Measurement of branching fractions and charge asymmetries in B decays to an η meson and a K ∗ meson

B. Aubert, M. Bona, D. Boutigny, F. Couderc, Y. Karyotakis, J. P. Lees, V. Poireau, V. Tisserand, A. Zghiche, E. Grauges, A. Palano, J. C. Chen, N. D. Qi, G. Rong, P. Wang, Y. S. Zhu, G. Eigen, I. Ofte, B. Stugu, G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, E. Charles, M. S. Gill, Y. Groysman, R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, G. Lynch, L. M. Mir, T. J. Orimoto, M. Pripstein, N. A. Roe, M. T. Ronan, W. A. Wenzel, P. del Amo Sanchez, M. Barrett, K. E. Ford, A. J. Hart, T. J. Harrison, C. M. Hawkes, A. T. Watson, T. Held, H. Koch, B. Lewandowski, M. Pelizaeus, K. Peters, T. Schroeder, M. Steinke, J. T. Boyd, J. P. Burke, W. N. Cottingham, D. Walker, D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom, C. Hearty, N. S. Knecht, T. S. Mattison, J. A. McKenna, A. Khan, P. Kyberd, M. Saleem, D. J. Sherwood, L. Teodorescu, V. E. Blinov, A. D. Bukin, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu Todyshev, M. Bondioli, M. Bruinsma, M. Chao, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, R. K. Mommsen, W. Roethel, D. P. Stoker, S. Abachi, C. Buchanan, S. D. Foulkes, J. W. Gary, O. Long, B. C. Shen, K. Wang, L. Zhang, H. K. Hadavand, E. J. Hill, H. P. Paar, S. Rahatlou, V. Sharma, J. W. Berryhill, C. Campagnari, A. Cunha, B. Dahmes, T. M. Hong, D. Kovalskyi, J. D. Richman, T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, G. Nesom, T. Schalk, B. A. Schumm, A. Seiden, P. Spradlin, D. C. Williams, M. G. Wilson, J. Albert, E. Chen, A. Dvoretskii, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter, A. Ryd, G. Mancinelli, B. T. Meadows, K. Mishra, M. D. Sokoloff, F. Blanc, P. C. Bloom, S. Chen, W. T. Ford, J. F. Hirschauer, A. Kreisel, M. Nagel, U. Nauenberg, A. Olivas, W. O. Ruddick, J. G. Smith, K. A. Ulmer, S. R. Wagner, J. Zhang, A. Chen, E. A. Eckhart, A. Soffer, W. H. Toki, R. J. Wilson, F. Winklmeier, Q. Zeng, D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, J. Merkel, A. Petzold, B. Spaan, T. Brandt, V. Klose, H. M. Lacker, W. F. Mader, R. Nogowski, J. Schubert, K. R. Schubert, R. Schwierz, J. E. Sundermann, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, Ch. Thiebaux, M. Verderi, P. J. Clark, W. Gradl, F. Muheim, S. Playfer, A. I. Robertson, Y. Xie, M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, G. Cibinetto, E. Luppi, M. Negrini, A. Petrella, L. Piemontese, E. Prencipe, F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Pacetti, P. Patteri, I. M. Peruzzi, ∗ M. Piccolo, M. Rama, A. Zallo, A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge, S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, S. Tosi, G. Brandenburg, K. S. Chaisanguanthum, M. Morii, J. Wu, R. S. Dubitzky, J. Marks, S. Schenk, U. Uwer, D. J. Bard, W. Bhimji, D. A. Bowerman, P. D. Dauncey, U. Egede, R. L. Flack, J. A. Nash, M. B. Nikolich, W. Panduro Vazquez, D. J. Bard, P. K. Behera, X. Chai, M. J. Charles, U. Mallik, N. T. Meyer, V. Ziegler, J. Cochran, H. B. Crawley, L. Dong, V. Eyges, W. T. Meyer, S. Prell, E. I. Rosenberg, A. E. Rubin, A. V. Gritsan, A. G. Denig, M. Fritsch, G. Schott, N. Arnaud, M. Davier, G. Grosdidier, A. Höcker, F. Le Diberder, V. Lepeltier, A. M. Lutz, A. Oyanguren, S. Pruvot, S. Rodier, P. Roudeau, M. H. Schune, A. Stocchi, W. F. Wang, G. Wormser, C. H. Cheng, D. J. Lange, D. M. Wright, C. A. Chavez, I. J. Forster, J. R. Fry, E. Gabathuler, R. Gamet, K. A. George, D. E. Hutchcroft, D. J. Payne, K. C. Schofield, C. Touramanis, A. J. Bevan, F. Di Lodovico, W. Menges, R. Sacco, G. Cowan, H. U. Flaecher, D. A. Hopkins, P. S. Jackson, T. R. McMahon, S. Ricciardi, F. Salvatore, A. C. Wren, D. N. Brown, C. L. Davis, J. Allison, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, M. T. Naisbit, J. C. Williams, J. I. Yi, C. Chen, W. D. Hulsbergen, A. Jawahery, C. K. Lae, D. A. Roberts, G. Simi, G. Blaylock, C. Dallapiccola, S. S. Hertzbach, X. Li, T. B. Moore, S. Saremi, H. Staengle, R. Cowan, G. Sciolla,

Charmless B decays to final states with strangeness are expected to be dominated by b ! s loop (''penguin'') amplitudes. The branching fraction for the decay B ! K is expected to be larger than most similar decays (though not as large as B ! 0 K) due to constructive interference between two penguin amplitudes [4].
While the decay B ! K 892 has been seen previously [5,6], there have been no searches for states with an meson accompanied by K 1430 mesons, and no theoretical predictions exist for these decays. In this Letter we present measurements of branching fractions and charge asymmetries for the decays 2 1430, and B ! K 2 1430, where we denote by K 0 the 0 component of the K spectrum. The charge asymmetry is defined as A ch ÿ ÿ ÿ ÿ =ÿ ÿ ÿ , where the superscript on the width ÿ corresponds to the sign of the B meson or the sign of the charged kaon for B 0 decays.
The results presented here are obtained from data collected with the BABAR detector (described in detail elsewhere [8]) at the PEP-II asymmetric e e ÿ collider located at the Stanford Linear Accelerator Center. The analysis uses an integrated luminosity of 313 fb ÿ1 , corresponding to 344 10 6 B B pairs, recorded at the 4S resonance [center-of-mass (CM) energy s p 10:58 GeV], and follows closely the technique described in detail in Ref. [6]. The sample is 3.9 times larger than that of Ref. [6].
All tracks from resonance candidates are required to have charged particle identification (PID) consistent with kaons or pions. We select , K 0 S , and 0 candidates from the decays ! ( ), ! ÿ 0 ( 3 ), K 0 S ! ÿ , and 0 ! . We impose the following requirements on the invariant masses (in MeV) of the particle candidate final states: 490 < m < 600 for , 520 < m < 570 for 3 , 486 < m < 510 for K 0 S , and 120 < m < 150 for 0 . For K 0 S candidates we require at least 3 standard-deviation () three-dimensional separation between the decay vertex and the e e ÿ collision point. Requirements are loose for the variables used in the maximum likelihood (ML) fit described below. For the K system, we define a lowmass region (LMR) by 755 < m K < 1035 MeV and a high-mass region (HMR) by 1035 < m K < 1535 MeV [9]. For the K we use the helicity frame, defined as the K rest frame with polar axis opposite to the direction of the B. We define H cos H , where the decay angle H is the polar angle of the kaon momentum in the helicity frame. For the LMR, we require ÿ0:95 < H < 1:0 for K 0 and K K 0 S , and ÿ0:7 < H < 1:0 for K K 0 . For the HMR, we require ÿ0:5 < H < 1:0 for all modes in order to remove the region in H having very large backgrounds.
A B-meson candidate is characterized kinematically by the energy-substituted mass m ES 1 4 s ÿ p 2 B 1=2 and en- is the B-meson four-momentum vector, and all values are expressed in the 4S frame. Signal events peak at zero for E, and at the B mass [10] for m ES , with a resolution for E (m ES ) of 30 -45 MeV (3.0 MeV). We require jEj 0:2 GeV and 5:25 m ES < 5:29 GeV.
The angle T between the thrust axis of the B candidate in the 4S frame and that of the rest of the charged tracks and neutral clusters in the event is used to reject the dominant continuum e e ÿ ! q q (q u; d; s; c) background events. The distribution of j cos T j is sharply peaked near 1.0 for combinations drawn from jetlike q q pairs, and nearly uniform for the almost isotropic B-meson decays; we require j cos T j 0:9. Further discrimination from continuum in the ML fit is obtained from energy flow in the event via a Fisher discriminant F that is described in detail elsewhere [6].
For the modes with ! , we reject B ! K background with the requirement j cos dec j 0:86, where dec is the decay angle defined, in the rest frame, as the angle between one of the photons and the B direction. When there are multiple candidates (fewer than 30% of events [9]), we choose the candidate with a value of the reconstructed mass closest to the Particle Data Group mass [10].
We use Monte Carlo (MC) simulations [11] for the few charmless B B background decays that survive the candidate selection and have characteristics similar to the signal. We find these contributions to be negligible for all modes with an ! ÿ 0 decay except 3 K 0 . For all other modes, we include a component in the ML fit to account for them.
We obtain yields and A ch for each decay chain from an extended unbinned maximum likelihood fit with the following input observables: E, m ES , F , m res (the masses of the and K candidates), and H . For each event i and hypothesis j (signal, continuum background, B B background), we define the probability density function (PDF), with resulting likelihood L as follows: where Y j is the yield of events of hypothesis j, and N is the number of events in the sample. The free parameters of the fit are the signal and background yields, between 9 and 11 q q background PDF parameters (see below), and the signal and q q background charge asymmetries. We determine the contributions from K 892, K 0 , and K 2 1430 by fits in the LMR and HMR. The fit in the LMR includes K 892 and K 0 signal components [K 2 1430 is negligible in this region], with the fixed K 0 yield determined from the result of the fit to the HMR. For the fit in the HMR, all three components are included; the K 892 yield is fixed from the result of the fit in the LMR, while the K 0 and K 2 1430 branching fractions are free in a simultaneous fit over the two (four) subdecay modes for K 0 (K ). For the generated K 0 spectrum, we use a LASS model [12] which consists of the K 0 1430 resonance together with an effective-range non- Mode   [13], 9.6% of the B ! K 0 branching fraction is in the region above m K 1535 MeV where the model is most uncertain. The K 2 1430 is generated as a relativistic Breit-Wigner shape with known mass and width [10].
For the signal and B B background components we determine the PDF parameters from MC. For background from continuum and nonpeaking combinations from B decays, we obtain the PDF from (m ES , E) sideband data for each decay, before applying the fit to data in the signal region; we refine this PDF by letting all parameters vary in the final fit. We parametrize each of the functions P sig m ES ; P sig E; P j F and the peaking components of P j m res with either a Gaussian, the sum of two Gaussians, or an asymmetric Gaussian function as required to describe the distribution. For P sig H we use a low order polynomial. Slowly varying distributions (all masses, E and H for continuum background) are represented by one or a combination of linear, quadratic, and phase-space motivated functions [6]. The fitted q q background PDF parameters are found to be in close agreement with the initial values. Control samples with topologies similar to our signal modes [e.g., B ! DK] are used to calibrate the simulated resolutions evaluated from MC [6].
Before applying the fitting procedure to the data we subject it to several tests. In particular, we evaluate possible biases in the yields from our neglect of small residual correlations among discriminating variables in the signal and charmless B B background PDFs. The bias is determined by fitting ensembles of simulated q q experiments generated from the PDFs into which we have embedded the expected number of signal and B B background events, randomly extracted from the fully simulated MC samples. The small biases are listed in Table I. We measure the correlations in the data and find them to be negligibly small.
We compute the branching fraction for each decay by subtracting the fit bias from the measured yield, and dividing the result by the efficiency and the number of produced B B pairs. We assume equal decay rates for the 4S to B B ÿ and B 0 B 0 . In Table I we show for each decay mode the measured branching fraction together with the event yield Y S , efficiency , and A ch . The significance is taken as the square root of the difference between the value of ÿ2 lnL (with systematic uncertainties included) for zero signal and the value at its minimum.
For the LMR the measurements for separate daughter decays are combined by adding the values of ÿ2 lnL as functions of the branching fractions, taking account of the correlated and uncorrelated systematic uncertainties [6] described below.
In Fig. 1 we show projections onto m ES of subsamples enriched with a threshold requirement on the signal likelihood (computed without the variable plotted) that optimizes the sensitivity. There are substantial signals in all four samples. For the HMR, separation of the K 0 and K 2 1430 signals is afforded mainly by the K mass and helicity shapes; projections of these distributions are shown in Fig. 2. The statistical correlations between the two signals are ÿ 0:42 in the HMR fits to both the B 0 and B decays.
The largest systematic uncertainties are due to the signal and B B PDF modeling, the fit bias correction, the modeling of the K mass distribution, the neutral selection efficiency, and neglect of interference between signal components. The PDF modeling error is largely included in the statistical uncertainty because all background parameters are free in the fit. The uncertainties in the signal PDF parameters are estimated from the consistency of fits to MC and data in control samples with similar final states. Varying the signal PDF parameters within these errors, we estimate the mode-dependent uncertainties to be 1-4 events. The uncertainty in the fit bias correction is taken to be half of the correction. We estimate the uncertainty from modeling the B B backgrounds to be less than 1 event. Uncertainties in the reconstruction efficiency, found from auxiliary studies of inclusive control samples [6], are 0.4% per track, 3.0% per = 0 , and 1.9% for a K 0 S . Our estimate of the systematic uncertainty for the number of B B pairs is 1.1%. Published data [10] provide the uncertainties for the B-daughter product branching fractions (1%-2%). The uncertainty due to the efficiency of the cos T requirement is 0.5%. The systematic uncertainty for A ch is estimated to be 2%, dominated by tracking and PID systematic effects [14].  short-dashed, blue). Points with uncertainties represent the data, solid curves the full fit functions, and dotted curves the full background functions.
Because our model does not account for interference among the components, we assign systematic uncertainties based on the mK dependence of the complex phases measured in Ref. [12], with allowance for unknown process-dependent overall phases. The effect is small for the LMR and about 10% for the HMR. For the HMR, the systematic uncertainties are applied after the combined fit, taking submode errors as correlated.
In summary, we have presented improved measurements of the branching fractions for the decays B 0 ! K 0 892 and B ! K 892, as well as measurements of the decays 2 1430, and B ! K 2 1430, which had not been seen previously. The first two supersede previous BABAR measurements [6] and agree with earlier results and theoretical predictions [1][2][3]. We also calculate the branching fraction for the resonant decays to K 0 1430 using the composition of K 0 from [13]. We find BB 0 ! K 0 0 1430 9:6 1:4 0:7 1:1 10 ÿ6 and BB ! K 0 1430 15:8 2:2 1:4 1:7 10 ÿ6 , where the third errors arise from the uncertainties on the branching fraction K 0 1430 ! K [10] and the resonant fraction of K 0 . There are no theoretical predictions for the decays involving spin-0 or 2 mesons. The measured values of A ch are mostly consistent with zero within their uncertainties; the value for B 0 ! K 0 892 shows evidence for direct CP violation.
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.