Measurement of B Decays to phi K gamma

We measure the branching fraction of the radiative B- decay B(B- ->phi K- gamma) = (3.46 +/- 0.57^{+0.39}_{-0.37}) 10^-6, and set an upper limit on the radiative B0 decay B(B0 ->phi K0 gamma)<2.71 10^-6 at 90% confidence level. We also measure the direct CP asymmetry of the B- ->phi K- gamma mode A_CP = (-26.4 +/- 14.3 +/- 4.8)%. The uncertainties are statistical and systematic, respectively. These measurements are based on 207 1/fb of data collected at the Y4S resonance with the BABAR detector.

Measurements of the branching fractions and CP asymmetries of b → sγ decays provide a sensitive probe of the Standard Model (SM).In the SM these decays are forbidden at tree level but allowed through electroweak penguin processes (Fig. 1).They are therefore sensitive to the possible effects of new physics [1] in the form of new heavy particles contributing to the loop diagram.Additional contributions to the decay amplitudes could affect branching fractions and CP violation.Furthermore, the radiated photon is polarized due to the left-handed nature of the weak interaction.The polarization can be probed by measuring the time-dependent CP asymmetry, which is sensitive to interference between B 0 -B 0 mixing and decay.Theoretical estimates in the SM [2] bound the mixing-induced CP asymmetry at about the 10% level.Here we focus on the time-integrated direct CP asymmetry, which is expected to be the same for charged and neutral B decays.
Although exclusive b → sγ decays present a theoretical challenge due to large non-perturbative QCD interactions, they are experimentally clean.There have already been results published for branching fraction and/or CP asymmetry measurements in several exclusive modes: B → K * γ [3], B 0 → K 0 S π 0 γ [4], B → η( ′ )Kγ [5], and various B → Kππγ [6] modes.Here, we present a measurement of the branching fraction for the charged mode B − → φK − γ and the neutral mode B 0 → φK 0 γ. 1 We also measure the direct CP asymmetry in the charged mode A CP = [N (B − ) − N (B + )]/[N (B − ) + N (B + )], where the flavor of the B is determined by the charge of the kaon.The Belle Collaboration has previously measured the branching fractions for these modes, using 90 fb −1 of BB data at the Υ (4S) resonance [7].We describe the first BABAR measurements of these modes using a dataset that is more than twice as large.
The data used in this analysis were collected with the BABAR detector at the PEP-II asymmetric e + e − storage ring.This analysis is based on a data set of 207 fb −1 corresponding to 228 million BB pairs collected at the Υ (4S) resonance.The BABAR detector is described in detail elsewhere [8].Important to this analysis are the tracking system composed of the silicon vertex tracker (SVT) and drift chamber (DCH), the detector of internally reflected Cherenkov light (DIRC), and the electromagnetic calorimeter (EMC).The SVT and DCH provide tracking and ionization energy loss (dE/dx) measurements for charged particles inside a 1.5 T magnetic field.The SVT is composed of five layers of double sided silicon strips and covers a polar angle range between 20.1 o and 150.2 o .
1 Throughout this paper, whenever a mode is given, the charge conjugate is also implied.
The DCH continues tracking outside the SVT volume.It consists of 40 layers of hexagonal cells filled with an 80:20 mixture of helium:isobutane.The DIRC is a ring imaging Cherenkov light detector.Below 700 MeV/c the tracking system provides most of the charged particle identification (PID) information, while the DIRC contributes more information at higher momenta.Photons are detected and their energy measured in the EMC, which is composed of 6580 thallium-doped CsI crystals.
We select events with EMC clusters of energy 1.5 − 2.6 GeV in the e + e − rest frame (CM frame) that are not associated with any charged track.Photon candidates are required to have an energy distribution consistent with the shower shape of an electromagnetic interaction, and they are required to be well isolated (> 25 cm) from other calorimeter clusters.A veto is applied to photon candidates that can be combined with other neutral EMC clusters above a minimum threshold energy to form an invariant mass consistent with a π 0 (115 − 155 MeV/c 2 ) or η (470 − 620 MeV/c 2 ).The threshold energy is 50 MeV for π 0 and 250 MeV for η.
We select φ candidates from pairs of oppositely charged kaon tracks, determined not to be pions based on a PID likelihood selection algorithm that uses dE/dx and Cherenkov light measurements.The same algorithm is used for the single K + in the charged mode.The tracks are fitted to a vertex using a Kalman decay chain fitter [9], and are required to have a χ 2 vertex probability greater than 0.1%.We select candidates with masses within a 10 MeV/c 2 window of the nominal φ mass [10].In the neutral mode, pairs of oppositely charged tracks are fitted to a common decay vertex and accepted as K 0 S candidates if the fit yields a probability greater tha 0.1%.The invariant mass of the pair is required to be within 10 MeV/c 2 of the K 0 S mass.The flight length of is required to be greater than three times the uncertainty of that length.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 a φK invariant mass within 10 MeV/c 2 of the D 0 mass.
The K, φ, and γ candidates are fitted to a common vertex and accepted as B candidates if the vertex probability is greater than 0.1%.To discriminate BB events against continuum background the ratio of Legendre moments L 2 /L 0 is required to be less than 0.55.The L i are defined by L i = j |p * j || cos θ * j | i , where the p * j are the CM momenta of all particles not used in reconstructing the signal B candidate, and the angle θ * j is between the particle's momentum and the thrust axis of the signal B. We require the cosine of the angle between the B candidate and the beamline, cos θ * B , to be in the range [-0.9,0.9] in the CM frame.We use two uncorrelated kinematic variables of the B candidate: the reconstructed mass m rec and the missing mass m miss .The reconstructed mass is the B candidate invariant mass calculated from the reconstructed energy and momentum.This is required to be within 4.98 − 5.48 GeV/c 2 .The missing mass squared is , where p Beams is the four-momentum of the beams and p mass const.

B
is the four-momentum of the B → φKγ candidate after a mass constraint on the B is applied.We require the missing mass to be in the range 5.12 − 5.32 GeV/c 2 .
To study event selection criteria we use simulated Monte Carlo (MC) events of signal, generic B decays, and e + e − → qq continuum background, where q = {u, d, s, c}.Events are generated using EVTGEN [11] and the detector response simulated with GEANT4 [12].Signal Monte Carlo is generated according to the inclusive b → sγ scheme presented in reference [13], using m b = 4.62 GeV/c 2 for the effective b quark mass.Exclusive signal MC is derived from this by using only the part of the hadronic mass spectrum above the φK threshold of 1.52 GeV/c 2 .Our selection criteria were chosen to optimize the figure of merit N S / √ N S + N B in the signal region, where N S and N B are the number of signal and background events, 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.
After all selection criteria are applied the average candidate multiplicity in events with at least one candidate is approximately 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 and from other B decay modes, which will be discussed later.
We use an extended maximum likelihood fit in four observables -m miss , m rec , L 2 /L 0 , and cos θ * B -to extract the signal and combinatoric background yields.The likelihood L is defined in the following way: N S and N B are the fitted number of signal and background events.N is the total number of events used in the fit.P i S and P i B are products of the signal and background probability density functions (PDFs) for each event i.In the charged mode, in order to fit the CP asymmetries of the signal and the background, the numbers of B + and B − events are determined separately: , where j = S or B; f is the flavor, defined as +1 for B − and −1 for B + ; n j and A j CP are the total yield and CP asymmetry of species j.In the neutral mode N j = n j .The signal PDFs for m miss and m rec are parametrized as asymmetric, variable-width Gaussian functions: ( The parameters σ L,R and α L,R determine the core width and variation of the width on either side of x = 0.The m miss background PDF is an ARGUS function [14], with the endpoint calculated on an event-by-event basis from the beam energy.The m rec background PDF is modelled as a 2 nd degree polynomial.The L 2 /L 0 distribution is modelled using a binned PDF with eight bins, because there is no a priori model for this distribution.There are seven parameters in the PDF due to the condition that the bins sum to unity.The signal and background models both use this form. The cos θ * B distribution is modelled as a 2 nd degree polynomial in both signal and background; for true B candidates it is expected to follow 1 − cos 2 θ * B .We use a high statistics B 0 → K * 0 (→ K + π − )γ control sample to determine our signal shape parameters.Once determined, these signal parameters are fixed for the fit to B → φKγ data, while all background shape parameters are allowed to vary.We fit for the number of signal and background events, and in the charged mode the signal and background CP asymmetry as well.The same fit is used with signal MC to determine the efficiency of the previously described selection criteria.Corrections to the efficiency are discussed below.
We apply several corrections to the fitted signal yield and efficiency before determining the branching fractions.Studies of simulated events show that our main sources of peaking backgrounds are nonresonant B → KK + K − γ events, and B → φKπ 0 , B → φKη, where the π 0 or η decay fakes a high energy photon.We estimate the amount of B → KK + K − γ contamination by fitting for the yield in φ mass sideband regions extending outside the signal region from 10 MeV/c 2 to 30 MeV/c 2 of the nominal φ mass.By interpolating into the signal region, we find and correct for 0.03±1.5 and 5.4 ± 4.2 events for the neutral and charged modes respectively.These contributions are subtracted from the event yield found in the fit.We also subtract the expected amount of B → φK * (→ Kπ 0 ) as determined by BABAR [16]: 0.27 neutral and 1.98 charged events.Because there have been no branching fraction measurements of B → φKπ 0 , B → φKη, we assume that the branching fraction of these modes is no more than three times that of B → φK * .Therefore, we assign an uncertainty Channel Yield Efficiency B(10 −6 ) A CP B − → φK − γ 85.0 ± 13.9 +7.3 −6.9 [21.9 ± 1. 6 1: Summary of the branching fractions and direct CP asymmetry.In B 0 → φK 0 γ the 90% confidence level upper limit is also given. of 0.51 neutral and 2.86 charged events due to nonresonant B → φK(π 0 /η) background.To correct for any fit bias, we generate 1000 pseudo-experiments using our maximum likelihood 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 +4.07 ± 0.45 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, and so we include 0.20 events in the systematic uncertainty of the yield.We correct for known efficiency differences between data and Monte Carlo in charged track, single photon, and K 0 S reconstruction.These corrections amount to 0.956 in the neutral mode and 0.975 in the charged mode.The corrected efficiencies are (15.3 ± 0.81)% 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 1.We calculate the central value of the branching fractions as: where N sig is the corrected number of signal candidates, N BB = (228.3± 2.5) × 10 6 is the number of BB pairs recorded by BABAR, ε is the corrected efficiency, and the (K 0 S → π + π − ) term is only used in the neutral mode.The partial branching fractions are given by Ref. [10].We measure B(B 0 → φK 0 γ) = (1.35± 0.92 +0.31  −0.30 ) × 10 −6 and B(B − → φK − γ) = (3.46 ± 0.57 +0.39 −0.37 ) × 10 −6 .In the charged mode we measure A CP = (−26.4±14.3±4.8)%.Fits to the missing mass and reconstructed mass distributions, projected into the signal region defined earlier, are shown in Figure 2. We use a set of 1000 pseudo-experiments in the neutral mode to determine the probability of obtaining a branching fraction less than or equal to our measured central value under the hypothesis that it is in fact the same as the charged mode.This was found to be 1.1%.
For the neutral mode we compute the 90% confidence level upper limit on the branching fraction.We use a Bayesian approach with an a priori probability for the branching ratio which is flat in the physical region 0 ≤ B ≤ 1, and zero elsewhere.The value of the likelihood function is computed by fixing the signal yield to a desired value and fitting the other free parameters on the data sample.The function is then integrated numerically.We account for systematic uncertainties on the yield by convolving the likelihood function with the distribution of the errors, before computing the upper limit.To determine the upper limit of the signal yield we use a Gaussian PDF having a width equal to the systematic uncertainty of the yield.Similarly for the efficiency uncertainty we use a Gaussian PDF having a width equal to the systematic error.After also applying the yield corrections discussed previously we obtain B(B 0 → φK 0 γ) < 2.71 × 10 −6 .
To determine the contribution from resonances decaying to φK we study the backgroundsubtracted [15], efficiency corrected φK invariant mass distribution, shown in Figure 3. Using the  charged mode, we find that no more than 50% of the spectrum in the 1.6 − 3.0 GeV/c 2 range comes from the K 2 (1770) resonance.We use this to bound our model uncertainty, described below.
We assign an uncertainty due to the fixed signal parameters in the fit.The parameters were obtained from the control sample, and therefore they have some statistical uncertainty.We varied these parameters within their uncertainties to determine the total uncertainty on the yields.We account for other systematic uncertainties in charged kaon tracking, kaon PID, K 0 S , φ, and photon selection efficiency.There are small uncertainties assigned with our L 2 /L 0 selection and the π 0 / η veto.To account for uncertainty due to the assumption of a specific φK mass spectrum for simulated events, we determine what our efficiency would have been in the scenario that half of the spectrum comes from K 2 (1770) resonant φK production, while the other half comes from our signal MC model.We assign the relative efficiency difference as an uncertainty.Adding all of the uncertainties in quadrature, we find a total acceptance/efficiency uncertainty of 5.2% in the neutral mode and 7.1% in the charged mode.The contributions for each mode are summarized in Table 2.
For the direct CP asymmetry measurement we assume that the efficiency corrections and uncertainties cancel out.To account for uncertainty due to peaking background we use the following procedure.We assume an a priori flat distribution for the CP asymmetry between −1 and 1, which has a root mean square width of 0.58.We multiply this by the expected fractional contamination in our 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 measurement [16] shows that the CP asymmetry is consistent with zero to within 9%.We therefore consider this to be negligible in our case.Using the control sample as we did with the branching fraction measurement, we vary the fixed input parameters of the fit to determine the uncertainty on the signal CP asymmetry.This was found to be 2.2%, bringing the total systematic uncertainty to 4.8%.
In summary, we have performed the first BABAR studies of B → φKγ decay modes.The B − → φK − γ branching fraction was measured, and an upper limit for the B 0 → φK 0 γ mode was determined.Our measurements are consistent with the assumption of isospin symmetry at the 1.1% level.We have made the first measurement of the direct CP asymmetry in B − → φK − γ.For comparison, we quote the Belle results [7]: B(B − → φK − γ) = (3.4± 0.9 ± 0.4) × 10 B(B 0 → φK 0 γ) < 8.3 × 10 −6 at 90% confidence level.The statistical uncertainties will improve as the B Factories collect more data over the next several years.In future measurements a large amount of CP violation would be a sign of physics beyond the Standard Model.

Figure 2 :
Figure 2: Missing mass (left) and reconstructed mass (right) fit projections in the signal region for the charged mode (upper) and the neutral mode (bottom).The dotted curves show the fitted background contribution while the solid curves show the signal.

Figure 3 :
Figure3: The background-subtracted and efficiency-corrected φK mass distributions (points with uncertainties) for the charged mode (left) and the neutral mode (right).The signal MC prediction for the mass spectrum, based on Ref.[13], is shown as a histogram without uncertainties.