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Measurements of the Branching Fractions and Bounds on the Charge Asymmetries

of Charmless Three-Body Charged

B

Decays

B. Aubert,1R. Barate,1D. Boutigny,1J.-M. Gaillard,1A. Hicheur,1Y. Karyotakis,1J. P. Lees,1P. Robbe,1V. Tisserand,1 A. Zghiche,1A. Palano,2A. Pompili,2J. C. Chen,3N. D. Qi,3G. Rong,3P. Wang,3Y. S. Zhu,3G. Eigen,4I. Ofte,4 B. Stugu,4G. S. Abrams,5A.W. Borgland,5A. B. Breon,5D. N. Brown,5J. Button-Shafer,5R. N. Cahn,5E. Charles,5

C. T. Day,5M. S. Gill,5A.V. Gritsan,5Y. Groysman,5R. G. Jacobsen,5R.W. Kadel,5J. Kadyk,5L. T. Kerth,5 Yu. G. Kolomensky,5J. F. Kral,5G. Kukartsev,5C. LeClerc,5M. E. Levi,5G. Lynch,5L. M. Mir,5P. J. Oddone,5 T. J. Orimoto,5M. Pripstein,5N. A. Roe,5A. Romosan,5M. T. Ronan,5V. G. Shelkov,5A.V. Telnov,5W. A. Wenzel,5 T. J. Harrison,6C. M. Hawkes,6D. J. Knowles,6R. C. Penny,6A. T. Watson,6N. K. Watson,6T. Deppermann,7K. Goetzen,7

H. Koch,7B. Lewandowski,7M. Pelizaeus,7K. Peters,7H. Schmuecker,7M. Steinke,7N. R. Barlow,8W. Bhimji,8 J. T. Boyd,8N. Chevalier,8W. N. Cottingham,8C. Mackay,8F. F. Wilson,8C. Hearty,9T. S. Mattison,9J. A. McKenna,9

D. Thiessen,9P. Kyberd,10A. K. McKemey,10V. E. Blinov,11A. D. Bukin,11V. B. Golubev,11V. N. Ivanchenko,11 E. A. Kravchenko,11A. P. Onuchin,11S. I. Serednyakov,11Yu. I. Skovpen,11E. P. Solodov,11A. N. Yushkov,11D. Best,12

M. Chao,12D. Kirkby,12A. J. Lankford,12M. Mandelkern,12S. McMahon,12R. K. Mommsen,12W. Roethel,12 D. P. Stoker,12C. Buchanan,13H. K. Hadavand,14 E. J. Hill,14D. B. MacFarlane,14H. P. Paar,14Sh. Rahatlou,14 U. Schwanke,14V. Sharma,14 J.W. Berryhill,15C. Campagnari,15B. Dahmes,15N. Kuznetsova,15S. L. Levy,15 O. Long,15A. Lu,15M. A. Mazur,15J. D. Richman,15W. Verkerke,15J. Beringer,16A. M. Eisner,16C. A. Heusch,16

W. S. Lockman,16T. Schalk,16R. E. Schmitz,16B. A. Schumm,16A. Seiden,16M. Turri,16W. Walkowiak,16 D. C. Williams,16 M. G. Wilson,16J. Albert,17 E. Chen,17M. P. Dorsten,17G. P. Dubois-Felsmann,17A. Dvoretskii,17

D. G. Hitlin,17I. Narsky,17F. C. Porter,17A. Ryd,17A. Samuel,17S. Yang,17S. Jayatilleke,18G. Mancinelli,18 B. T. Meadows,18M. D. Sokoloff,18T. Barillari,19F. Blanc,19P. Bloom,19P. J. Clark,19W. T. Ford,19U. Nauenberg,19 A. Olivas,19P. Rankin,19J. Roy,19J. G. Smith,19W. C. van Hoek,19L. Zhang,19J. L. Harton,20T. Hu,20A. Soffer,20

W. H. Toki,20R. J. Wilson,20J. Zhang,20D. Altenburg,21T. Brandt,21J. Brose,21T. Colberg,21M. Dickopp,21 R. S. Dubitzky,21A. Hauke,21H. M. Lacker,21E. Maly,21R. Mu¨ller-Pfefferkorn,21R. Nogowski,21S. Otto,21 K. R. Schubert,21R. Schwierz,21B. Spaan,21L. Wilden,21D. Bernard,22G. R. Bonneaud,22F. Brochard,22 J. Cohen-Tanugi,22Ch. Thiebaux,22G. Vasileiadis,22M. Verderi,22A. Khan,23D. Lavin,23F. Muheim,23S. Playfer,23 J. E. Swain,23J. Tinslay,23C. Bozzi,24L. Piemontese,24A. Sarti,24E. Treadwell,25F. Anulli,26,* R. Baldini-Ferroli,26

A. Calcaterra,26R. de Sangro,26D. Falciai,26G. Finocchiaro,26P. Patteri,26I. M. Peruzzi,26,* M. Piccolo,26A. Zallo,26 A. Buzzo,27R. Contri,27G. Crosetti,27M. Lo Vetere,27M. Macri,27M. R. Monge,27S. Passaggio,27F. C. Pastore,27 C. Patrignani,27E. Robutti,27A. Santroni,27S. Tosi,27S. Bailey,28M. Morii,28G. J. Grenier,29S.-J. Lee,29U. Mallik,29

J. Cochran,30H. B. Crawley,30J. Lamsa,30W. T. Meyer,30S. Prell,30E. I. Rosenberg,30J. Yi,30M. Davier,31 G. Grosdidier,31A. Ho¨cker,31S. Laplace,31F. Le Diberder,31V. Lepeltier,31A. M. Lutz,31T. C. Petersen,31 S. Plaszczynski,31M. H. Schune,31L. Tantot,31G. Wormser,31R. M. Bionta,32V. Brigljevic´,32C. H. Cheng,32 D. J. Lange,32D. M. Wright,32A. J. Bevan,33J. R. Fry,33E. Gabathuler,33R. Gamet,33M. Kay,33D. J. Payne,33 R. J. Sloane,33C. Touramanis,33M. L. Aspinwall,34D. A. Bowerman,34P. D. Dauncey,34U. Egede,34I. Eschrich,34 G.W. Morton,34J. A. Nash,34P. Sanders,34G. P. Taylor,34J. J. Back,35G. Bellodi,35P. F. Harrison,35H.W. Shorthouse,35

P. Strother,35P. B. Vidal,35G. Cowan,36H. U. Flaecher,36S. George,36M. G. Green,36A. Kurup,36C. E. Marker,36 T. R. McMahon,36S. Ricciardi,36F. Salvatore,36G. Vaitsas,36M. A. Winter,36D. Brown,37C. L. Davis,37J. Allison,38 R. J. Barlow,38A. C. Forti,38P. A. Hart,38F. Jackson,38G. D. Lafferty,38A. J. Lyon,38J. H. Weatherall,38J. C. Williams,38 A. Farbin,39A. Jawahery,39D. Kovalskyi,39C. K. Lae,39V. Lillard,39D. A. Roberts,39G. Blaylock,40C. Dallapiccola,40 K. T. Flood,40S. S. Hertzbach,40R. Kofler,40V. B. Koptchev,40T. B. Moore,40H. Staengle,40S. Willocq,40R. Cowan,41 G. Sciolla,41F. Taylor,41R. K. Yamamoto,41D. J. J. Mangeol,42M. Milek,42P. M. Patel,42A. Lazzaro,43F. Palombo,43 J. M. Bauer,44L. Cremaldi,44V. Eschenburg,44R. Godang,44R. Kroeger,44J. Reidy,44D. A. Sanders,44D. J. Summers,44 H.W. Zhao,44C. Hast,45P. Taras,45H. Nicholson,46C. Cartaro,47N. Cavallo,47G. De Nardo,47F. Fabozzi,47,†C. Gatto,47

L. Lista,47P. Paolucci,47D. Piccolo,47C. Sciacca,47M. A. Baak,48G. Raven,48J. M. LoSecco,49T. A. Gabriel,50 B. Brau,51T. Pulliam,51J. Brau,52R. Frey,52M. Iwasaki,52C. T. Potter,52N. B. Sinev,52D. Strom,52E. Torrence,52 F. Colecchia,53A. Dorigo,53F. Galeazzi,53M. Margoni,53M. Morandin,53M. Posocco,53M. Rotondo,53F. Simonetto,53

R. Stroili,53G. Tiozzo,53C. Voci,53M. Benayoun,54H. Briand,54J. Chauveau,54P. David,54Ch. de la Vaissie`re,54 L. Del Buono,54O. Hamon,54Ph. Leruste,54J. Ocariz,54M. Pivk,54L. Roos,54J. Stark,54S. T’Jampens,54

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P. F. Manfredi,55V. Re,55L. Gladney,56Q. H. Guo,56J. Panetta,56C. Angelini,57G. Batignani,57S. Bettarini,57 M. Bondioli,57F. Bucci,57G. Calderini,57M. Carpinelli,57F. Forti,57M. A. Giorgi,57A. Lusiani,57G. Marchiori,57

F. Martinez-Vidal,57,‡M. Morganti,57N. Neri,57E. Paoloni,57M. Rama,57G. Rizzo,57F. Sandrelli,57J. Walsh,57 M. Haire,58D. Judd,58K. Paick,58D. E. Wagoner,58N. Danielson,59P. Elmer,59C. Lu,59V. Miftakov,59J. Olsen,59 A. J. S. Smith,59E.W. Varnes,59F. Bellini,60G. Cavoto,59,60D. del Re,60R. Faccini,14,60F. Ferrarotto,60F. Ferroni,60 M. Gaspero,60E. Leonardi,60M. A. Mazzoni,60S. Morganti,60M. Pierini,60G. Piredda,60F. Safai Tehrani,60M. Serra,60 C. Voena,60S. Christ,61G. Wagner,61R. Waldi,61T. Adye,62N. De Groot,62B. Franek,62N. I. Geddes,62G. P. Gopal,62

E. O. Olaiya,62S. M. Xella,62R. Aleksan,63S. Emery,63A. Gaidot,63S. F. Ganzhur,63P.-F. Giraud,63 G. Hamel de Monchenault,63W. Kozanecki,63M. Langer,63G.W. London,63B. Mayer,63G. Schott,63G. Vasseur,63 Ch. Yeche,63M. Zito,63M.V. Purohit,64A.W. Weidemann,64F. X. Yumiceva,64D. Aston,65R. Bartoldus,65N. Berger,65

A. M. Boyarski,65O. L. Buchmueller,65M. R. Convery,65D. P. Coupal,65D. Dong,65J. Dorfan,65D. Dujmic,65 W. Dunwoodie,65R. C. Field,65T. Glanzman,65S. J. Gowdy,65E. Grauges-Pous,65T. Hadig,65V. Halyo,65T. Hryn’ova,65 W. R. Innes,65C. P. Jessop,65M. H. Kelsey,65P. Kim,65M. L. Kocian,65U. Langenegger,65D.W. G. S. Leith,65S. Luitz,65 V. Luth,65H. L. Lynch,65H. Marsiske,65S. Menke,65R. Messner,65D. R. Muller,65C. P. O’Grady,65V. E. Ozcan,65

A. Perazzo,65M. Perl,65S. Petrak,65B. N. Ratcliff,65S. H. Robertson,65A. Roodman,65A. A. Salnikov,65 R. H. Schindler,65J. Schwiening,65G. Simi,65A. Snyder,65A. Soha,65J. Stelzer,65D. Su,65M. K. Sullivan,65 H. A. Tanaka,65J. Va’vra,65S. R. Wagner,65M. Weaver,65A. J. R. Weinstein,65W. J. Wisniewski,65D. H. Wright,65 C. C. Young,65P. R. Burchat,66T. I. Meyer,66C. Roat,66S. Ahmed,67J. A. Ernst,67 W. Bugg,68M. Krishnamurthy,68 S. M. Spanier,68R. Eckmann,69H. Kim,69J. L. Ritchie,69R. F. Schwitters,69J. M. Izen,70I. Kitayama,70X. C. Lou,70 S. Ye,70F. Bianchi,71M. Bona,71F. Gallo,71D. Gamba,71C. Borean,72L. Bosisio,72G. Della Ricca,72S. Dittongo,72 S. Grancagnolo,72L. Lanceri,72P. Poropat,72,xL. Vitale,72G. Vuagnin,72R. S. Panvini,73Sw. Banerjee,74C. M. Brown,74 D. Fortin,74P. D. Jackson,74R. Kowalewski,74J. M. Roney,74H. R. Band,75S. Dasu,75M. Datta,75A. M. Eichenbaum,75

H. Hu,75J. R. Johnson,75R. Liu,75F. Di Lodovico,75A. K. Mohapatra,75Y. Pan,75R. Prepost,75S. J. Sekula,75 J. H. von Wimmersperg-Toeller,75J. Wu,75S. L. Wu,75Z. Yu,75and H. Neal76

(BABARCollaboration)

1Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France 2Universita` di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy

3Institute of High Energy Physics, Beijing 100039, China 4University of Bergen, Institute of Physics, N-5007 Bergen, Norway

5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 6University of Birmingham, Birmingham, B15 2TT, United Kingdom

7Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany 8University of Bristol, Bristol BS8 1TL, United Kingdom

9University of British Columbia, Vancouver, BC, Canada V6T 1Z1 10Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

11Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia 12University of California at Irvine, Irvine, California 92697, USA 13University of California at Los Angeles, Los Angeles, California 90024, USA

14University of California at San Diego, La Jolla, California 92093, USA 15University of California at Santa Barbara, Santa Barbara, California 93106, USA

16University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA 17California Institute of Technology, Pasadena, California 91125, USA

18University of Cincinnati, Cincinnati, Ohio 45221, USA 19University of Colorado, Boulder, Colorado 80309, USA 20Colorado State University, Fort Collins, Colorado 80523, USA

21Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany 22Ecole Polytechnique, LLR, F-91128 Palaiseau, France

23University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom

24Universita` di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy 25Florida A&M University, Tallahassee, Florida 32307, USA

26Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy 27Universita` di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy

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31Laboratoire de l’Acce´le´rateur Line´aire, F-91898 Orsay, France 32Lawrence Livermore National Laboratory, Livermore, California 94550, USA

33University of Liverpool, Liverpool L69 3BX, United Kingdom 34University of London, Imperial College, London, SW7 2BW, United Kingdom

35Queen Mary, University of London, E1 4NS, United Kingdom

36University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom 37University of Louisville, Louisville, Kentucky 40292, USA

38University of Manchester, Manchester M13 9PL, United Kingdom 39University of Maryland, College Park, Maryland 20742, USA 40University of Massachusetts, Amherst, Massachusetts 01003, USA

41Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA 42McGill University, Montre´al, QC, Canada H3A 2T8

43Universita` di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy 44University of Mississippi, University, Mississippi 38677, USA

45Universite´ de Montre´al, Laboratoire Rene´ J. A. Le´vesque, Montre´al, QC, Canada H3C 3J7 46Mount Holyoke College, South Hadley, Massachusetts 01075, USA

47Universita` di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy 48NIKHEF, National Institute for Nuclear Physics and High Energy Physics, 1009 DB Amsterdam, The Netherlands

49University of Notre Dame, Notre Dame, Indiana 46556, USA 50Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

51The Ohio State University, Columbus, Ohio 43210, USA 52University of Oregon, Eugene, Oregon 97403, USA

53Universita` di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy 54Universite´s Paris VI et VII, Lab de Physique Nucle´aire H. E., F-75252 Paris, France

55Universita` di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy 56University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

57Universita` di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy 58Prairie View A&M University, Prairie View, Texas 77446, USA

59Princeton University, Princeton, New Jersey 08544, USA

60Universita` di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy 61Universita¨t Rostock, D-18051 Rostock, Germany

62Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom 63DAPNIA, Commissariat a` l’Energie Atomique/Saclay, F-91191 Gif-sur-Yvette, France

64University of South Carolina, Columbia, South Carolina 29208, USA 65Stanford Linear Accelerator Center, Stanford, California 94309, USA

66Stanford University, Stanford, California 94305-4060, USA 67State University of New York, Albany, New York 12222, USA 68University of Tennessee, Knoxville, Tennessee 37996, USA

69University of Texas at Austin, Austin, Texas 78712, USA 70University of Texas at Dallas, Richardson, Texas 75083, USA

71Universita` di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy 72Universita` di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy

73Vanderbilt University, Nashville, Tennessee 37235, USA 74University of Victoria, Victoria, BC, Canada V8W 3P6 75University of Wisconsin, Madison, Wisconsin 53706, USA

76Yale University, New Haven, Connecticut 06511, USA

(Received 3 April 2003; published 29 July 2003)

We present measurements of branching fractions and charge asymmetries for charmlessB-meson decays to three-body final states of charged pions and kaons. The analysis uses 81:8 fb1 of data

collected at the 4S resonance with the BABAR detector at the SLAC PEP-II asymmetric B Factory. We measure the branching fractions BB! 10:93:31:6 106, BB!K 59:13:83:2 106, and BB!KKK 29:62:11:6

106 and provide 90% C.L. upper limits for other decays. We observe no charge asymmetries for

these modes.

DOI: 10.1103/PhysRevLett.91.051801 PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh

The study of charmless hadronicB decays can make important contributions to the understanding ofCP vio-lation in the standard model, as well as to models of hadronic decays. Reference [1] proposes that the inter-ference between various charmless decays and the c0

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charged-B-meson decays to three-body final states of charged pions and kaons [3], with no assumptions about intermediate resonances and with charm contributions subtracted, which allows us to set a tight bound on the charmless contribution to the measurement of [1]. Upper limits and measurements of some of these branch-ing fractions have been obtained previously with smaller statistics [4].

The data used in this analysis were collected at the PEP-II asymmetric ee storage ring with the BABAR

detector, described in detail elsewhere [5]. The on-resonance data sample consists of 88:8 106 BB pairs collected at the 4S resonance during the years 1999 –2002. We also use 9:6 fb1 of off-resonance data, collected 40 MeV below the4Sresonance, to charac-terize the backgrounds fromeeannihilation into light qq pairs. We assume that the 4S decays equally to neutral and chargedB meson pairs.

Hadronic events are selected based on track multiplic-ity and event topology. Backgrounds from nonhadronic events are reduced by requiring the ratio of Fox-Wolfram moments H2=H0 [6] to be less than 0.98. Candidate B decays are formed by combining three charged tracks, where each track is required to have at least 12 hits in the tracking chamber, a minimum transverse momentum of 100 MeV=c, and to be consistent with originating from the beam spot.

Signal decays are identified using two kinematic vari-ables: (i) the difference Ebetween the center-of-mass (CM) energy of theBcandidate andps=2, wherepsis the total CM energy, and (ii) the beam-energy substituted massmES

s=2pipB2=E2ip2B

q

, where theB mo-mentumpB and the four-momentum of the initial state

(Ei;pi) are defined in the laboratory frame. TheEand

mES distributions of signal events are Gaussian with

resolutions of 20 MeV and 2:7 MeV=c2, respectively. The typicalEseparation between modes that differ by substituting a kaon for a pion in the final state is 45 MeV, assuming the pion mass hypothesis.

Charged pions and kaons are identified using energy loss (dE=dx) in the silicon detector and tracking cham-ber and, for tracks with momenta above700 MeV=c, the Cherenkov angle and number of photons measured by the Cherenkov detector. The efficiency of selecting kaons is approximately 80%, which includes the geometri-cal acceptance, while the probability of misidentifying pions as kaons is below 5%, up to a laboratory momen-tum of 4:0 GeV=c. Pions are required to fail both the kaon selection and an electron selection algorithm based on information from dE=dx, shower shapes in the calo-rimeter, and the ratio of the shower energy and track momentum.

We removeBcandidates when the invariant mass of the combination of any two of its daughter tracks (of opposite charge) are within 6 of the mass of the D0 meson or within3of the mass of the J= , 2Sor c0 mesons

[7]. Here,is10 MeV=c2forD0,15 MeV=c2 forJ= and

2S, and18 MeV=c2 for

c0.

To suppress background from light-quark and charm continuum production, two event-shape variables are computed in the CM frame. The first is the cosine of the angle T between the thrust axis of the selected B candidate and the thrust axis of the rest of the event, i.e., all charged tracks and neutral particles not assigned to the B candidate. For jetlike continuum backgrounds,

jcosTj is strongly peaked towards unity, while it is essentially uniform for signal events. For each signal mode we fix an upper limit on jcosTj, between 0.575 and 0.850. This rejects between 95% and 85% of the background, depending on the decay mode.

The second event-shape variable is a Fisher discrimi-nant [8], which is formed from the summed scalar mo-menta of all charged and neutral particles from the rest of the event within nine 10-wide nested cones coaxial with the thrust axis of theBcandidate. The coefficients of the Fisher discriminant are chosen to maximize the sepa-ration between signal and continuum background events and are calculated for each signal mode separately using Monte Carlo simulated signal and continuum events. A further 50% to 75% of the remaining background is rejected, depending on the decay mode, by applying selection requirements on this variable.

Bdecay candidates passing the above selection criteria are required to lie in a signal region defined as follows:

jmESmBj<8 MeV=c2 and jE hEij<60 MeV,

wherehEi 7 MeVis the mean value ofEmeasured from on-resonance data for the calibration sampleB!

D0; D0!K, andm

B is the nominal mass of the

charged B meson [7]. Figure 1 shows the projections of the on-resonance data in the signal region onto the E and mES axes. Each plot shows the expected levels of

continuum and BB background, where the latter is pa-rametrized from Monte Carlo samples.

The residual continuum background level is estimated from the observed number of events in the grand sideband (GSB) region, defined to be 5:21< mES<5:25 GeV=c2

andjE hEij<100 MeV, and extrapolating into the signal region. The shape of the mES distribution of the

background is parametrized according to the phenomeno-logically motivated ARGUS function [9] and is measured using off-resonance data and the upper sideband in the E variable in on-resonance data (0:10<E < 0:25 GeV). A quadratic function is used to parametrize the E distribution of the background. The ratio of the integrals over the signal and GSB regions of the product of the EandmES shape functions,R, gives the ratio of the number of background events in the two areas.

The branching fraction for each channel is measured over the whole Dalitz plot, which is divided into28 28 cells of equal area 1 GeV2=c42 to enable us to find the selection efficiency as a function of position in the Dalitz plot. Takingi to be the efficiency of reconstructing the

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Monte Carlo simulated events, the branching fraction for each signal mode is given by

B 1

NBB

X

i

N1iRN2iNxpi

i

nxnb

; (1)

whereN1i andN2iare the number of events observed in the signal and GSB regions, respectively, whileNxpi,nx, and nb are background contributions that are defined

below. NBB is the total number of BB pairs in the data sample. No significant differences were found for the value of R (defined earlier) in different regions of the Dalitz plot, so an average value is used for all bins.

The probability of a kaon being misidentified as a pion is 20%. This means there is significant cross feed into the signal region from the decay mode that has one more kaon, which is subtracted for each bin i. This is repre-sented by the Nxpi=i term in Eq. (1), where Nx is the total number of events that is the source of the cross feed, andpiis the probability for the cross feed events to pass

the selection criteria for the ith bin, which is estimated from Monte Carlo samples. The B !KKK mode has Nx0, since it has no cross feed backgrounds. For

the other decays, Nx is obtained by multiplying NBB by

the branching fraction of the signal mode that has a kaon substituting a pion in the final state. There is also second-order cross feed where either two kaons are misidentified as pions (probability of 4%), or one of the pions is mis-identified as a kaon (probability of 2%). This is repre-sented by the nx term in Eq. (1).

Finally, the nb term represents the small number of otherBB backgrounds that are subtracted. For all signal modes except B!KKK, nb is obtained from the

number ofD0 andDD0 candidates whose invariant mass is beyond the6range. ForB!K, there is also a contribution from B!#0!$0Kdecays, which is estimated from the selection efficiency from Monte Carlo simulated decays, and the branching fraction quoted in Ref. [7]. By using a mixture of Monte Carlo-simulated charm and charmless decays, we found that there were no other significantBBbackgrounds.

We do not divide the Dalitz plot into cells for the standard model-suppressed modes B !K and B!KKand instead use the average values of the signal efficiency and cross feed terms.

The branching fraction results are summarized in Table I, where the first four rows show the total number of events in the signal and GSB regions, the average signal efficiencies hi, and the values of R for each mode. The absolute efficiency variation across the Dalitz plot typi-cally varies between2%and5%fromhi.

Rows A and B represent the total number of events and the amount of continuum background in the signal region, corrected for efficiency. The uncertainties for row A come from the statistical errors in N1i, while the

uncertainties for row B correspond to the statistical er-rors inN2iand the systematic errors fromR, which arise

from the limited statistics in the sideband region and off-resonance data.

Row C shows the expected background from cross feed events. The first and second uncertainties of these quantities represent the systematic errors in pi and Nx, respectively, except for the channel B !KK, where the uncertainty represents the average of the pi

and Nx contributions. The second-order cross feed

termsnx are shown in row D. Note that the nx term for

B!K is negative, which corrects for the B!KKK cross feed intoB!KK, which in turn contributes to the cross feed background for B!K.

0 50 100 (a) 0 100 200 (b) + π + π → + B 0 100 (c) 0 200 (d) + π + K+ B Events/8 MeV 0 50 (e) 2

Events/2 MeV/c 0

100 (f) + π K + K+ B 0 50 100 (g) 0 100 (h) + K K + K+ B 0 50 (i) 0 50 100 (j) + π + π K+ B 0 20 (k) 0 20 40 (l) + K + K+ B

-0.2 -0.1 0 0.1 0.2

E (GeV)

5.2 5.22 5.24 5.26 5.28 5.3

mES (GeV/c2)

FIG. 1. Projections ofE and mES forB! (a)

(6)

Rows E and F show the expected backgrounds fromD0 and#0Kdecays, which include the uncertainties from the selection efficiencies and the branching fractions of the background decays [7]. The sum of these two rows gives the value ofnb in Eq. (1).

Row G shows the signal yield, obtained by subtracting rows B to F from row A. The first uncertainty is the combination of the statistical errors of the number of events in the signal and GSB regions. The second uncer-tainty corresponds to the sum in quadrature of all the systematic errors from rows B to F. The third error is from the bin-by-bin uncertainty of the selection efficiency. This is zero forB!K andB !KK, where we use only the average efficiencies. The last uncertainty originates from global systematic errors in the signal efficiencies due to charged-particle tracking (0.8% per track), event-shape variable selections (1.0 to 2.5%), and from particle identification (1.4% and 1.0% per pion and kaon track, respectively).

The next row in Table I shows the branching fraction results, where the first uncertainties are from the statisti-cal errors in the number of events, while the second uncertainties are the sum in quadrature of all systematic errors mentioned above.

The significance of each branching fraction result, under the null hypothesis, is defined as the ratio of the signal yield to the total (statistical and systematic) un-certainty of the background in the signal region. We ob-serve significant signals for the modesB!, B!K, andB !KKKand provide 90% C.L. upper limits for the other channels, using the for-malism in Ref. [10]. The branching fraction of the con-trol sample B !D0; D0 !K, which has the same final state as B!K, is measured to be

190310 106, which agrees with the average of published measurements20120 106 [7].

We have also measured the charge asymmetries for the modes with observed signals using a method similar to

that used for the branching fraction measurements. The charge asymmetries are defined as A NN=

NN, whereN(N) is the signal yield for nega-tively (posinega-tively) charged B candidates, as defined by row G in Table I. The normalization factor NBB cancels out in the asymmetry ratio, while the cross feed and BB background contributions cancel in the asymmetry nu-merator. The measured charge asymmetries areAB!

0:390:330:12,AB!K 0:010:070:03, and AB!KKK 0:02

0:070:03, where the first uncertainties are statistical and the second are systematic, which include the charge bias of the tracking and particle identification selection requirements (1%).

In summary, we have measured the branching fraction of B ! for the first time, which is smaller than that assumed in Ref. [1], and we have also observed the channels B !K and B !KKK. We observed no charge asymmetries in these decays.

We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues and for the substantial dedicated effort from the computing organizations that supportBABAR. The collaborating in-stitutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (U.S.), 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 the A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation.

*Also with Universita` di Perugia, Perugia, Italy.

Also with Universita` della Basilicata, Potenza, Italy.

TABLE I. Branching fraction results for on-resonance data. The quantities and their uncertainties are explained in the text.

Signal Mode K KK KKK K KK

P

iN1i 1029 1502 733 646 494 209

P

iN2i 5577 5209 4012 1308 3268 1025

hi(%) 12:70:5 12:81:4 13:90:9 14:90:9 18:50:9 15:30:7

R 0:1440:003 0:1460:003 0:1500:003 0:1580:006 0:1550:003 0:1570:006

A)PiN1i=i 7597275 11056327 5071216 4011182 2670120 136694

B)PiRN2i=i 593894117 560489111 40417280 13814655 27384853 10523340

C)PiNxpi=i 4743340 22130 6711559 34431

D)nx 18934 110128 535

E)D0Bkgnd 21624 26828 476 335 315

F)#0KBkgnd 10630

G) Signal Yield 970291130 5246339127 202227163 263018855 10112953 11410051

2250 39247 169 12124 05 05

B( 106) 10:93:31:6 59:13:83:2 2:32:61:8 29:62:11:6 1:11:50:6 1:31:10:6

Significance () 5.7 >6 1.1 >6

(7)

Also with IFIC, Instituto de Fı´sica Corpuscular,

CSIC-Universidad de Valencia, Valencia, Spain.

x

Deceased.

[1] B. Bajcet al., Phys. Lett. B447, 313 (1999).

[2] A. E. Snyder and H. R. Quinn, Phys. Rev. D 48, 2139 (1993).

[3] Throughout this Letter, flavor-eigenstate decay modes imply also their charge conjugate.

[4] CLEO Collaboration, T. Bergfeld et al., Phys. Rev. Lett. 77, 4503 (1996); BELLE Collabora-tion, A. Garmash et al., Phys. Rev. D 65, 092005 (2002).

[5] BABAR Collaboration, B. Aubertet al., Nucl. Instrum. Methods Phys. Res., Sect. A479, 1 (2002).

[6] G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).

[7] Particle Data Group, K. Hagiwaraet al., Phys. Rev. D66, 010001 (2002).

[8] CLEO Collaboration, D. M. Asneret al., Phys. Rev. D53, 1039 (1996).

[9] ARGUS Collaboration, H. Albrecht et al., Z. Phys. C: Part. Fields 48, 543 (1990).

Figure

Table I, where the first four rows show the total numberThe branching fraction results are summarized inof events in the signal and GSB regions, the average signalefficiencies h�i, and the values of R for each mode
TABLE I.Branching fraction results for on-resonance data. The quantities and their uncertainties are explained in the text.

References

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