Measurement of Branching Fractions in Radiative B Decays to eta K gamma and Search for B Decays to eta' K gamma

We present measurements of the B->eta K gamma branching fractions and upper limits for the B->eta' K gamma branching fractions. For B->eta K+ gamma we also measure the time-integrated charge asymmetry. The data sample, collected with the BaBar detector at the Stanford Linear Accelerator Center, represents 232 million produced B B-bar pairs. The results for branching fractions and upper limits at 90% C.L. in units of 10^{-6} are: Br(B0->eta K0 gamma)=11.3+2.8-2.6+/-0.6, Br(B+->eta K+gamma)=10.0+/-1.3+/-0.5, Br(B0->eta' K0 gamma)<6.6, Br(B+->eta' K+ gamma)<4.2. The charge asymmetry in the decay B+->eta K+ gamma is Ach =-0.09+/-0.12+/-0.01. The first errors are statistical and the second systematic.

PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er Radiative B meson decays have long been recognized as a sensitive probe to test the Standard Model (SM) and to look for new physics (NP) [1] . In the SM, flavorchanging neutral current processes such as b → sγ proceed via radiative loop (penguin) diagrams. The loop diagrams may also contain new heavy particles, and therefore are sensitive to NP. Measurements of the branching fractions of a few of the exclusive decay modes exist: K * (892)γ [2,3], K 1 (1270)γ [4], K * 2 (1430)γ [2,5], Kππγ [5], φKγ [6] and K + ηγ [7]. The measured branching fraction of inclusive b → sγ and exclusive radiative B decays are in good agreement with SM predictions [8,9]. Direct [10] and mixing-induced [11] CP asymmetries in exclusive radiative B decays are expected to be very small in the SM. Measurement of direct CP asymmetries in exclusive radiative decays can provide a clear sign of NP [12].
We present analyses of the exclusive decay modes B + → ηK + γ and B 0 → ηK 0 γ [13] , which have previously been measured by the Belle Collaboration [7], and B + → η ′ K + γ and B 0 → η ′ K 0 γ which are studied for the first time. The results presented here are based on data collected with the BABAR detector [14] at the PEP-II asymmetric-energy e + e − collider [15] located at the Stanford Linear Accelerator Center. The analyses use an integrated luminosity of 211 fb −1 , corresponding to 232 million BB pairs, recorded at the Υ(4S) resonance (at a center-of-mass energy of √ s = 10.58 GeV).
Charged particles from e + e − interactions are detected, and their momenta measured, by a combination of a vertex tracker (SVT) consisting of five layers of double-sided silicon microstrip detectors, and a 40-layer central drift chamber (DCH), both operating in the 1.5 T magnetic field of a superconducting solenoid. We identify photons and electrons using a CsI(Tl) electromagnetic calorimeter (EMC). Further charged-particle identification is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring-imaging Cherenkov detector (DIRC) covering the central region. A K/π separation of better than four standard deviations is achieved for momenta below 3 GeV/c, decreasing to 2.5σ at the highest momenta in the B decay final states.
We reconstruct the primary photon, originating from the B decay candidate, using an EMC shower not associated with a track. We require that the photon candidate fall within the fiducial region of the EMC, has the expected lateral shower shape, and is well-separated from other tracks and showers in the EMC. The primary photon energy, calculated in the Υ(4S) frame, is required to be in the range 1.6 -2.7 GeV. We veto photons from π 0 (η) decays by requiring that the invariant mass of the primary photon candidates combined with any other photon candidate of laboratory energy greater than 50 (250) MeV not be within the range 115-155 (507-587) MeV/c 2 . Charged K candidates are selected from tracks, by using particle identification from the DIRC and the dE/dx measured in the SVT and DCH.
Neutral K candidates are formed from pairs of oppositely-charged tracks with a vertex χ 2 probability larger than 0.001, 486 < m(π + π − ) < 510 MeV/c 2 and a reconstructed decay length greater than three times its uncertainty. We require the momentum of the η or η ′ in the Υ(4S) frame to be greater than 0.9 GeV/c (0.6 GeV/c in modes with η ′ ηππ ). The invariant mass of ηK and η ′ K systems is required to be less than 3.25 GeV/c 2 . In η ′ Kγ final states, we suppress background from the decay J/ψ K, with J/ψ → η ′ γ by applying a veto on the reconstructed η ′ γ invariant mass. Defining the helicity frame for a meson as its rest frame with polar axis along the direction of the boost from the parent rest frame, and the decay angle θ dec as the polar angle of a daughter momentum in this helicity frame, we require for the η ′ ργ decays | cos θ ρ dec | < 0.9, and for η γγ decays | cos θ η dec | < 0.9, to suppress combinatorial background.
A B meson candidate is reconstructed by combining an η or η ′ candidate, a charged or neutral kaon and a primary photon candidate. It is characterized kinematically by the energy-substituted mass where the subscripts 0 and B refer to the initial Υ(4S) and to the B candidate in the lab-frame, respectively, and the asterisk denotes the Υ(4S) frame.
Background arises primarily from random track combinations in e + e − → qq events. We reduce this background by using the angle θ T between the thrust axis of the B candidate in the Υ(4S) frame and the thrust axis of the rest of the event. The distribution of | cos θ T | is sharply peaked near 1 for combinations drawn from jet-like qq events, and is nearly uniform for BB events. We require | cos θ T | < 0.9. Furthermore events should contain at least the number of charged tracks in the candidate decay mode plus one. For η γγ K + γ we require at least 3 charged tracks in the event. If an event has multiple B candidates, we select the candidate with the highest B vertex χ 2 probability.
We obtain signal event yields from unbinned extended maximum-likelihood fits. The principal input observables are ∆E, m ES and a Fisher discriminant F . Where relevant, the invariant masses m res of the intermediate resonances and | cos θ ρ dec | are also used. The Fisher discriminant F combines four variables: the angles with respect to the beam axis of the B momentum and the B decay product's thrust axis (in the Υ(4S) frame), and the zeroth and second angular moments L 0,2 of the energy flow about the B 0 thrust axis. The moments are defined by L j = i p i × |cos θ i | j , where θ i is the angle with respect to the B thrust axis of track or neutral cluster i, p i is its momentum, and the sum excludes the B candidate daughters.
We estimate BB backgrounds using simulated samples of B decays [16]. Signal and inclusive b → sγ events are simulated according to the Kagan-Neubert model [17]. The branching fractions in the simulation are based on measured values and theoretical predictions.
For each event i and hypothesis j (signal, continuum or BB background), the likelihood function is where N is the number of input events, n j is the number of events for hypothesis j and P j (x i ) is the corresponding probability density function (PDF), evaluated with the observables x i of the ith event. Since correlations among the observables are small, we take each P as the product of the PDFs for the separate variables. We determine the PDF parameters from Monte Carlo simulation for the signal and BB background, while using sideband data (5.25 < m ES < 5.27 GeV/c 2 ; 0.1 < |∆E| < 0.2 GeV) to model the PDFs of continuum background. We parameterize each of the functions P sig (m ES ), P sig (∆E), P j (F ), and the components of P j (m res ) that peak in m ES with either a Gaussian, the sum of two Gaussian distributions, or an asymmetric Gaussian function, as required, to describe the distribution. Distributions of ∆E for BB and continuum background and | cos θ ρ dec | are represented by linear or quadratic functions. The BB and continuum background in m ES is described by the ARGUS function s and a parameter ξ [18]. We allow continuum background PDF parameters to vary in the fit.
Large control samples of B decays to charmed final states of similar topology are used to verify the simulated resolutions in ∆E and m ES . Where the control data samples reveal differences from the Monte Carlo (MC) in mass or energy resolution, we shift or scale the resolution used in the likelihood fits. Any bias in the fit is determined from a large set of simulated experiments in which the qq background is generated from the PDFs, and into which we have embedded the expected number of BB background and signal events chosen randomly from fully simulated Monte Carlo samples.
In Table I we show the signal yield, the efficiency, and the product of daughter branching fractions for each decay mode. The efficiency is calculated as the ratio of the number of signal MC events entering into the ML fit to the total generated. We compute the branching fractions from the fitted signal event yields, reconstruction efficiencies, daughter branching fractions, and the number of produced B mesons, assuming equal production rates of charged and neutral B pairs. We correct the yield for any bias estimated by the simulations. We combine results from different channels by combining their likelihood functions, taking into account the correlated and uncorrelated systematic errors. We report the statistical significance and branching fraction for the individual decay channel; for combined measurements having a significance smaller than 5σ, we also report the 90% confidence level (C.L.) upper limit.
The statistical error on the signal yield is taken as the change in the central value when the quantity −2 ln L increases by one unit from its minimum value. The significance is the square root of the difference between the value of −2 ln L (with systematic uncertainties included) for zero signal and the value at its minimum. The 90% C.L. upper limit is taken to be the branching fraction below which lies 90% of the total likelihood integral in the positive branching fraction region. Bi, significance S (σ)(including systematic uncertainties), measured branching fraction B with statistical error for each decay mode. For the combined measurements we give the significance (with systematic uncertainties included) and the branching fraction with statistical and systematic uncertainty (in parentheses the 90% C.L. upper limit). For the ηK + γ mode we also list the measured signal charge asymmetry A ch .

Mode
Yield The measured charge asymmetry in the decay B + → ηK + γ is corrected for an estimated bias of −0.005 ± 0.010, determined from studies of signal Monte Carlo events and data control samples and from calculation of the asymmetry due to particles interacting in the detector. The result is A ch = −0.09 ± 0.12 ± 0.01 with an asymmetry interval [−0.282, 0.113] at 90% C.L.. Figure 1 shows, as representative fits, the projections onto m ES and ∆E for the decays ηK + γ, ηK 0 γ, η ′ K + γ and η ′ K 0 γ for a subset of the data for which the signal likelihood (computed without using the variable plotted) exceeds a mode-dependent threshold that optimizes the sensitivity. Figure 2 shows the distribution of the ηK invariant mass for signal events obtained by the event-weighting technique (sPlot) described in Ref. [19]. We use the covariance matrix and PDFs from the ML fit to determine a probability for each signal event. The resulting distributions (points with errors) are normalized to the signal yield. This mass distribution is useful to compare with theoretical predictions for radiative decays [17].
The main sources of systematic error include uncertainties in the PDF parameterization and ML fit bias. For the signal, the uncertainties in PDF parameters are estimated by comparing MC and data in control samples. Varying the signal PDF parameters within these errors, we estimate yield uncertainties of 1-2 events, depending on the mode. The uncertainty from fit bias is taken as half the correction itself (1-3 events). Systematic uncertainties due to lack of knowledge of the primary photon spectrum are estimated to be in the range 2-6% depending on the decay mode. Uncertainties in our knowledge of the efficiency, found from auxiliary studies, include 0.8% × N t and 1.5% × N γ , where N t and N γ are the numbers of tracks and photons, respectively, in the B candidate. There is a systematic error of 2.1% in the efficiency of K 0 S reconstruction. The uncertainty in the total number of BB pairs in the data sample is 1.1%. Published data [8] provide the uncertainties in the B daughter product branching fractions (0.7-3.4%). We assign a systematic uncertainty of 0.010 to A ch for the bias correction.
In conclusion, we have measured the central values and 90% C.L. upper limits in units of 10 −6 for the branching fractions: B(B 0 → ηK 0 γ) = 11.3 +2.8 −2.6 ± 0.6 ,  < 4.2). The measured branching fractions of the decay modes B + → ηK + γ and B 0 → ηK 0 γ are in good agreement with the values reported by the Belle Collaboration [7]. We do not find evidence of the decays B 0 → η ′ K 0 γ and B + → η ′ K + γ. The B → η ′ Kγ decays may be suppressed with respect to B → ηKγ decays due to destructive interference between two penguin amplitudes [20]. This effect has been measured in B decays to η ′ K and ηK, for which the branching fraction of the former is enhanced with respect to that of the latter [21]. We have also measured the charge asymmetry in the decay B + → ηK + γ to be A ch = −0.09 ± 0.12 ± 0.01, consistent with zero. The A ch interval at 90% C.L. is [−0.28, 0.11].
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 and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from CONACyT (Mexico), Marie Curie EIF (European Union), the A. P. Sloan Foundation, the Research Corporation, and the Alexander von Humboldt Foundation. * Also at Laboratoire de Physique Corpusculaire, Clermont-Ferrand, France