Branching Fractions and CP-Violating Asymmetries in Radiative B Decays to eta K gamma

We present measurements of the CP-violation parameters S and C for the radiative decay B0 ->eta K0s gamma; for B ->eta K gamma we also measure the branching fractions and for B+ ->eta K+ gamma the time-integrated charge asymmetry Ach. The data, collected with the BaBar detector at the Stanford Linear Accelerator Center, represent $465 \times 10^6$ BBbar pairs produced in $e^{+} e^{-}$ annihilation. The results are $S = -0.18^{+0.49}_{-0.46} \pm 0.12$, $C = -0.32^{+0.40}_{-0.39} \pm 0.07$, BF(B0 ->eta K0 gamma) = $(7.1^{+2.1}_{-2.0} \pm 0.4) \times 10^{-6}$, BF(B+ ->eta K+ gamma) = $(7.7+-1.0 \pm 0.4) \times 10^{-6}$, and Ach = $(-9.0^{+10.4}_{-9.8} \pm 1.4) \times 10^{-2}$. The first error quoted is 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) [1,2]. In the SM, flavorchanging neutral current processes, such as b → sγ, proceed via radiative loop diagrams. The loop diagrams may also contain new heavy particles, and therefore are sensitive to NP. The measured branching fractions of inclusive b → sγ and exclusive radiative B decays are in agreement with SM predictions [2,3,4]. Recent estimates of the branching fraction of the inclusive b → sγ decay are affected by a theoretical uncertainties as large as the experimental ones [5].
In the SM the photon polarization in radiative decays is dominantly left (right) handed for b (b) decays, resulting in the suppression of mixing-induced [6] CP asymmetries. Because we do not measure the photon helicity, we sum the decay rates for the left-handed and righthanded helicity states. Observation of significant CPviolation in these radiative decay modes would provide a clear sign of NP [7]. We search also for direct CP asymmetry in charged B decays, measuring the charge asymmetry A ch ≡ (Γ − − Γ + )/(Γ − + Γ + ), where Γ is the partial decay width of the B meson, and the superscript corresponds to its charge. This asymmetry in the SM is expected to be very small [8].
In this letter, we present the first measurement of the mixing-induced CP violation in the decay mode B 0 → ηK 0 γ. Branching fractions for the decay modes B 0 → ηK 0 γ and B + → ηK + γ [9] and time-integrated charge-asymmetry for B + → ηK + γ have been measured previously by the Belle [10] and BABAR [11] Collaborations. We update our previous measurements with a data sample that is twice as large.
The results presented here are based on data collected with the BABAR detector [12] at the PEP-II asymmetricenergy e + e − collider [13] located at the Stanford Linear Accelerator Center. We use an integrated luminosity of 423 fb −1 , corresponding to 465 ± 5 million BB pairs, recorded at the Υ(4S) resonance (at a center-of-mass energy of √ s = 10.58 GeV). Description of the BABAR detector and of the reconstruction of charged and neutral particles can be found elsewhere [14]. The B decay daughter candidates are reconstructed through their decays π 0 → γγ, η → γγ (η γγ ), and η → π + π − π 0 (η 3π ). Reconstruction and selection criteria of charged and neutral mesons, and primary photons and the study of continuum and BB backgrounds are described in our previous paper [11].
A B meson candidate is reconstructed by com-bining an 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) rest frame. We require 5.25 < m ES < 5.29 GeV/c 2 and |∆E| < 0.2 GeV.
From a candidate BB pair we reconstruct a B 0 decaying into ηK 0 S γ (B rec ). We also reconstruct the decay point of the other B meson (B tag ) and identify its flavor. The difference ∆t ≡ t rec − t tag of the proper decay times t rec and t tag of the reconstructed and tag B mesons, respectively, is obtained from the measured distance between the B rec and B tag decay vertices and from the boost (βγ = 0.56) of the e + e − system. The ∆t distribution [15] is given by: The upper (lower) sign denotes a decay accompanied by a B 0 (B 0 ) tag, τ is the mean B 0 lifetime, ∆m d is the mixing frequency, and the mistag parameters w and ∆w are the average and difference, respectively, of the probabilities that a true B 0 is incorrectly tagged as a B 0 or vice versa. In the flavor tagging algorithm [16] there are six mutually exclusive tagging categories of different response purities and untagged events with no tagging informations. Tagging and ∆t informations are used for the measurement of the CP -violation parameters S and C in the decay mode B 0 → ηK 0 γ. We use the same technique developed for B 0 → π 0 K 0 S γ decays [15] to reconstruct the B 0 → η γγ K 0 S γ decay point, using the knowledge of the K 0 S trajectory and the average interaction point in a geometric fit. The extraction of ∆t has been extensively validated in data [17] and in a full detector simulation. In about 70% of the selected events the ∆t resolution is sufficient for the time-dependent CPviolation measurement. For the remaining events the ∆t information is not used. For both η γγ K 0 S γ and η 3π K 0 S γ modes we use the events which satisfy the requirements |∆t| < 20 ps and σ ∆t < 2.5 ps, where σ ∆t is the per-event error on ∆t.
We obtain signal event yields and CP -violation parameters from unbinned extended maximum-likelihood (ML) fits. We indicate with j the species of event: signal, qq continuum background, BB peaking background (BP ), and BB non-peaking background (BNP ). The input observables are m ES , ∆E, the output of a Neural Network (NN ), the η invariant mass m η , and ∆t. The NN combines four variables: the absolute values of the cosines of the polar angles with respect to the beam axis in the Υ(4S) frame of the B candidate momentum and the B thrust axis, the ratio of the second and zeroth Fox-Wolfram moments [18], and the absolute value of the cosine of the angle θ T between the thrust axis of the B candidate and that of the rest of the tracks and neutral clusters in the event, calculated in the Υ(4S) frame.
For each species j and tagging category c, we define a total probability density function (PDF) for event i as The factored form of the PDF is a good approximation since correlations between input observables are small. With n j defined to be the number of events of the species j and f j,c the fraction of events of species j for each category c, we write the extended likelihood function for all events belonging to category c as where n j,c is the yield of events of species j found by the fitter in category c and N c the number of events of category c in the sample. We fix f sig,c , f BNP,c , and f BP,c to f B flav ,c , the values measured with a large sample of B-decays to fully reconstructed flavor eigenstates (B flav ) [19]. The total likelihood function L d for decay mode d is given as the product over the seven tagging categories. Finally, when combining decay modes we form the grand likelihood L = L d . The PDF P sig (∆t, σ ∆t ; c), for each category c, is the convolution of F (∆t; c) (Eq. 1) with the signal resolution function (sum of three Gaussians) determined from the B flav sample. The other PDF forms are: the sum of two Gaussians for P sig (m ES ), P sig (∆E), and P sig (m η ); the sum of three Gaussians for P qq (∆t), P BNP (∆t), and P BP (∆t); a non-parametric step function for P j (NN ) [20]; a linear dependence for P qq (∆E), P BNP (∆E), and P BP (∆E); a first-order polynomial plus a Gaussian for P qq (m η ), P BNP (m η ), and P BP (m η ); and for P qq (m ES ), P BNP (m ES ), and P BP (m ES ), the func- , where for the BP PDFs we add a Gaussian. We allow qq background PDF parameters to vary in the fit.
We determine the PDF parameters from Monte Carlo (MC) simulation for the signal and BB backgrounds, 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. Large control samples of B decays to charmed final states with similar topology and a smearing procedure applied to photons during the event reconstruction are used to verify the simulated resolutions in m ES and ∆E. Where the control data samples reveal differences from the MC in mass resolution, we shift or scale the resolution used in the likelihood fits. The largest shift in m ES is 0.6 MeV/c 2 . Any bias in the fit is determined from a large set of simulated experiments in which the qq and BNP backgrounds are generated from the PDFs, and into which we have embedded the expected number of BP and signal events chosen randomly from fully simulated MC samples.
We compute the branching fractions and charge asymmetry from fits made without ∆t or flavor tagging. The free parameters in the fit are: the signal, qq , BNP and BP background yields; the bin weights of the step function for P qq (NN ); the slopes of P qq (∆E) and P qq (m η ); ξ; and for charged modes the signal and background A ch . We apply the same procedure to extract S and C. In this case we add in the fit the ∆t variable and the flavor-tagging information. As free parameters we have also S, C, and the parameters of the P qq (∆t) PDF. Table I lists the results of the fits. The corrected signal yield is the fitted yield minus the fit bias which is in the range 2 − 4%. The efficiency is calculated as the ratio of the number of signal MC events entering the ML fit to the total generated. We compute the branching fractions from the corrected signal yields, reconstruction efficiencies, daughter branching fractions, and the number of produced B mesons. We assume that the branching fractions of the Υ(4S) to B + B − and B 0 B 0 are each equal to 50%. We combine results from different channels by adding their likelihood functions, taking into account the correlated and uncorrelated systematic errors.
The statistical error on the signal yield, S, C and the signal charge asymmetry 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 S (σ) 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. Figure 1 shows, as representative fits, the projections onto m ES and ∆E while Fig. 2 shows the projections onto ∆t and the raw asymmetry between B 0 and B 0 tags. In these projections a subset of the data is used for which the signal likelihood (computed without the variable plotted) exceeds a threshold that optimizes the sensitivity. Figure 3 shows the distribution of the ηK invariant mass for signal events obtained by the event-weighting technique (sPlot) described in Ref. [22]. We use the covariance matrix and PDFs from the ML fit to determine a probability for each signal event. The resulting distri- I: Number of events N in the sample, corrected signal yield, detection efficiency ǫ, daughter branching fraction product Q Bi, significance S (σ) (including systematic uncertainties), and measured branching fraction B with statistical error for each decay mode. For the combined measurements we give S (σ) and the branching fraction with statistical and systematic uncertainty. For the neutral mode we give the S and C parameters for each decay mode and for their combination. For the charged modes we also give the measured signal charge asymmetry A ch . butions (points with errors) are normalized to the signal yield. This mass distribution is useful to compare with theoretical predictions for radiative decays.
The main sources of systematic uncertainties for the time-dependent measurements come from the variation of the signal PDF shape parameters within their errors (0.08 for S, 0.04 for C), and from BB backgrounds (0.09 for S, 0.06 for C). Other minor sources are SVT alignment, beam spot position and size, and interference between the CKM-suppressedb →ūcd amplitude and the favored b → cūd amplitude for some tag-side B decays [23]. The B flav sample is used to determine the errors associated with the signal ∆t resolutions, tagging efficiencies, and mistag rates. Published measurements [4] for τ and ∆m d are used to determine the errors associated with them. Summing all systematic errors in quadrature, we obtain ±0.12 for S and ±0.07 for C.
The main sources of systematic uncertainties for the branching fraction measurements 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 3-23 events, depending on the mode. The uncertainty (1-3 events) from fit bias is taken as half the correction itself. Systematic uncertainties due to lack of knowledge of the primary photon spectrum are estimated to be in the range 2-3% depending on the decay mode. Uncertainties in our knowledge of the efficiency, found from auxiliary studies [14], include 0.4% × N t and 1.8% × 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 [4] provide the uncertainties in the B daughter branching fraction products (0.7-1.8%). A systematic uncertainty of 0.014 is assigned to A ch . This uncertainty is estimated from studies with signal MC events and data control samples and from calculation of the asymmetry due to particles interacting in the detector.
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), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation. * Deceased † Now at Temple University, Philadelphia, Pennsylvania 19122, USA ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy ¶ Also with Università di Sassari, Sassari, Italy * * Also with Università di Roma La Sapienza, I-00185 Roma, Italy † † Now at University of South Alabama, Mobile, Alabama 36688, USA