Measurement of B --> K-*(892)gamma Branching Fractions and CP and Isospin Asymmetries

We present an analysis of the decays B 0 ! K (cid:1) 0 ð 892 Þ (cid:1) and B þ ! K (cid:1)þ ð 892 Þ (cid:1) using a sample of about 383 (cid:2) 10 6 B (cid:1) B events collected with the BABAR detector at the PEP-II asymmetric energy B factory. We measure the branching fractions B ð B 0 ! K (cid:1) 0 (cid:1) Þ ¼ ð 4 : 47 (cid:3) 0 : 10 (cid:3) 0 : 16 Þ (cid:2) 10 (cid:4) 5 and B ð B þ ! K (cid:1)þ (cid:1) Þ ¼ ð 4 : 22 (cid:3) 0 : 14 (cid:3) 0 : 16 Þ (cid:2) 10 (cid:4) 5 . We constrain the direct CP asymmetry to be

À0:033 < AðB ! K Ã Þ < 0:028 and the isospin asymmetry to be 0:017 < Á 0À < 0:116, where the limits are determined by the 90% confidence interval and include both the statistical and systematic uncertainties. DOI In the standard model (SM), the decays B ! K Ã [1] proceed dominantly through one-loop b ! s electromagnetic penguin transitions. Some extensions of the SM predict new high-mass particles that can exist in the loop and alter the branching fractions from their SM predictions. Previous measurements of the branching fractions [2][3][4] are in agreement with and are more precise than SM predictions [5][6][7][8][9], which suffer from large hadronic uncertainties.
The time-integrated CP (A) and isospin (Á 0À ) asymmetries have smaller theoretical uncertainties [10], and therefore provide more stringent tests of the SM. They are defined by where the symbol À denotes the partial width. The SM predictions for A are on the order of 1% [11], while those for Á 0À range from 2% to 10% [8,12]. However, new physics could alter these parameters significantly [12][13][14], and thus precise measurements can constrain those models. In particular, constraining the isospin asymmetry to be positive can exclude significant regions of the minimal supersymmetric model parameter space [12].
In this Letter, we report measurements of BðB 0 ! K Ã0 Þ, BðB þ ! K Ãþ Þ, Á 0À , and A. We use a data sample containing about 383 Â 10 6 B " B events, corresponding to an integrated luminosity of 347 fb À1 , recorded at a center-of-mass (c.m.) energy corresponding to the Çð4SÞ mass. The data were taken with the BABAR detector [15] at the PEP-II asymmetric e þ e À collider. We also make use of events simulated using Monte Carlo (MC) methods and a GEANT4 [16] detector simulation. These results supercede the previous BABAR measurements [3].
B ! K Ã decays are reconstructed in the following K Ã modes: For each signal decay mode, the selection requirements described below have been optimized for the maximum statistical sensitivity of S= ffiffiffiffiffiffiffiffiffiffiffiffiffi S þ B p , where S and B are the rates for signal and background, respectively, and the assumed signal branching fraction is 4:0 Â 10 À5 [3]. The dominant source of background is continuum events [e þ e À ! q " qðÞ, with q ¼ u; d; s; c] that contain a highenergy photon from a % 0 or decay or from an initial-state radiation process. Backgrounds coming from B " B events are mostly from higher-multiplicity b ! s decays, where one or more particles have not been reconstructed, and from decays of one B ! K Ã mode that enter the signal selection of another mode by misreconstructing the K Ã meson.
Photon candidates are identified as localized energy deposits in the calorimeter (EMC) that are not associated with any charged track. The signal photon candidate is required to have a c.m. energy between 1.5 and 3.5 GeV, to be well isolated and to have a shower shape consistent with an individual photon [17]. In order to veto photons from % 0 and decays, we form photon pairs composed of the signal photon candidate and all other photon candidates in the event. We then reject signal photon candidates consistent with coming from a % 0 or decay based on a likelihood ratio that uses the energy of the partner photon, and the invariant mass of the pair.
Charged particles, except those used to form K S candidates, are selected from well-reconstructed tracks that have at least 12 hits in the drift chamber (DCH), and are required to be consistent with coming from the e þ e À interaction region. They are identified as K or % mesons by the Cherenkov angle measured in the Cherenkov photon detector (DIRC) as well as by energy loss of the track (dE=dx) in the silicon vertex tracker and DCH. The K S candidates are reconstructed from two oppositely charged tracks that come from a common vertex. In the K Ã0 ! K S % 0 (K Ãþ ! K S % þ ) mode, we require the invariant mass of the pair to be 0:49 < m % þ % À < 0:52 GeV=c 2 (0:48 < m % þ % À < 0:52 GeV=c 2 ) and the reconstructed decay length of the K S to be at least 9.3(10) times its uncertainty.
We form % 0 candidates by combining two photons (excluding the signal photon candidate) in the event, each of which has an energy greater than 30 MeV in the laboratory frame. We require the invariant mass of the pair to be 0:112 < m < 0:15 GeV=c 2 and 0:114 < m < 0:15 GeV=c 2 for the K Ã0 ! K S % 0 and K Ãþ ! K þ % 0 modes, respectively. In order to refine the % 0 threemomentum vector, we perform a mass-constrained fit of the two photons.
The K Ã and high-energy photon candidates are combined to form B candidates. We define in the c.m. frame (the asterisk denotes a c.m. quantity) B is the energy of the B meson candidate and E Ã beam is the beam energy. The beam-energy-substituted mass is week ending 20 NOVEMBER 2009 tum of the B candidate. In addition, we consider the helicity angle H of the K Ã , defined as the angle between the momenta one of the daughters of the K Ã meson and the B candidate in the K Ã rest frame. The distribution of cos H is sin 2 for signal events. Signal events have ÁE close to zero with a Gaussian resolution of approximately 50 MeV, and an m ES distribution centered at the mass of the B meson with a Gaussian resolution of approximately 3 MeV=c 2 . We only consider candidates in the ranges À0:3 < ÁE < 0:3 GeV, m ES > 5:22 GeV=c 2 , and j cos H j < 0:75. To eliminate badly reconstructed events, we apply a loose selection criterion to the vertex separation (and its uncertainty) along the beam axis between the B meson candidate and the rest of the event (ROE). The ROE is defined as all charged tracks and neutral energy deposits in the calorimeter that are not used to reconstruct the B candidate.
In order to reject continuum background, we combine 13 variables into a neural network. One class of these variables exploits the topological differences between isotropically distributed signal events and jetlike continuum events by considering correlations between the B meson candidate and the ROE. The other class exploits the fact that B meson decays tend to not conserve flavor, while continuum events tend to be flavor-conserving. The discriminating variables are described in Ref. [18]. Each signal mode has a separately trained neural network, whose output peaks at a value of one for signal-like events and zero for backgroundlike events. A selection is made upon the output.
After applying all the selection criteria, there are, on average, $1:1B 0 =B þ candidates per event in simulated signal events. In events with multiple candidates, we select the candidate with the reconstructed K Ã mass closest to the nominal K Ã mass [19].
We perform an unbinned extended maximum likelihood fit to extract the signal yield, constructing a separate fit for each mode. Since the correlations among the three observables ðm ES ; ÁE; cos H Þ j are small, we use uncorrelated probability distribution functions (PDFs) each representing the observables to construct the likelihood function. The likelihood function is where N is the number of events, M ¼ 3 is the number of hypotheses (signal, continuum, and B " B), and n i is the yield of a particular hypothesis. P i is the product of onedimensional PDFs over the three dimensionsx, and represents the fit parameters. All types of B " B background are included in the B " B component, which is suppressed by the use of cos H . The signal m ES distribution for the K Ã0 ! K S % 0 and K Ãþ ! K þ % 0 modes is described by a Crystal Ball function [20], which has two tail parameters that are fixed to values obtained from MC simulation. For the K Ã0 ! K þ % À and K Ãþ ! K S % þ modes, the signal m ES distribution is parametrized as a piecewise function fðxÞ ¼ expfÀðx À "Þ 2 =½' 2 L;R þ L;R ðx À "Þ 2 g, defined to the left (L) and right (R) of ", which is the peak position of the distribution. Here, ' L;R and L;R are the widths and measures of the tails, respectively, to the left and right of the peak. We constrain ' L ¼ ' R , which is floated, and fix L;R to values obtained from MC simulation. This same function also describes the signal ÁE distribution for each mode, but with different values for the parameters. In addition, we allow ' L and ' R to float independently. The cos H distribution for the signal component is modeled by a second-order polynomial, with all of its parameters floating in the fit. For the continuum hypothesis, the m ES PDF is parametrized by an ARGUS function [21], with its shape parameter floating in the fit. The continuum ÁE and cos H shapes are modeled by a first-or second-order polynomial with its parameters floating in the fit. Various functional forms are used to describe the B " B background, all parameters of which are taken from MC simulation and held fixed. All of the component yields are floating. Figure 1 and Table I show the results of the likelihood fit to data. The branching fractions have been obtained using BðÇð4SÞ ! B 0 " B 0 Þ ¼ 0:484 AE 0:006; BðÇð4SÞ ! B þ B À Þ ¼ 0:516 AE 0:006 [19]. Also shown are the combined branching fractions, which have been calculated taking into account correlated systematic errors.
The CP asymmetry A is measured in three modes: In each of these modes, the final state of the signal B meson is determined by its final state daughters. The fit is accomplished by performing a simultaneous fit to the two flavor subsamples (K Ã and " K Ã ) in each mode. All shape parameters are assumed to be flavor independent and the A of each component is floated in the fit. Table I gives the individual and combined A results. Table II lists the sources of systematic uncertainty for the branching fractions for all four modes. The ''fit model'' systematic incorporates uncertainties due to imperfect knowledge of the normalization and shape of the inclusive B ! X s spectra, and the choice of fixed parameters. The ''signal PDF bias'' systematic uncertainty characterizes any bias resulting from correlations among the three observables, or incorrect modeling of the signal PDFs. The remaining sources of error on the signal efficiency are studied using control samples in the data. From all of these studies, we derive signal efficiency correction factors and associated uncertainties. The total corrections are 0.953, 0.897, 0.919, and 0.936 for the K Ã0 ! K þ % À , K Ã0 ! K S % 0 , K Ãþ ! K þ % 0 , and K Ãþ ! K S % þ modes, respectively. The systematic error on A comes entirely from the hadronic interaction of the final state mesons with the detector material. This can cause asymmetries in tracking efficiency, which is studied using existing hadronic interaction data, and in particle identification, which is studied using a D Ãþ ! D 0 % þ ðD 0 ! K À % þ Þ control sample. The D Ãþ control sample gives a shift of À0:33% for K's and þ0:03% for %'s, while the hadronic data give a shift of À0:38% for K's and þ0:02% for %'s. The systematic errors for the isospin asymmetry are calculated from the branching fractions, taking into account correlated systematic errors.
We combine the branching fractions and the ratio of the B þ and B 0 lifetime ( þ =( 0 ¼ 1:071 AE 0:009 [19] to obtain the isospin asymmetry Á 0À ¼ 0:066 AE 0:021 AE 0:022, which corresponds to 0:017 < Á 0À < 0:116 at the 90% confidence interval. We also measure AðB þ ! K Ãþ Þ ¼ 0:018 AE 0:028 AE 0:007. The total combined CP asymmetry is A ¼ À0:003 AE 0:017 AE 0:007, with a 90% confidence interval of À0:033 < A < 0:028. Figure 2 shows the relativistic P-wave Breit-Wigner line shape fit to the K% invariant mass distribution of data events weighted using the sPlot technique [22] to project out the signal component. For the K Ã0 ! K S % 0 and K Ãþ ! K þ % 0 modes, we convolve the Breit-Wigner line shape with a Gaussian with a width of 10 MeV (determined  from MC simulation) to account for detector resolution. For the K Ã0 ! K þ % À and the K Ãþ ! K S % þ modes, the detector resolution is negligible. The results are consistent with the signal events containing only P-wave K Ã mesons and no other K% resonances. We estimate the contribution from the K Ã ð1430Þ to the invariant mass regions m K þ % À , m K þ % 0 , and m K S % þ defined above by using the measured values of the branching fractions of B 0 ! K Ã0 ð1430Þ and B þ ! K Ãþ ð1430Þ [23]. We find that the contribution is $1 event or less.
We conclude that, using a sample that is almost 5 times larger than previously used, we have made considerably more precise measurements of the B ! K Ã decay processes than Refs. [2][3][4]. The measured isospin and CP asymmetries and branching fractions are consistent with SM expectations. By tightly constraining these observables, we have set limits on supersymmetric and other new physics processes, which can interfere with SM processes.
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.