A Measurement of the Branching Fractions of exclusive \kern 1.8pt\overline{\kern-1.8ptB}{}\rightarrow D^{(*)}(\pi)\ell^{-}\bar{\nu}_% {\ell} Decays in Events with a Fully Reconstructed B Meson

A Measurement of the Branching Fractions of exclusive Decays in Events with a Fully Reconstructed Meson

B. Aubert    M. Bona    Y. Karyotakis    J. P. Lees    V. Poireau    X. Prudent    V. Tisserand    A. Zghiche Laboratoire de Physique des Particules, IN2P3/CNRS et Université de Savoie, F-74941 Annecy-Le-Vieux, France    J. Garra Tico    E. Grauges Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain    L. Lopez    A. Palano    M. Pappagallo Università di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy    G. Eigen    B. Stugu    L. Sun University of Bergen, Institute of Physics, N-5007 Bergen, Norway    G. S. Abrams    M. Battaglia    D. N. Brown    J. Button-Shafer    R. N. Cahn    R. G. Jacobsen    J. A. Kadyk    L. T. Kerth    Yu. G. Kolomensky    G. Kukartsev    G. Lynch    I. L. Osipenkov    M. T. Ronan    K. Tackmann    T. Tanabe    W. A. Wenzel Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA    P. del Amo Sanchez    C. M. Hawkes    N. Soni    A. T. Watson University of Birmingham, Birmingham, B15 2TT, United Kingdom    H. Koch    T. Schroeder Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany    D. Walker University of Bristol, Bristol BS8 1TL, United Kingdom    D. J. Asgeirsson    T. Cuhadar-Donszelmann    B. G. Fulsom    C. Hearty    T. S. Mattison    J. A. McKenna University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1    M. Barrett    A. Khan    M. Saleem    L. Teodorescu Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom    V. E. Blinov    A. D. Bukin    A. R. Buzykaev    V. P. Druzhinin    V. B. Golubev    A. P. Onuchin    S. I. Serednyakov    Yu. I. Skovpen    E. P. Solodov    K. Yu. Todyshev Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia    M. Bondioli    S. Curry    I. Eschrich    D. Kirkby    A. J. Lankford    P. Lund    M. Mandelkern    E. C. Martin    D. P. Stoker University of California at Irvine, Irvine, California 92697, USA    S. Abachi    C. Buchanan University of California at Los Angeles, Los Angeles, California 90024, USA    J. W. Gary    F. Liu    O. Long    B. C. Shen    G. M. Vitug    Z. Yasin    L. Zhang University of California at Riverside, Riverside, California 92521, USA    H. P. Paar    S. Rahatlou    V. Sharma University of California at San Diego, La Jolla, California 92093, USA    C. Campagnari    T. M. Hong    D. Kovalskyi    J. D. Richman University of California at Santa Barbara, Santa Barbara, California 93106, USA    T. W. Beck    A. M. Eisner    C. J. Flacco    C. A. Heusch    J. Kroseberg    W. S. Lockman    T. Schalk    B. A. Schumm    A. Seiden    M. G. Wilson    L. O. Winstrom University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA    E. Chen    C. H. Cheng    D. A. Doll    B. Echenard    F. Fang    D. G. Hitlin    I. Narsky    T. Piatenko    F. C. Porter California Institute of Technology, Pasadena, California 91125, USA    R. Andreassen    G. Mancinelli    B. T. Meadows    K. Mishra    M. D. Sokoloff University of Cincinnati, Cincinnati, Ohio 45221, USA    F. Blanc    P. C. Bloom    W. T. Ford    J. F. Hirschauer    A. Kreisel    M. Nagel    U. Nauenberg    A. Olivas    J. G. Smith    K. A. Ulmer    S. R. Wagner University of Colorado, Boulder, Colorado 80309, USA    R. Ayad Now at Temple University, Philadelphia, Pennsylvania 19122, USA    A. M. Gabareen    A. Soffer Now at Tel Aviv University, Tel Aviv, 69978, Israel    W. H. Toki    R. J. Wilson Colorado State University, Fort Collins, Colorado 80523, USA    D. D. Altenburg    E. Feltresi    A. Hauke    H. Jasper    M. Karbach    J. Merkel    A. Petzold    B. Spaan    K. Wacker Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany    V. Klose    M. J. Kobel    H. M. Lacker    W. F. Mader    R. Nogowski    J. Schubert    K. R. Schubert    R. Schwierz    J. E. Sundermann    A. Volk Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany    D. Bernard    G. R. Bonneaud    E. Latour    Ch. Thiebaux    M. Verderi Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France    P. J. Clark    W. Gradl    S. Playfer    A. I. Robertson    J. E. Watson University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom    M. Andreotti    D. Bettoni    C. Bozzi    R. Calabrese    A. Cecchi    G. Cibinetto    P. Franchini    E. Luppi    M. Negrini    A. Petrella    L. Piemontese    E. Prencipe    V. Santoro Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy    F. Anulli    R. Baldini-Ferroli    A. Calcaterra    R. de Sangro    G. Finocchiaro    S. Pacetti    P. Patteri    I. M. Peruzzi Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy    M. Piccolo    M. Rama    A. Zallo Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy    A. Buzzo    R. Contri    M. Lo Vetere    M. M. Macri    M. R. Monge    S. Passaggio    C. Patrignani    E. Robutti    A. Santroni    S. Tosi Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy    K. S. Chaisanguanthum    M. Morii Harvard University, Cambridge, Massachusetts 02138, USA    R. S. Dubitzky    J. Marks    S. Schenk    U. Uwer Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany    D. J. Bard    P. D. Dauncey    J. A. Nash    W. Panduro Vazquez    M. Tibbetts Imperial College London, London, SW7 2AZ, United Kingdom    P. K. Behera    X. Chai    M. J. Charles    U. Mallik University of Iowa, Iowa City, Iowa 52242, USA    J. Cochran    H. B. Crawley    L. Dong    V. Eyges    W. T. Meyer    S. Prell    E. I. Rosenberg    A. E. Rubin Iowa State University, Ames, Iowa 50011-3160, USA    Y. Y. Gao    A. V. Gritsan    Z. J. Guo    C. K. Lae Johns Hopkins University, Baltimore, Maryland 21218, USA    A. G. Denig    M. Fritsch    G. Schott Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany    N. Arnaud    J. Béquilleux    A. D’Orazio    M. Davier    J. Firmino da Costa    G. Grosdidier    A. Höcker    V. Lepeltier    F. Le Diberder    A. M. Lutz    S. Pruvot    P. Roudeau    M. H. Schune    J. Serrano    V. Sordini    A. Stocchi    W. F. Wang    G. Wormser Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11, Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France    D. J. Lange    D. M. Wright Lawrence Livermore National Laboratory, Livermore, California 94550, USA    I. Bingham    J. P. Burke    C. A. Chavez    J. R. Fry    E. Gabathuler    R. Gamet    D. E. Hutchcroft    D. J. Payne    C. Touramanis University of Liverpool, Liverpool L69 7ZE, United Kingdom    A. J. Bevan    K. A. George    F. Di Lodovico    R. Sacco    M. Sigamani Queen Mary, University of London, E1 4NS, United Kingdom    G. Cowan    H. U. Flaecher    D. A. Hopkins    S. Paramesvaran    F. Salvatore    A. C. Wren University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom    D. N. Brown    C. L. Davis University of Louisville, Louisville, Kentucky 40292, USA    K. E. Alwyn    N. R. Barlow    R. J. Barlow    Y. M. Chia    C. L. Edgar    G. D. Lafferty    T. J. West    J. I. Yi University of Manchester, Manchester M13 9PL, United Kingdom    J. Anderson    C. Chen    A. Jawahery    D. A. Roberts    G. Simi    J. M. Tuggle University of Maryland, College Park, Maryland 20742, USA    C. Dallapiccola    S. S. Hertzbach    X. Li    E. Salvati    S. Saremi University of Massachusetts, Amherst, Massachusetts 01003, USA    R. Cowan    D. Dujmic    P. H. Fisher    K. Koeneke    G. Sciolla    M. Spitznagel    F. Taylor    R. K. Yamamoto    M. Zhao Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA    S. E. Mclachlin    P. M. Patel    S. H. Robertson McGill University, Montréal, Québec, Canada H3A 2T8    A. Lazzaro    V. Lombardo    F. Palombo Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy    J. M. Bauer    L. Cremaldi    V. Eschenburg    R. Godang    R. Kroeger    D. A. Sanders    D. J. Summers    H. W. Zhao University of Mississippi, University, Mississippi 38677, USA    S. Brunet    D. Côté    M. Simard    P. Taras    F. B. Viaud Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7    H. Nicholson Mount Holyoke College, South Hadley, Massachusetts 01075, USA    G. De Nardo    L. Lista    D. Monorchio    C. Sciacca Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy    M. A. Baak    G. Raven    H. L. Snoek NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands    C. P. Jessop    K. J. Knoepfel    J. M. LoSecco University of Notre Dame, Notre Dame, Indiana 46556, USA    G. Benelli    L. A. Corwin    K. Honscheid    H. Kagan    R. Kass    J. P. Morris    A. M. Rahimi    J. J. Regensburger    S. J. Sekula    Q. K. Wong Ohio State University, Columbus, Ohio 43210, USA    N. L. Blount    J. Brau    R. Frey    O. Igonkina    J. A. Kolb    M. Lu    R. Rahmat    N. B. Sinev    D. Strom    J. Strube    E. Torrence University of Oregon, Eugene, Oregon 97403, USA    G. Castelli    N. Gagliardi    A. Gaz    M. Margoni    M. Morandin    M. Posocco    M. Rotondo    F. Simonetto    R. Stroili    C. Voci Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy    E. Ben-Haim    H. Briand    G. Calderini    J. Chauveau    P. David    L. Del Buono    O. Hamon    Ph. Leruste    J. Malclès    J. Ocariz    A. Perez    J. Prendki Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France    L. Gladney University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA    M. Biasini    R. Covarelli    E. Manoni Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy    C. Angelini    G. Batignani    S. Bettarini    M. Carpinelli Also with Universita’ di Sassari, Sassari, Italy    A. Cervelli    F. Forti    M. A. Giorgi    A. Lusiani    G. Marchiori    M. Morganti    M. A. Mazur    N. Neri    E. Paoloni    G. Rizzo    J. J. Walsh Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy    J. Biesiada    Y. P. Lau    D. Lopes Pegna    C. Lu    J. Olsen    A. J. S. Smith    A. V. Telnov Princeton University, Princeton, New Jersey 08544, USA    E. Baracchini    G. Cavoto    D. del Re    E. Di Marco    R. Faccini    F. Ferrarotto    F. Ferroni    M. Gaspero    P. D. Jackson    M. A. Mazzoni    S. Morganti    G. Piredda    F. Polci    F. Renga    C. Voena Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy    M. Ebert    T. Hartmann    H. Schröder    R. Waldi Universität Rostock, D-18051 Rostock, Germany    T. Adye    B. Franek    E. O. Olaiya    W. Roethel    F. F. Wilson Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom    S. Emery    M. Escalier    A. Gaidot    S. F. Ganzhur    G. Hamel de Monchenault    W. Kozanecki    G. Vasseur    Ch. Yèche    M. Zito DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France    X. R. Chen    H. Liu    W. Park    M. V. Purohit    R. M. White    J. R. Wilson University of South Carolina, Columbia, South Carolina 29208, USA    M. T. Allen    D. Aston    R. Bartoldus    P. Bechtle    J. F. Benitez    R. Cenci    J. P. Coleman    M. R. Convery    J. C. Dingfelder    J. Dorfan    G. P. Dubois-Felsmann    W. Dunwoodie    R. C. Field    T. Glanzman    S. J. Gowdy    M. T. Graham    P. Grenier    C. Hast    W. R. Innes    J. Kaminski    M. H. Kelsey    H. Kim    P. Kim    M. L. Kocian    D. W. G. S. Leith    S. Li    B. Lindquist    S. Luitz    V. Luth    H. L. Lynch    D. B. MacFarlane    H. Marsiske    R. Messner    D. R. Muller    H. Neal    S. Nelson    C. P. O’Grady    I. Ofte    A. Perazzo    M. Perl    B. N. Ratcliff    A. Roodman    A. A. Salnikov    R. H. Schindler    J. Schwiening    A. Snyder    D. Su    M. K. Sullivan    K. Suzuki    S. K. Swain    J. M. Thompson    J. Va’vra    A. P. Wagner    M. Weaver    W. J. Wisniewski    M. Wittgen    D. H. Wright    H. W. Wulsin    A. K. Yarritu    K. Yi    C. C. Young    V. Ziegler Stanford Linear Accelerator Center, Stanford, California 94309, USA    P. R. Burchat    A. J. Edwards    S. A. Majewski    T. S. Miyashita    B. A. Petersen    L. Wilden Stanford University, Stanford, California 94305-4060, USA    S. Ahmed    M. S. Alam    R. Bula    J. A. Ernst    B. Pan    M. A. Saeed    S. B. Zain State University of New York, Albany, New York 12222, USA    S. M. Spanier    B. J. Wogsland University of Tennessee, Knoxville, Tennessee 37996, USA    R. Eckmann    J. L. Ritchie    A. M. Ruland    C. J. Schilling    R. F. Schwitters University of Texas at Austin, Austin, Texas 78712, USA    J. M. Izen    X. C. Lou    S. Ye University of Texas at Dallas, Richardson, Texas 75083, USA    F. Bianchi    D. Gamba    M. Pelliccioni Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy    M. Bomben    L. Bosisio    C. Cartaro    F. Cossutti    G. Della Ricca    L. Lanceri    L. Vitale Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy    V. Azzolini    N. Lopez-March    F. Martinez-Vidal    D. A. Milanes    A. Oyanguren IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain    J. Albert    Sw. Banerjee    B. Bhuyan    K. Hamano    R. Kowalewski    I. M. Nugent    J. M. Roney    R. J. Sobie University of Victoria, Victoria, British Columbia, Canada V8W 3P6    T. J. Gershon    P. F. Harrison    J. Ilic    T. E. Latham    G. B. Mohanty Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom    H. R. Band    X. Chen    S. Dasu    K. T. Flood    J. J. Hollar    P. E. Kutter    Y. Pan    M. Pierini    R. Prepost    C. O. Vuosalo    S. L. Wu University of Wisconsin, Madison, Wisconsin 53706, USA
July 18, 2019
Abstract

We report a measurement of the branching fractions for decays based on 341.1 fb of data collected at the resonance with the BABAR detector at the PEP-II  storage rings. Events are tagged by fully reconstructing one of the mesons in a hadronic decay mode. We obtain , , , , , , and .

pacs:
13.20He,12.38.Qk,14.40Nd

BABAR-PUB-07/071

SLAC-PUB-13056

thanks: Deceasedthanks: Deceasedthanks: Deceased

The BABAR Collaboration

The determination of the individual exclusive branching fractions of decays ell () is important for the study of the semileptonic decays of the meson. Improvement in the knowledge of these branching fractions is also important to reduce the systematic uncertainty in the measurements of the Cabibbo-Kobayashi-Maskawa CKM () matrix elements and . For example, one of the leading sources of systematic uncertainty in the extraction of from the exclusive decay is the limited knowledge of the background due to . Improved measurements of decays will also benefit the accuracy of the extraction of , as analyses are extending into kinematic regions in which these decays represent a sizable background.

Based on current measurements aleph (); delphi (); babar-1 (); babar-2 (); belle () the rate of inclusive semileptonic decays exceeds the sum of the measured exclusive decay rates pdg (). While and decays account for about 70% of this total, the contribution of other states, including resonant and non-resonant (denoted by ), is not yet well measured and may help to explain the inclusive-exclusive discrepancy.

In this letter, we present measurements of the branching fractions for decays, separately for charged and neutral mesons.

The analysis is based on data collected with the BABAR detector detector () at the PEP-II asymmetric-energy storage rings. The data consist of a total of 341.1 fb recorded at the resonance, corresponding to 378 million  pairs. An additional 36 fb off-peak data sample, taken at a center-of-mass (CM) energy 40 MeV below the resonance, is used to study background from events (continuum production). A detailed GEANT4-based Monte Carlo (MC) simulation Geant () of  and continuum events is used to study the detector response, its acceptance, and to test the analysis techniques. The simulation models decays using calculations based on Heavy Quark Effective Theory HQETBaBar (), decays using the ISGW2 model ISGW (), and decays using the Goity-Roberts model Goity ().

We select semileptonic decays in events containing a fully reconstructed meson (), which allows us to constrain the kinematics, reduce the combinatorial background, and determine the charge and flavor of the signal meson.

We first reconstruct the semileptonic decay, selecting a lepton with momentum in the center-of-mass frame higher than 0.6 GeV/. Electrons from photon conversions and Dalitz decays are removed by searching for pairs of oppositely charged tracks that form a vertex with an invariant mass compatible with a photon conversion or a Dalitz decay. Candidate mesons, having the correct charge-flavor correlation with the lepton, are reconstructed in the , , , , , , , , and channels, and mesons in the , , , , , , and channels. In events with multiple candidates, the candidate with the best - vertex fit is selected. Candidate mesons are reconstructed by combining a candidate with a pion or a photon in the , , , and channels. In events with multiple candidates, we choose the candidate with the smallest based on the deviations from the nominal values of the invariant mass and the invariant mass difference between the and the , using the measured resolution.

We reconstruct decays of the type , where represents a collection of hadrons with a total charge of , composed of , where , , and . Using and as seeds for decays, we reconstruct about 1000 different decay chains.

The kinematic consistency of a candidate with a meson decay is evaluated using two variables: the beam-energy substituted mass , and the energy difference . Here refers to the total CM energy, and and denote the momentum and energy of the candidate in the CM frame. For correctly identified decays, the distribution peaks at the meson mass, while is consistent with zero. We select a candidate in the signal region defined as 5.27 GeV/ 5.29 GeV/, excluding candidates with daughter particles in common with the charm meson or the lepton from the semileptonic decay. In the case of multiple candidates in an event, we select the one with the smallest value. The and the candidates are required to have the correct charge-flavor correlation. Mixing effects in the sample are accounted for as described in BBmixing (). Cross-feed effects, , candidates erroneously reconstructed as a neutral (charged) , are subtracted using estimates from the simulation.

For decays, candidates are selected within 2 (1.5-2.5, depending on the decay mode) of the mass ( mass difference), with typically around 8 (1-7) MeV. We also require the cosine of the angle between the directions of the candidate and the lepton in the CM frame to be less than zero, to reduce background from non- semileptonic decays.

We reconstruct and decays starting from the corresponding samples and selecting events with only one additional reconstructed charged track that has not been used for the reconstruction of the , the signal , or the lepton. For the and the decays, we additionally require the invariant mass difference to be greater than 0.18 GeV/ to veto events. To reduce the combinatorial background in the mode, we also require the total extra energy in the event, obtained by summing the energy of all the showers in the electromagnetic calorimeter that have not been assigned to the or the candidates, to be less than 1 GeV.

The exclusive semileptonic decays are identified by the missing mass squared in the event, , defined in terms of the particle four-momenta in the CM frame of the reconstructed final states. For correctly reconstructed signal events, the only missing particle is the neutrino, and peaks at zero. Other semileptonic decays, where one particle is not reconstructed (feed-down) or is erroneously added (feed-up) to the charm candidate, exhibit higher or lower values in . To obtain the semileptonic signal yields, we perform a one-dimensional extended binned maximum likelihood fit Barlow () to the distributions. The fitted data samples are assumed to contain four different types of events: signal events, feed-down or feed-up from other semileptonic decays, combinatoric  and continuum background, and hadronic decays (mainly due to hadrons misidentified as leptons). For the fit to the distributions of the channel, we also include a component corresponding to other misreconstructed decays. We use the MC predictions for the different semileptonic decay distributions to obtain the Probability Density Functions (PDFs). The combinatoric  and continuum background shape is also estimated by the MC simulation, and we use the off-peak data to provide the continuum background normalization. The shape of the continuum background distribution predicted by the MC simulation is consistent with that obtained from the off-peak data.

The distributions are compared with the results of the fits in Fig. 1 for each of the channels. The fitted signal yields and the signal efficiencies, accounting for the reconstruction, are listed in Table 1.

Figure 1: (Color online) Fit to the distribution for a) , b) , c) , d) , e) , f) , g) , and h) : the data (points with error bars) are compared to the results of the overall fit (sum of the solid histograms). The PDFs for the different fit components are stacked and shown in different colors.

To reduce the systematic uncertainty, the exclusive branching fractions relative to the inclusive semileptonic branching fraction are measured. A sample of events is selected by identifying a charged lepton with CM momentum greater than 0.6 GeV/ and the correct charge-flavor correlation with the candidate. In the case of multiple candidates in an event, we select the one reconstructed in the decay channel with the highest purity, defined as the fraction of signal events in the signal region. Background components peaking in the signal region include cascade meson decays (, the lepton does not come directly from the ) and hadronic decays, and are subtracted by using the corresponding MC distributions. The total yield for the inclusive decays is obtained from a maximum likelihood fit to the distribution of the candidates using an ARGUS function Argus () for the description of the combinatorial  and continuum background, and a Crystal Ball function CrystallBall () for the signal. Additional Crystal Ball and ARGUS functions are used to model a broad-peaking component, included in the signal definition, due to real decays for which, in the reconstruction, neutral particles have not been identified or have been interchanged with the semileptonic decays. Fig. 2 shows the distribution of the candidates in the and sample. The fit yields 159896 1361 events for the sample and 96771 968 events for the sample.

Figure 2: (Color online) distributions of the a) , and b) samples. The data (points with error bars) are compared to the result of the fit (solid line). The dashed lines show the broad-peaking component and the sum of the combinatorial and continuum background.

The relative branching fractions are obtained by correcting the signal yields for the reconstruction efficiencies (estimated from  MC events) and normalizing to the inclusive signal yield, following the relation . Here, is the number of signal events for the various modes, reported in Table 1 together with the corresponding reconstruction efficiencies , is the signal yield, and is the corresponding reconstruction efficiency including the reconstruction, equal to 0.36% and 0.23% for the and decays, respectively. The absolute branching fractions are then determined using the semileptonic branching fraction and the ratio of the and the lifetimes  pdg ().

Decay Mode Decay Mode
1635 61 1.71 0.02 174 25 1.02 0.03
3050 73 1.27 0.01 306 27 1.26 0.03
  852 40 0.94 0.02 107 20 0.60 0.03
2045 55 0.91 0.01 130 20 0.66 0.02
Table 1: Signal yields and reconstruction efficiencies for the decays.

Numerous sources of systematic uncertainties have been investigated. The uncertainties due to the detector simulation are established by varying, within bounds given by data control samples, the tracking efficiency of all charged tracks (resulting in 1.2-2.7% relative systematic uncertainty among the different decay modes), the calorimeter efficiency (0.5-1.8%), the lepton identification efficiency (0.4-3%), and the reconstruction efficiency for low momentum charged (1.2%) and neutral pions (1.3%). We evaluate the systematic uncertainties associated with the MC simulation of various signal and background processes: photon conversion and Dalitz decay (0.04-0.4%), cascade decay contamination (0.6-1%), and flavor cross-feed (0.2-0.3%). We vary the and form factors within their measured uncertainties HQETBaBar () (0.4-0.8%) and we include the uncertainty on the branching fractions of the reconstructed and modes (2.3-4.4%), and on the absolute branching fraction used for the normalization (1.9%). We also include a systematic uncertainty due to differences in the efficiency of the selection in the exclusive selection of decays and the inclusive reconstruction (0.9-5.6%), and the extraction of the (0.4-1.8%) and (0.5-0.9%) signal yields. The complete set of systematic uncertainties is given in Ref. epaps ().

We measure the following branching fractions:

The accuracy of the branching fraction measurements for the decays is comparable to that of the current world average pdg (). We compute the total branching fractions of the decays assuming isospin symmetry, , to estimate the branching fractions of final states, obtaining:

where we assume the systematic uncertainties on the and modes to be completely correlated. These results are consistent with, but have smaller uncertainties than, recent results from the Belle collaboration belle ().

By comparing the sum of the measured branching fractions for with the inclusive branching fraction pdg (), a discrepancy is observed, which is most likely due to decays with .

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), MIST (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

References

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Systematic uncertainty on
Tracking efficiency 1.4 1.2 1.4 1.5
Neutral reconstruction 0.7 1.9 0.5 1.1
lepton ID 0.5 0.4 0.5 0.6
Soft particle efficiency - 1.3 - 1.2
Monte Carlo corrections
Conversion and Dalitz decay background 0.04 0.07 0.06 0.05
Cascade decay background 0.6 0.6 1.0 1.0
cross-feed 0.2 0.3 0.2 0.3
Form factors 0.4 0.8 0.4 0.8
branching fractions 2.3 2.1 4.1 2.6
branching fractions - 2.8 - 0.8
branching fraction 1.9 1.9 1.9 1.9
selection 0.9 1.7 1.8 1.3
Fit technique
yield 0.5 0.5 0.9 0.9
yield 0.6 0.4 1.2 0.4
Total systematic error 3.7 5.2 5.4 4.5
Table 2: Systematic uncertainties (relative errors in %) in the measurement of .
Systematic uncertainty on
Tracking efficiency 1.8 2.7 1.5 1.7
Neutral reconstruction 1.7 1.8 1.1 1.8
lepton ID 2.3 3.0 2.6 1.8
Soft particle efficiency - 1.2 - 1.3
Monte Carlo corrections
Conversion and Dalitz decay background 0.15 0.4 0.05 0.2
Cascade decay background 0.6 0.6 1.0 1.0
cross-feed 0.2 0.3 0.2 0.3
Form factors 0.4 0.8 0.4 0.8
branching fractions 4.2 2.8 2.5 2.9
branching fractions - 0.9 - 3.3
branching fraction 1.9 1.9 1.9 1.9
selection 5.0 4.3 4.0 5.6
Fit technique
yield 0.5 0.5 0.9 0.9
yield 1.2 0.9 1.8 1.5
Total systematic error 7.7 7.3 6.4 8.4
Table 3: Systematic uncertainties (relative errors in %) in the measurement of .
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