and experimental measurements [3] of the b → sγ inclusive branching fraction have uncertainties of about 10% and are consistent with each other.Although exclusive b → sγ branching fractions are experimentally easier to determine than inclusive ones, calculations for the exclusive modes are theoretically challenging due to large nonperturbative quantum chromodynamic effects.The expected direct CP asymmetry between B + and B − decay rates in the SM is −(0.1 − 1)% [4], while the timedependent CP asymmetry in neutral CP eigenstates such as B 0 → φK 0 S γ should be a few percent [5].A significantly larger CP asymmetry of either type would be a sign of new physics.
There have already been results published for branching fraction and/or CP asymmetry measurements in several exclusive modes: B → K * γ [6], B 0 → K 0 S π 0 γ [7], B → η( ′ )Kγ [8], and various B → Kππγ [9] modes.The Belle collaboration has measured B(B − → φK − γ) = (3.4±0.9±0.4)×10−6 and B(B 0 → φK 0 γ) < 8.3×10 −6 at the 90% confidence level using 96 million BB pairs [10].We present the first BABAR measurement of the branching fraction for the charged mode B − → φK − γ and a search for the neutral mode B 0 → φK 0 γ [21] using 228 million BB pairs.We also measure for the first time the direct CP asymmetry in the charged mode where the flavor of the B is determined by the charge of the kaon.
The data used in this analysis were recorded with the BABAR detector at the PEP-II asymmetric storage rings, in which 9.0 GeV electrons collide with 3.1 GeV positrons to produce Υ (4S) mesons.The BABAR detector is described in detail elsewhere [11].Most important to this analysis are the tracking system composed of the silicon vertex tracker (SVT) and drift chamber (DCH) inside a 1.5 T magnetic field, the ring-imaging detector of internally reflected Cherenkov light (DIRC), and the electro-magnetic calorimeter (EMC).The tracking system can reconstruct a B decay vertex with a resolution of 70 µm along the direction of the beam, and has a transverse momentum resolution of 0.52% at 500 MeV/c.The DIRC provides kaon-pion separation of at least 4σ significance for momenta up to 3 GeV/c.The EMC detects photons over an energy range from 20 MeV to 9 GeV, with a resolution of 2.6% at 2.5 GeV.A detailed Monte Carlo (MC) simulation of signal and background processes was performed using the EVTGEN generator [12] and the GEANT4 package [13].
We search for B → φKγ candidates based on charged track combinations and the presence of a high-energy photon using a kinematic fitter [14] to reconstruct the intermediate mesons and the B. Each decay vertex is required to have a χ 2 probability greater than 0.1%.Candidates for φ → K + K − are selected from pairs of oppositely charged tracks that have been distinguished from pions based on a particle identification (PID) likelihood selection algorithm that uses dE/dx and Cherenkov light measurements.The same PID algorithm is used for the single K − from the B − in the charged mode.We keep φ candidates with masses within a ±10 MeV/c 2 window of the nominal φ mass [15].In the neutral mode, pairs of oppositely charged tracks are accepted as K 0 S candidates if they have a combined invariant mass within ±10 MeV/c 2 of the K 0 S mass and if the K 0 S flight length is greater than three times its uncertainty.We require the combined φK invariant mass to be less than 3.0 GeV/c 2 .In the neutral mode a D 0 veto is applied by removing candidates with combined φK invariant mass within ±10 MeV/c 2 of the D 0 mass.Photon candidates are reconstructed from EMC clusters that are not associated with charged tracks, are isolated from other clusters, and have the expected photon lateral shower shape.We require an energy of 1.5 − 2.6 GeV in the e + e − rest frame (CM frame) and we veto photon candidates that form a π 0 (η) candidate with invariant mass between 115 − 155 MeV/c 2 (470 − 620 MeV/c 2 ) when combined with another photon of energy greater than 50 MeV (250 MeV).
We identify signal B decays through the distributions of two quantities, missing mass and reconstructed mass, that peak around the nominal B mass.The missing mass is , where p Υ (4S) is the Υ (4S) four-momentum and p B is the four-momentum of the B → φKγ candidate after a mass constraint on the B is applied.The reconstructed mass m rec is the B candidate invariant mass calculated from the reconstructed energy and momentum.We require 5.12 < m miss < 5.32 GeV/c 2 and 4.98 < m rec < 5.48 GeV/c 2 .To further discriminate B decays from continuum e + e − → qq (q = u, d, s, c) background we use two topological quantities: the ratio of Legendre moments L 2 /L 0 and the cosine of the angle between the B candidate and the e − direction in the CM frame | cos θ * B |.We require L 2 /L 0 < 0.55, where is the CM momentum of each particle j not used in the B candidate, and θ * j is the CM angle between the particle's momentum and the thrust axis of the B candidate.We also require | cos θ * B | < 0.9.The selection criteria described above are chosen to optimize N S / √ N S + N B in the signal region, where N S and N B are the MC simulated signal and background yields, respectively, and the signal region is defined by 5.05 < m rec < 5.4 GeV/c 2 , 5.27 < m miss < 5.29 GeV/c 2 , | cos θ * B | < 0.8, and L 2 /L 0 < 0.48.Signal MC is based on inclusive B → X s γ events generated according to the model of Kagan and Neubert [16], using m b = 4.62 GeV/c 2 for the effective b quark mass.Only the part of the hadronic mass spectrum above the φK threshold of 1.52 GeV/c 2 is used, with X s forced to decay to φK.This model does not take resonances into account.
After all criteria are applied, the average candidate multiplicity in events with at least one candidate are 1.01 and 1.07 in the neutral and charged modes respectively.If multiple B candidates are found in an event, we select the best one based on a χ 2 formed from the value and uncertainty of the mass of the φ candidate and, in the neutral mode, the K 0 S candidate.The remaining background comes from continuum combinatorics, nonresonant B → KK + K − γ, B → φKπ 0 , and B → φKη.
Signal and background yields are extracted from a fit to an unbinned extended maximum likelihood function defined by N S and N B are the number of signal and background events respectively, the index i labels each event in the data set, and N is the total number of events used in the fit.P S and P B are products of the one-dimensional signal and background probability density functions (PDFs) for each of the observables x = {m miss , m rec , L 2 /L 0 , cos θ * B }.The signal shape parameters are fixed in the fit while the background parameters α are allowed to vary.In order to fit the CP asymmetries of signal and background in the charged mode, the number of B + and B − events is determined separately: N ± j = 1 2 (1 ∓ A j CP )n j , where j = S or B, n j and A j CP are the total yield and CP asymmetry of species j, respectively, and the upper (lower) signs correspond to the positively (negatively) charged B mesons.The signal PDFs for m miss and m rec are parametrized by where the parameters σ L,R and α L,R determine the core width and variation of the width on either side of x = 0, x being the difference from the nominal B mass of m miss or m rec .The m miss background PDF is an ARGUS function [17], with the endpoint calculated event-by-event from the beam energy.The m rec background PDF is modeled as a 2 nd degree polynomial.The signal and background models for L 2 /L 0 both use a binned PDF with eight bins.The cos θ * B distribution is modeled as a 2 nd degree polynomial in both signal and background; true B candidates follow a 1 − cos 2 θ * B distribution if the detector efficiency is flat in cos θ * B .To determine the signal PDF parameters we use a highstatistics B 0 → K * 0 (→ K + π − )γ sample.Once determined, these parameters are fixed for the fit to B → φKγ data.We determine the selection efficiency by performing a fit of the yields on signal MC.
We apply several corrections to the signal yield and efficiency before determining the branching fractions.Studies of simulated events show that the main sources of signal-like (peaking) backgrounds are nonresonant B → KK + K − γ events, and B → φKπ 0 or B → φKη, where one of the photons from the π 0 or η decay is lost and the other is picked up as the signal high-energy photon.We estimate the amount of B → KK + K − γ contamination by fitting for the yield in φ mass sideband regions defined by 989 < m φ < 1009 MeV/c 2 and 1029 < m φ < 1049 MeV/c 2 .By interpolating into the signal region, we find and correct for 0.0 ± 1.5 and 5 ± 4 events for the neutral and charged modes respectively.These contributions are subtracted from the event yields determined in the fit.From the known branching fraction [18] of B → φK * (→ Kπ 0 ) we correct for a contamination of 0.27 ± 0.16 neutral and 1.98 ± 0.32 charged events.There have been no branching fraction measurements of B → φKπ 0 or B → φKη.We assume that the branching fraction of the first is no more than onethird that of B → φK * and that of the latter is no more than B → φK * .Based on this we assign an uncertainty of 0.5 neutral and 2.9 charged events due to nonresonant B → φK(π 0 /η) background.To correct for any fit bias, we generate 1000 simulated experiments using PDFs with separate components for BB and continuum, and embedding signal events from the full simulation.The background components are generated using shape parameters determined from the full MC simulation.We correct for a bias of +4.1±0.5 events in the charged mode, due to correlations among the observables in signal MC events that are not accounted for in the fit.In the neutral mode we find a bias of −0.06 ± 0.20, so we apply no correction but include 0.20 events in the systematic uncertainty of the yield.We correct for efficiency differences between data and MC in charged track, single photon, and K 0 S reconstruction.These multiplicative efficiency corrections are 0.956 in the neutral mode and 0.975 in the charged mode.The corrected efficiencies are (15.3 ± 0.8)% in the neutral mode and (21.9 ± 1.6)% in the charged mode, where the uncertainties are systematic (discussed below).
The signal yields, efficiencies, branching fractions, and charged-mode CP asymmetry are reported in Table I.We calculate the central value of the branching fractions by where i labels either the neutral or charged mode, N i S is the corrected signal yield, N BB = (228.3± 2.5) × 10 6 is the number of BB pairs recorded, ε i is the corrected efficiency, and b i is in the neutral mode and B(φ → K + K − ) in the charged mode.The world average branching fractions are taken from Ref. [15].We measure B(B − → φK − γ) = (3.5 ± 0.6 ± 0.4)×10 −6 and B(B 0 → φK 0 γ) = (1.3±1.0±0.3)×10−6 .In the charged mode we measure A CP = (−26±14±5)%.In Fig. 1 we show fits to the data projected onto m miss and m rec .In all cases, the displayed distribution is created with the signal region selection applied to all other fit variables.We determine the consistency of the branching fraction measurements with the assumption of isospin symmetry using 1000 simulated experiments in each mode with the number of signal events determined by the average branching fraction, B av = 2.8 × 10 −6 .From the distribution of the differences in branching fraction between the modes we find an 8.9% probability to measure a difference greater than or equal to that observed in data.
For the neutral mode we compute the 90% confidence level upper limit on the branching fraction.We use a Bayesian approach with a flat prior probability for the branching fraction in the physical region 0 ≤ B ≤ 1 and zero elsewhere.As the likelihood (Eq. 1) is a function of several parameters, we determine its dependence on N S by fixing N S to a series of values and recomputing the likelihood at each one, allowing N B and α to be reoptimized to obtain the maximum likelihood at each point.We convolve this function with a Gaussian distribution of width equal to the systematic uncertainty of the yield.Similarly, for the efficiency uncertainty we also use a Gaussian distribution of width equal to the efficiency systematic uncertainty.We determine the branching fraction upper bound B UB from the following expression: After applying the previously discussed corrections to the yield and efficiency, and including systematic uncertainties, we obtain B(B 0 → φK 0 γ) < 2.7 × 10 −6 .We assign a systematic uncertainty to the yield due to the fixed signal parameters in the fit.We vary these parameters within the ranges allowed by the K * γ sample to determine the total uncertainty of the yields.We account for other systematic uncertainties due to efficiency differences between data and MC in charged kaon tracking, kaon PID, and K 0 S , φ, and photon selection.There are small uncertainties assigned to the L 2 /L 0 selection and the π 0 / η veto, also due to data-MC efficiency differences.
Figure 2 shows the efficiency-corrected φK invariant mass distributions, using the background subtraction technique described in Ref. [20].In the charged mode, we find that no more than 50% of the spectrum in the 1.6 − 3.0 GeV/c 2 range can come from the K 2 (1770) resonance, and we use this information to bound the uncertainty due to the assumed MC φK mass spectrum.We determine what the efficiency would have been if half of the mass spectrum came from resonant K 2 (1770) → φK production, while the other half came from the signal MC model.We assign the relative efficiency difference between this and the nominal model as an uncertainty.Adding all of the previously discussed uncertainties in quadrature, we find a total multiplicative uncertainty of 5.2% in the neutral mode and 7.1% in the charged mode.The complete systematic uncertainties for each mode are summarized in Table II.  .The signal MC model for the mass spectrum, based on Ref. [16], is shown as a histogram without uncertainties and is normalized to the efficiency-corrected signal yield obtained in data.
For the direct CP asymmetry measurement we bound the K + /K − efficiency asymmetry of the detector by using the measured combinatoric background asymmetry, which is consistent with zero within an uncertainty of 1.8%.To account for uncertainty due to various peaking background sources we assume that each source can have a CP asymmetry of up to ±58%, which is the root mean square width of a flat distribution between −1 and 1.We multiply this by the expected fractional contamination in the data sample to obtain the systematic uncertainty.For B − → φK − (π 0 /η) we assign 1.8% uncertainty, while for B − → K − K + K − γ we assign 3.5% uncertainty.For resonant B → φK * (→ Kπ 0 ) events, the previous BABAR and Belle measurements [19] show that the CP asymmetry is

±11
consistent with zero to within 15%.We therefore consider it to be negligible.As was done with the branching fraction measurement, we vary the fixed signal parameters of the fit to obtain a 2.2% uncertainty for the signal CP asymmetry.Adding the uncertainties in quadrature we find a total A CP systematic uncertainty of 5%.
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible.The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR.The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them.This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), Institute of High Energy Physics (China), the Commissariat à l'Energie Atomique and Institut National de Physique Nucléaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Science and Technology of the Russian Federation, Ministerio de Educación y Ciencia (Spain), and the Particle Physics and Astronomy Research Council (United Kingdom).Individuals have received support from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation.

FIG. 1 :
FIG. 1: Missing mass (a) and reconstructed mass (b) fits in the signal region for the charged mode and the neutral mode (c,d).The dotted curves show the background contribution while the solid curves show the sum of signal and background.

FIG. 2 :
FIG.2:The background-subtracted and efficiency-corrected φK mass distributions (points with uncertainties) for the charged mode (a) and the neutral mode (b).The signal MC model for the mass spectrum, based on Ref.[16], is shown as a histogram without uncertainties and is normalized to the efficiency-corrected signal yield obtained in data.

TABLE II :
Summary of the systematic uncertainties.Except where noted, all uncertainties are given as percentages.