Branching Fraction Measurements of Charged B Decays to $K^{*+}K^+K^-, K^{*+}\pi^+K^-, K^{*+}K^+\pi^-$ and $K^{*+}\pi^+\pi^-$ Final States

arXiv:hep-ex/0607113v2 14 Sep 2006

B B

SLAC-PUB-11965

Branching Fraction Measurements of Charged B Decays

to K

K

_K

_{, K}

_π

_K

_{, K}

_K

_π

_{and K}

_π

_π

_{Final States}

B. Aubert,1 _{R. Barate,}1 _{M. Bona,}1_{D. Boutigny,}1 _{F. Couderc,}1 _{Y. Karyotakis,}1 _{J. P. Lees,}1 _{V. Poireau,}1

V. Tisserand,1 _{A. Zghiche,}1 _{E. Grauges,}2 _{A. Palano,}3 _{J. C. Chen,}4 _{N. D. Qi,}4 _{G. Rong,}4 _{P. Wang,}4 _{Y. S. Zhu,}4

G. Eigen,5 _{I. Ofte,}5 _{B. Stugu,}5 _{G. S. Abrams,}6 _{M. Battaglia,}6_{D. N. Brown,}6_{J. Button-Shafer,}6 _{R. N. Cahn,}6

E. Charles,6 _{M. S. Gill,}6 _{Y. Groysman,}6 _{R. G. Jacobsen,}6 _{J. A. Kadyk,}6 _{L. T. Kerth,}6 _{Yu. G. Kolomensky,}6

G. Kukartsev,6_{G. Lynch,}6 _{L. M. Mir,}6 _{T. J. Orimoto,}6_{M. Pripstein,}6 _{N. A. Roe,}6 _{M. T. Ronan,}6 _{W. A. Wenzel,}6

P. del Amo Sanchez,7 _{M. Barrett,}7 _{K. E. Ford,}7_{T. J. Harrison,}7 _{A. J. Hart,}7 _{C. M. Hawkes,}7 _{S. E. Morgan,}7

A. T. Watson,7_{T. Held,}8 _{H. Koch,}8 _{B. Lewandowski,}8 _{M. Pelizaeus,}8_{K. Peters,}8_{T. Schroeder,}8_{M. Steinke,}8

J. T. Boyd,9 _{J. P. Burke,}9 _{W. N. Cottingham,}9 _{D. Walker,}9_{T. Cuhadar-Donszelmann,}10_{B. G. Fulsom,}10

C. Hearty,10 _{N. S. Knecht,}10 _{T. S. Mattison,}10 _{J. A. McKenna,}10 _{A. Khan,}11 _{P. Kyberd,}11 _{M. Saleem,}11

D. J. Sherwood,11 _{L. Teodorescu,}11_{V. E. Blinov,}12 _{A. D. Bukin,}12 _{V. P. Druzhinin,}12 _{V. B. Golubev,}12

A. P. Onuchin,12 _{S. I. Serednyakov,}12 _{Yu. I. Skovpen,}12 _{E. P. Solodov,}12_{K. Yu Todyshev,}12 _{D. S. Best,}13

M. Bondioli,13_{M. Bruinsma,}13_{M. Chao,}13_{S. Curry,}13 _{I. Eschrich,}13_{D. Kirkby,}13_{A. J. Lankford,}13 _{P. Lund,}13

M. Mandelkern,13 _{R. K. Mommsen,}13 _{W. Roethel,}13 _{D. P. Stoker,}13 _{S. Abachi,}14 _{C. Buchanan,}14 _{S. D. Foulkes,}15

J. W. Gary,15_{O. Long,}15 _{B. C. Shen,}15 _{K. Wang,}15 _{L. Zhang,}15_{H. K. Hadavand,}16 _{E. J. Hill,}16 _{H. P. Paar,}16

S. Rahatlou,16 _{V. Sharma,}16 _{J. W. Berryhill,}17 _{C. Campagnari,}17 _{A. Cunha,}17 _{B. Dahmes,}17 _{T. M. Hong,}17

D. Kovalskyi,17_{J. D. Richman,}17_{T. W. Beck,}18 _{A. M. Eisner,}18 _{C. J. Flacco,}18 _{C. A. Heusch,}18 _{J. Kroseberg,}18

W. S. Lockman,18 _{G. Nesom,}18 _{T. Schalk,}18 _{B. A. Schumm,}18 _{A. Seiden,}18 _{P. Spradlin,}18 _{D. C. Williams,}18

M. G. Wilson,18 _{J. Albert,}19 _{E. Chen,}19 _{A. Dvoretskii,}19 _{F. Fang,}19 _{D. G. Hitlin,}19 _{I. Narsky,}19_{T. Piatenko,}19

F. C. Porter,19 _{A. Ryd,}19 _{A. Samuel,}19 _{G. Mancinelli,}20 _{B. T. Meadows,}20 _{K. Mishra,}20 _{M. D. Sokoloff,}20

F. Blanc,21 _{P. C. Bloom,}21 _{S. Chen,}21 _{W. T. Ford,}21_{J. F. Hirschauer,}21 _{A. Kreisel,}21_{M. Nagel,}21 _{U. Nauenberg,}21

A. Olivas,21 _{W. O. Ruddick,}21 _{J. G. Smith,}21 _{K. A. Ulmer,}21 _{S. R. Wagner,}21 _{J. Zhang,}21 _{A. Chen,}22

E. A. Eckhart,22 _{A. Soffer,}22_{W. H. Toki,}22 _{R. J. Wilson,}22 _{F. Winklmeier,}22 _{Q. Zeng,}22_{D. D. Altenburg,}23

E. Feltresi,23 _{A. Hauke,}23 _{H. Jasper,}23 _{A. Petzold,}23 _{B. Spaan,}23 _{T. Brandt,}24 _{V. Klose,}24 _{H. M. Lacker,}24

W. F. Mader,24 _{R. Nogowski,}24_{J. Schubert,}24 _{K. R. Schubert,}24 _{R. Schwierz,}24_{J. E. Sundermann,}24 _{A. Volk,}24

D. Bernard,25_{G. R. Bonneaud,}25 _{P. Grenier,}25, ∗ _{E. Latour,}25 _{Ch. Thiebaux,}25 _{M. Verderi,}25 _{P. J. Clark,}26

W. Gradl,26 _{F. Muheim,}26 _{S. Playfer,}26 _{A. I. Robertson,}26_{Y. Xie,}26 _{M. Andreotti,}27 _{D. Bettoni,}27 _{C. Bozzi,}27

R. Calabrese,27_{G. Cibinetto,}27 _{E. Luppi,}27 _{M. Negrini,}27_{A. Petrella,}27_{L. Piemontese,}27_{E. Prencipe,}27_{F. Anulli,}28

R. Baldini-Ferroli,28 _{A. Calcaterra,}28_{R. de Sangro,}28 _{G. Finocchiaro,}28 _{S. Pacetti,}28_{P. Patteri,}28 _{I. M. Peruzzi,}28, †

M. Piccolo,28_{M. Rama,}28 _{A. Zallo,}28 _{A. Buzzo,}29 _{R. Capra,}29 _{R. Contri,}29 _{M. Lo Vetere,}29 _{M. M. Macri,}29

M. R. Monge,29_{S. Passaggio,}29_{C. Patrignani,}29_{E. Robutti,}29 _{A. Santroni,}29 _{S. Tosi,}29 _{G. Brandenburg,}30

K. S. Chaisanguanthum,30_{M. Morii,}30_{J. Wu,}30 _{R. S. Dubitzky,}31_{J. Marks,}31_{S. Schenk,}31 _{U. Uwer,}31 _{W. Bhimji,}32

D. A. Bowerman,32 _{P. D. Dauncey,}32 _{U. Egede,}32_{R. L. Flack,}32 _{J .A. Nash,}32_{M. B. Nikolich,}32_{W. Panduro}

Vazquez,32_{P. K. Behera,}33 _{X. Chai,}33 _{M. J. Charles,}33_{U. Mallik,}33 _{N. T. Meyer,}33_{V. Ziegler,}33 _{J. Cochran,}34

H. B. Crawley,34 _{L. Dong,}34 _{V. Eyges,}34 _{W. T. Meyer,}34 _{S. Prell,}34 _{E. I. Rosenberg,}34 _{A. E. Rubin,}34

A. V. Gritsan,35_{A. G. Denig,}36_{M. Fritsch,}36 _{G. Schott,}36_{N. Arnaud,}37 _{M. Davier,}37 _{G. Grosdidier,}37 _{A. H¨ocker,}37

F. Le Diberder,37 _{V. Lepeltier,}37 _{A. M. Lutz,}37 _{A. Oyanguren,}37 _{S. Pruvot,}37 _{S. Rodier,}37 _{P. Roudeau,}37

M. H. Schune,37 _{A. Stocchi,}37 _{W. F. Wang,}37 _{G. Wormser,}37_{C. H. Cheng,}38 _{D. J. Lange,}38 _{D. M. Wright,}38

C. A. Chavez,39_{I. J. Forster,}39 _{J. R. Fry,}39_{E. Gabathuler,}39 _{R. Gamet,}39 _{K. A. George,}39_{D. E. Hutchcroft,}39

D. J. Payne,39_{K. C. Schofield,}39 _{C. Touramanis,}39_{A. J. Bevan,}40 _{F. Di Lodovico,}40_{W. Menges,}40_{R. Sacco,}40

G. Cowan,41 _{H. U. Flaecher,}41_{D. A. Hopkins,}41 _{P. S. Jackson,}41_{T. R. McMahon,}41 _{S. Ricciardi,}41_{F. Salvatore,}41

A. C. Wren,41 _{D. N. Brown,}42 _{C. L. Davis,}42 _{J. Allison,}43 _{N. R. Barlow,}43 _{R. J. Barlow,}43_{Y. M. Chia,}43

C. L. Edgar,43 _{G. D. Lafferty,}43 _{M. T. Naisbit,}43 _{J. C. Williams,}43 _{J. I. Yi,}43 _{C. Chen,}44 _{W. D. Hulsbergen,}44

A. Jawahery,44_{C. K. Lae,}44 _{D. A. Roberts,}44 _{G. Simi,}44 _{G. Blaylock,}45_{C. Dallapiccola,}45_{S. S. Hertzbach,}45_{X. Li,}45

T. B. Moore,45 _{S. Saremi,}45_{H. Staengle,}45_{R. Cowan,}46_{G. Sciolla,}46 _{S. J. Sekula,}46 _{M. Spitznagel,}46 _{F. Taylor,}46

F. Palombo,48 _{J. M. Bauer,}49 _{L. Cremaldi,}49 _{V. Eschenburg,}49_{R. Godang,}49 _{R. Kroeger,}49_{D. A. Sanders,}49

D. J. Summers,49 _{H. W. Zhao,}49_{S. Brunet,}50 _{D. Cˆot´e,}50_{M. Simard,}50 _{P. Taras,}50_{F. B. Viaud,}50 _{H. Nicholson,}51

N. Cavallo,52, ‡_{G. De Nardo,}52 _{F. Fabozzi,}52, ‡ _{C. Gatto,}52_{L. Lista,}52_{D. Monorchio,}52_{P. Paolucci,}52_{D. Piccolo,}52

C. Sciacca,52 _{M. Baak,}53 _{G. Raven,}53 _{H. L. Snoek,}53 _{C. P. Jessop,}54 _{J. M. LoSecco,}54 _{T. Allmendinger,}55

G. Benelli,55 _{K. K. Gan,}55 _{K. Honscheid,}55 _{D. Hufnagel,}55 _{P. D. Jackson,}55_{H. Kagan,}55_{R. Kass,}55_{A. M. Rahimi,}55

R. Ter-Antonyan,55_{Q. K. Wong,}55_{N. L. Blount,}56 _{J. Brau,}56 _{R. Frey,}56 _{O. Igonkina,}56_{M. Lu,}56 _{R. Rahmat,}56

N. B. Sinev,56 _{D. Strom,}56 _{J. Strube,}56 _{E. Torrence,}56 _{A. Gaz,}57 _{M. Margoni,}57 _{M. Morandin,}57 _{A. Pompili,}57

M. Posocco,57_{M. Rotondo,}57 _{F. Simonetto,}57 _{R. Stroili,}57 _{C. Voci,}57_{M. Benayoun,}58_{J. Chauveau,}58 _{H. Briand,}58

P. David,58 _{L. Del Buono,}58_{Ch. de la Vaissi`ere,}58_{O. Hamon,}58 _{B. L. Hartfiel,}58_{M. J. J. John,}58 _{Ph. Leruste,}58

J. Malcl`es,58 _{J. Ocariz,}58_{L. Roos,}58_{G. Therin,}58 _{L. Gladney,}59 _{J. Panetta,}59 _{M. Biasini,}60 _{R. Covarelli,}60

C. Angelini,61 _{G. Batignani,}61 _{S. Bettarini,}61 _{F. Bucci,}61_{G. Calderini,}61 _{M. Carpinelli,}61 _{R. Cenci,}61 _{F. Forti,}61

M. A. Giorgi,61 _{A. Lusiani,}61 _{G. Marchiori,}61 _{M. A. Mazur,}61 _{M. Morganti,}61_{N. Neri,}61_{G. Rizzo,}61 _{J. J. Walsh,}61

M. Haire,62 _{D. Judd,}62 _{D. E. Wagoner,}62 _{J. Biesiada,}63_{N. Danielson,}63 _{P. Elmer,}63 _{Y. P. Lau,}63 _{C. Lu,}63

J. Olsen,63_{A. J. S. Smith,}63 _{A. V. Telnov,}63_{F. Bellini,}64 _{G. Cavoto,}64_{A. D’Orazio,}64 _{D. del Re,}64_{E. Di Marco,}64

R. Faccini,64 _{F. Ferrarotto,}64 _{F. Ferroni,}64 _{M. Gaspero,}64 _{L. Li Gioi,}64 _{M. A. Mazzoni,}64 _{S. Morganti,}64

G. Piredda,64 _{F. Polci,}64 _{F. Safai Tehrani,}64 _{C. Voena,}64 _{M. Ebert,}65 _{H. Schr¨oder,}65_{R. Waldi,}65_{T. Adye,}66 _{N. De}

Groot,66_{B. Franek,}66 _{E. O. Olaiya,}66 _{F. F. Wilson,}66 _{R. Aleksan,}67 _{S. Emery,}67_{A. Gaidot,}67 _{S. F. Ganzhur,}67

G. Hamel de Monchenault,67 _{W. Kozanecki,}67_{M. Legendre,}67_{G. Vasseur,}67_{Ch. Y`eche,}67_{M. Zito,}67_{X. R. Chen,}68

H. Liu,68_{W. Park,}68_{M. V. Purohit,}68 _{J. R. Wilson,}68 _{M. T. Allen,}69 _{D. Aston,}69 _{R. Bartoldus,}69 _{P. Bechtle,}69

N. Berger,69_{R. Claus,}69 _{J. P. Coleman,}69 _{M. R. Convery,}69_{M. Cristinziani,}69 _{J. C. Dingfelder,}69 _{J. Dorfan,}69

G. P. Dubois-Felsmann,69 _{D. Dujmic,}69 _{W. Dunwoodie,}69 _{R. C. Field,}69 _{T. Glanzman,}69 _{S. J. Gowdy,}69

M. T. Graham,69 _{V. Halyo,}69 _{C. Hast,}69 _{T. Hryn’ova,}69 _{W. R. Innes,}69 _{M. H. Kelsey,}69 _{P. Kim,}69

D. W. G. S. Leith,69_{S. Li,}69_{S. Luitz,}69_{V. Luth,}69 _{H. L. Lynch,}69_{D. B. MacFarlane,}69_{H. Marsiske,}69_{R. Messner,}69

D. R. Muller,69 _{C. P. O’Grady,}69 _{V. E. Ozcan,}69 _{A. Perazzo,}69_{M. Perl,}69 _{T. Pulliam,}69 _{B. N. Ratcliff,}69

A. Roodman,69 _{A. A. Salnikov,}69 _{R. H. Schindler,}69 _{J. Schwiening,}69 _{A. Snyder,}69 _{J. Stelzer,}69 _{D. Su,}69

M. K. Sullivan,69 _{K. Suzuki,}69 _{S. K. Swain,}69 _{J. M. Thompson,}69_{J. Va’vra,}69_{N. van Bakel,}69_{M. Weaver,}69

A. J. R. Weinstein,69 _{W. J. Wisniewski,}69_{M. Wittgen,}69 _{D. H. Wright,}69 _{A. K. Yarritu,}69_{K. Yi,}69_{C. C. Young,}69

P. R. Burchat,70 _{A. J. Edwards,}70 _{S. A. Majewski,}70_{B. A. Petersen,}70_{C. Roat,}70_{L. Wilden,}70 _{S. Ahmed,}71

M. S. Alam,71 _{R. Bula,}71 _{J. A. Ernst,}71 _{V. Jain,}71_{B. Pan,}71 _{M. A. Saeed,}71 _{F. R. Wappler,}71 _{S. B. Zain,}71

W. Bugg,72_{M. Krishnamurthy,}72_{S. M. Spanier,}72 _{R. Eckmann,}73 _{J. L. Ritchie,}73 _{A. Satpathy,}73_{C. J. Schilling,}73

R. F. Schwitters,73 _{J. M. Izen,}74 _{X. C. Lou,}74 _{S. Ye,}74 _{F. Bianchi,}75 _{F. Gallo,}75 _{D. Gamba,}75 _{M. Bomben,}76

L. Bosisio,76 _{C. Cartaro,}76_{F. Cossutti,}76 _{G. Della Ricca,}76 _{S. Dittongo,}76 _{L. Lanceri,}76 _{L. Vitale,}76 _{V. Azzolini,}77

F. Martinez-Vidal,77_{Sw. Banerjee,}78_{B. Bhuyan,}78 _{C. M. Brown,}78 _{D. Fortin,}78_{K. Hamano,}78 _{R. Kowalewski,}78

I. M. Nugent,78 _{J. M. Roney,}78_{R. J. Sobie,}78_{J. J. Back,}79_{P. F. Harrison,}79 _{T. E. Latham,}79 _{G. B. Mohanty,}79

M. Pappagallo,79 _{H. R. Band,}80_{X. Chen,}80 _{B. Cheng,}80_{S. Dasu,}80 _{M. Datta,}80 _{K. T. Flood,}80 _{J. J. Hollar,}80

P. E. Kutter,80 _{B. Mellado,}80_{A. Mihalyi,}80_{Y. Pan,}80_{M. Pierini,}80 _{R. Prepost,}80_{S. L. Wu,}80_{Z. Yu,}80_{and H. Neal}81

(The BA_BAR _{Collaboration)}

1_{Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France} 2_{Universitat de Barcelona, Facultat de Fisica Dept. ECM, E-08028 Barcelona, Spain}

3_{Universit`a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy} 4_{Institute of High Energy Physics, Beijing 100039, China}

5_{University of Bergen, Institute of Physics, N-5007 Bergen, Norway}

6_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 7_{University of Birmingham, Birmingham, B15 2TT, United Kingdom}

8_{Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany} 9_{University of Bristol, Bristol BS8 1TL, United Kingdom}

10_{University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1} 11_{Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom}

12_{Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia} 13_{University of California at Irvine, Irvine, California 92697, USA} 14_{University of California at Los Angeles, Los Angeles, California 90024, USA}

15_{University of California at Riverside, Riverside, California 92521, USA} 16_{University of California at San Diego, La Jolla, California 92093, USA} 17_{University of California at Santa Barbara, Santa Barbara, California 93106, USA}

19_{California Institute of Technology, Pasadena, California 91125, USA} 20_{University of Cincinnati, Cincinnati, Ohio 45221, USA} 21_{University of Colorado, Boulder, Colorado 80309, USA} 22_{Colorado State University, Fort Collins, Colorado 80523, USA} 23_{Universit¨at Dortmund, Institut f¨ur Physik, D-44221 Dortmund, Germany}

24_{Technische Universit¨at Dresden, Institut f¨ur Kern- und Teilchenphysik, D-01062 Dresden, Germany} 25_{Ecole Polytechnique, Laboratoire Leprince-Ringuet, F-91128 Palaiseau, France}

26_{University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom}

27_{Universit`a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy</sub> 28<sub>Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy</sub> 29<sub>Universit`a di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy}

30_{Harvard University, Cambridge, Massachusetts 02138, USA}

31_{Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany} 32_{Imperial College London, London, SW7 2AZ, United Kingdom}

33_{University of Iowa, Iowa City, Iowa 52242, USA} 34_{Iowa State University, Ames, Iowa 50011-3160, USA} 35_{Johns Hopkins University, Baltimore, Maryland 21218, USA}

36_{Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany} 37_{Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS et Universit´e Paris-Sud 11,}

Centre Scientifique d’Orsay, B.P. 34, F-91898 ORSAY Cedex, France 38_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA}

39_{University of Liverpool, Liverpool L69 7ZE, United Kingdom} 40_{Queen Mary, University of London, E1 4NS, United Kingdom}

41_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom} 42_{University of Louisville, Louisville, Kentucky 40292, USA}

43_{University of Manchester, Manchester M13 9PL, United Kingdom} 44_{University of Maryland, College Park, Maryland 20742, USA} 45_{University of Massachusetts, Amherst, Massachusetts 01003, USA}

46_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA} 47_{McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8}

48_{Universit`a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy} 49_{University of Mississippi, University, Mississippi 38677, USA}

50_{Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7} 51_{Mount Holyoke College, South Hadley, Massachusetts 01075, USA}

52_{Universit`a di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy}

53_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands} 54_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

55_{Ohio State University, Columbus, Ohio 43210, USA} 56_{University of Oregon, Eugene, Oregon 97403, USA}

57_{Universit`a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy}

58_{Universit´es Paris VI et VII, Laboratoire de Physique Nucl´eaire et de Hautes Energies, F-75252 Paris, France} 59_{University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA}

60_{Universit`a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy}

61_{Universit`a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy} 62_{Prairie View A&M University, Prairie View, Texas 77446, USA}

63_{Princeton University, Princeton, New Jersey 08544, USA}

64_{Universit`a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy} 65_{Universit¨at Rostock, D-18051 Rostock, Germany}

66_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom} 67_{DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France}

68_{University of South Carolina, Columbia, South Carolina 29208, USA} 69_{Stanford Linear Accelerator Center, Stanford, California 94309, USA}

70_{Stanford University, Stanford, California 94305-4060, USA} 71_{State University of New York, Albany, New York 12222, USA}

72_{University of Tennessee, Knoxville, Tennessee 37996, USA} 73_{University of Texas at Austin, Austin, Texas 78712, USA} 74_{University of Texas at Dallas, Richardson, Texas 75083, USA}

75_{Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy</sub> 76<sub>Universit`a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy}

77_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain} 78_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6} 79_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom}

80_{University of Wisconsin, Madison, Wisconsin 53706, USA} 81_{Yale University, New Haven, Connecticut 06511, USA}

(Dated: October 28, 2018)

Branching fraction and asymmetry measurements of charmless B+ _→K∗+_h+ 1h

−

2 (where h1,2 = K, π) decays are presented, using a data sample of 232 million Υ (4S) → BB decays collected with the BABAR_{detector at the SLAC PEP-II asymmetric-energy B factory. Using a maximum likelihood}

fit, the following branching fraction results were obtained: B(B+ _→K∗+_K+_K−_{) = (36.2 ± 3.3 ±} 3.6) × 10−6_{and B(B}+_→

K∗+_π+

π−_{) = (75.3 ± 6.0 ± 8.1) × 10}−6_{. Upper limits were set for B(B}+ → _K∗+_π+

K−_{) < 11.8 × 10}−6 _{and B(B}+ _→

K∗+_K+

π−_{) < 6.1 × 10}−6 _{at 90% confidence level.} The charge asymmetries for the decays B+_→K∗+_K+_K−_{and B}+_→K∗+_π+_π−_{were measured to} be AK∗KK= 0.11 ± 0.08 ± 0.03 and AK∗ππ= 0.07 ± 0.07 ± 0.04, respectively. The first error quoted on branching fraction and asymmetry measurements is statistical and the second systematic.

PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er

Charmless decays of B mesons to three-body final states are very important in aiding the understanding of the weak interaction and complex quark couplings de-scribed by the Cabibbo-Kobayashi-Maskawa (CKM) ma-trix elements [1]. Improved experimental measurements of these charmless decays, combined with theoretical de-velopments, can provide significant constraints on the CKM matrix parameters or uncover evidence for physics beyond the Standard Model. For example, the branch-ing fraction of the decay B+

→ K∗+_π+_K− _{is sensitive}

to CKM matrix elements Vtdand Vub(see Figure 1).

Ad-ditionally, a B+

→ K∗+_π+_K− _{branching fraction value}

equal to or smaller than the branching fraction of the Standard Model suppressed decay B+

→ K∗+_K+_π−

would be an indication of new physics.

b + W d (a) ,g γ t , c , u u u s s u u + π -K *+ K + B (b) b + W u s s u d u u + π -K *+ K + B

FIG. 1: Penguin (a) and tree (b) Feynman diagrams for the decay B+ _→

K∗+_π+ K−_.

We identify K∗+_{mesons through their decay to K}0

Sπ

+_.

Charged B-meson decays to K0

Sπ +_h+ 1h − 2 (where h1,2= K or π) are dominated by K∗+_h+ 1h −

2, but can also proceed

via a nonresonant component as well as through observed intermediate charmless resonances such as B+

→ K∗+_φ

or B+

→ K∗+_ρ0 _{[2, 3, 4], or other as-yet-unobserved}

intermediate charmless resonances. To date, there are only limits on the charmless decays B+ _{→ K}∗+_h+

1h−2,

measured by the ARGUS experiment [5] using less than 0.2 fb−1_.

Asymmetry measurements of charmless B decays can be used to probe for CP violation where the CP

asym-metry is defined as:

AK∗h1h2= Γ_K∗−h− 1h + 2 − ΓK∗+h + 1h−2 ΓK∗−h− 1h + 2 + ΓK∗+h + 1h − 2 , (1)

and Γ is the partial width of the charged B decay in the subscript.

In the analyses presented in this paper, branching frac-tions of B+ _{→ K}∗+_K+_K− _{and B}+ _{→ K}∗+_π+_π− _were

measured for the first time, and upper limits were set for B+ _{→ K}∗+_π+_K− _{and the Standard Model suppressed}

decay B+_{→ K}∗+_K+_π−_{, where charge-conjugate decays}

are also implied. The selection criteria required events with a reconstructed K0

Sπ

+_h+

1h−2 final state such that

the total charmless contribution to the K∗+_h+

1h−2 Dalitz

plot could be measured (with charmed and charmonium resonances removed), including contributions from reso-nant charmless substructure. Finally, the AK∗h1h2 val-ues for the observed decays B+

→ K∗+_K+_K− _and

B+

→ K∗+_π+_π− _{were measured.}

The data used in this analysis were collected at the PEP-II asymmetric-energy e+_e− _{storage ring with}

the BA_BAR _{detector [6]. The B}A_BAR _{detector consists}

of a double-sided five-layer silicon tracker, a 40-layer drift chamber, a Cherenkov detector, an electromagnetic calorimeter and a magnet with instrumented flux return. The data sample has an integrated luminosity of 210 fb−1

collected at the Υ (4S) resonance, which corresponds to (231.8 ± 2.5) × 106 _{BB pairs. It was assumed that the}

Υ (4S) decayed equally to neutral and charged B-meson pairs. In addition, 21.6 fb−1_{of data collected at 40 MeV}

below the Υ (4S) resonance were used for background studies.

Candidate B mesons were reconstructed from three tracks and a K0

S, where the K

0

S was reconstructed from π+_π− _{candidates. Each of the three tracks that were not}

associated with the K0

S were required to have at least 12 hits in the drift chamber, a transverse momentum greater than 100 MeV/c and to be consistent with orig-inating from the beam-spot. These tracks were identi-fied as either pion or kaon candidates using energy loss (dE/dx) measured in the tracking system and the num-ber of photons measured by the Cherenkov detector and

their corresponding Cherenkov angles. Furthermore, the tracks were required to fail the electron selection based on dE/dx information, their ratio of energy in the calorime-ter to momentum in the drift chamber, and the shower shape of the signal in the calorimeter. The K0

S candi-dates were required to have a reconstructed mass within 15 MeV/c2 _{of the nominal K}0 _{mass [7], a decay}

ver-tex separated from the B+ _{decay vertex by at least five}

standard deviations, and a cosine of the angle between the line joining the B and K0

S decay vertices and the K

0

S momentum greater than 0.999.

To characterize signal events, three kinematic vari-ables and one event-shape variable were used. The first kinematic variable ∆E, is the difference between the center-of-mass (CM) energy of the B-candidate and √s/2, where √s is the total CM energy. The second is the beam-energy-substituted mass mES =

p(s/2 + pi· pB)2/Ei2− p 2

B, where pB is the B

momen-tum and (Ei, pi) is the four-momentum of the Υ (4S) in

the laboratory frame. The third kinematic variable is the K0

Sπ

+ _{invariant mass, m}

K∗, used to identify K∗+ candidates. Using these three kinematic variables, candi-dates were required to be in the ranges |∆E| < 0.1 GeV, 5.25 < mES < 5.29 GeV/c2 and 0.772 < mK∗ < 0.992 GeV/c2_{. The event-shape variable is a Fisher}

discrimi-nant (F) [8], constructed from a linear combination of the cosine of the angle between the B-candidate momentum and the beam axis, the cosine of the angle between the B-candidate daughters thrust axis and the beam axis, and the zeroth and second angular moments of energy flow about the thrust axis of the reconstructed B.

Continuum quark production (e+_e− _{→ q¯q where q =}

u,d,s,c) was the dominant source of background. This was suppressed using another event-shape variable which was the cosine of the angle θT between the thrust axis

of the selected B-candidate and the thrust axis of the rest of the event. For continuum background, the distri-bution | cos θT| is strongly peaked towards unity whereas

the distribution is flat for signal events. Therefore, the relative amount of continuum background was reduced by requiring | cos θT| < 0.8.

Simulated Monte Carlo (MC) events were used to study background from other B-meson decays. The largest B-background for B+

→ K∗+_π+_π− _candidates

comes from decays including charmonium mesons such as J/ψK∗+_{, χ}

c0K∗+ and ψ(2S)K∗+, where the

char-monium meson decays to µ+_µ− _{which are}

misidenti-fied as pions, or where the charmonium meson decays directly to π+_π−_{. These background events were}

re-moved by vetoing reconstructed π+_π− _{masses in the}

range 3.04 < mπ+_π− < 3.17 GeV/c2, 3.32 < mπ+_π− < 3.53 GeV/c2 _{and 3.60 < m}

π+_π− < 3.78 GeV/c2, iden-tifying the J/ψ, χc0 and ψ(2S) mesons, respectively.

For B+_{→ K}∗+_K+_K− _{candidates, J/ψK}+_{and χ} c0K∗+

events were removed by rejecting events with a recon-structed invariant mass in the range 3.04 < mK∗+K− <

3.17 GeV/c2_{and 3.32 < m}

K+_K−< 3.53 GeV/c2, respec-tively.

Potential charm contributions from B+

→ ¯D0_(→

K∗+_h− 1)h

+

2 events were removed from corresponding

B+

→ K∗+_h+

2h−1 candidates by vetoing events with

a reconstructed K∗+_h−

1 invariant mass in the range

1.83 < mK∗h < 1.91 GeV/c2. Additional decays such

as B+ _{→ D}−_{(→ K}0

Sπ

−_)π+_π+ _{and B}+ _{→ K}∗+_D¯0_(→

K+_π−_{) were removed from B}+_{→ K}∗+_π+_π− _{and B}+_→

K∗+_π+_K−_/K∗+_K+_π− _{candidates, respectively by}

veto-ing events with reconstructed Kπ invariant masses in the range 1.83 < mKπ < 1.91 GeV/c2, using the same veto

range for ¯D0 _{and D}+ _{candidates. Studies of MC events}

showed that the largest remaining charmed background was B+

→ ¯D0_{(→ K}∗+_π−_)π+_{, with 18% of these events}

passing the veto. Surviving charmed events had a recon-structed D mass outside the veto as a result of using the wrong π+_{, K}+_{or K}0

S which was incorrectly selected from the other B decay in the event.

After the above selection criteria were applied, a frac-tion of events for all decays had more than one candi-date. For those events, one candidate alone was selected by choosing the candidate whose fitted B decay vertex had the smallest χ2_{value. Studies of MC events showed}

the selection of B+ _{→ K}∗+_π+_π− _{events produced the}

largest number of multiple candidates, in 29% of events, where for these multiple candidates the correct one was reconstructed 70% of the time.

After all requirements, there were five main sources of B-background: two-body decays proceeding via a char-monium meson; two and three-body decays proceeding via a D meson; combinatorial background from three unrelated particles (K∗+_h+

1h −

2); charmless two or

four-body B decays with an extra or missing particle and three-body decays with one or more particles misidenti-fied. Along with selection efficiencies obtained from MC simulation, existing branching fractions for these modes [9] were used to estimate their background contributions which were included in fits to data.

In order to extract the signal event yield for the channel under study, an unbinned extended maximum likelihood fit was used. The likelihood function for N candidates is:

L = 1 N !exp − M X i=1 ni ! _N Y j=1 M X i=1 niPi(~α, ~xj) ! , (2)

where i and j are integers, M is the number of hypothe-ses (signal, continuum background and B-background), niis the number of events for each hypothesis determined

by maximizing the likelihood function and Pi(~α, ~xj) is

a probability density function (PDF) with the param-eters ~α associated with ~x, where ~x can be any of the four variables mES, ∆E, F, and mK∗. The PDF is a product Pi(~α, ~x) = Pi(~αmES, mES) · Pi(~α∆E, ∆E) ·

showed correlations between these variables were small for signal and continuum background hypotheses. How-ever for B-background, correlations were observed be-tween mES and ∆E, which were taken into account by

forming a 2-dimensional PDF for these variables. The parameters of the signal and B-background PDFs were determined from MC simulation. The continuum back-ground parameters were allowed to vary in the fit, to help reduce systematic effects from this dominant event type. Upper sideband data, defined to be in the region 0.1 < ∆E < 0.3 GeV and 5.25 < mES < 5.29 GeV/c2,

was used to model the continuum background PDFs. For the mESPDFs, a Gaussian distribution was used for

signal, a threshold function [10] for continuum and the combination of a Gaussian and threshold function for B-background. For the ∆E PDFs, a sum of two Gaussian distributions with the same mean was used for the signal, a first-order polynomial for the continuum background and the combination of the two Gaussians and a first-order polynomial was used for B-background. The F sig-nal, continuum and B-background PDFs were described using the sum of two Gaussian distributions with distinct means and widths. Finally for mK∗ PDFs, the sum of a Breit-Wigner and a first-order polynomial was used to describe the signal, continuum and B-background distri-butions. The first-order polynomial component of the mK∗ PDFs was used to model misreconstructed events for signal and background.

In order to allow uncertainties and corrections due to MC simulation to be calculated and applied to the signal modes under study, the decay B+

→ ¯D0_{(→ K}∗+_π−_)π+

was used as a calibration channel. These events were selected using the B+

→ K∗+_π+_π− _{selection criteria,}

but requiring the reconstructed K∗+_π− _{invariant mass}

be in the range 1.84 < mK∗+π− < 1.88 GeV/c2. With more than 1800 signal events and approximately a 4 to 1 signal to background ratio in the total number of B+

→ ¯

D0_{(→ K}∗+_π−_)π+ _{candidates, it was possible to fit the}

signal PDF parameters for this mode.

Branching fractions, B, are usually calculated using the following equation, B = nsig/(N_BB× ǫ), where nsig

is the fitted number of signal events, ǫ is the average signal efficiency obtained from MC simulation and N_BB is the total number of BB events. For the charmless B+

→ K∗+_h+ 1h

−

2 branching fraction, the average

effi-ciency cannot be taken directly from MC events. This was because the efficiency varies over the Dalitz plane and the distribution of events in the Dalitz plane is un-known before fits to data. To calculate the branching fraction, a weight was assigned to each event, j, as:

Wj= P iVsig,iPi(~α, ~xj) P knkPk(~α, ~xj) , (3)

where k is an integer and Vsig,i is the signal row of the

covariance matrix obtained from the fit [11]. This

proce-dure is effectively a background subtraction where these weights have the propertyP

jWj = nsig. The branching

fraction is then calculated as B = P

jWj/(ǫj× NBB) where ǫj (a function of m2_K∗+_h− 1 , m2 h− 1h + 2 and the K∗+_→ K0 Sπ +

decay helicity angle, HK∗+) varies across phase space and is simulated in bins using over seven million MC events for each channel. The size of the bins are op-timized to provide continuous coverage of the efficiency distribution.

Figure 2 shows the fitted projections for B+ _→

K∗+_K+_K−_{, B}+ _{→ K}∗+_π+_K−_{, B}+ _{→ K}∗+_K+_π− _and

B+

→ K∗+_π+_π− _{candidates, while the fitted signal}

yield, measured branching fractions, upper limits and asymmetries are shown in Table I. The candidates in Figure 2 are signal-enhanced, with a requirement on the probability ratio Psig/(Psig + Pbkg), optimized to

en-hance the visibility of potential signal, where Psig and

Pbkg are the signal and the total background

probabil-ities, respectively (computed without using the variable plotted). The 90% confidence level (C.L.) branching frac-tion upper limits (BUL) were determined by integrating

the likelihood distribution (with systematics uncertain-ties included) as a function of the branching fraction from 0 to BUL, so thatRB UL 0 LdB = 0.9 R∞ 0 LdB. 0 50 0 50 (a) 0 50 0 50 (b) 0 20 40 0 20 40 (c) 0 100 200 0 100 200 _(d) 5.25 5.26 5.27 5.28 5.29 m_ES (GeV/c2) E v e n ts /( 2 M e V /c 2)

FIG. 2: Maximum likelihood fit projections of mESfor signal-enhanced samples of charmless B+_→

K∗+_h+ 1h

−

2 candidates. The dashed line is the fitted background PDF while the solid line is the sum of the signal and background PDFs. The points indicate the data. The plot labeled (a) shows a projec-tion of B+_→K∗+_K+_K−_{candidates, (b) B}+_→K∗+_π+_K− candidates, (c) B+ _→K∗+_K+_π−_{candidates and (d) B}+_→ K∗+_π+

π−_candidates.

Contributions to the branching fraction systematic er-ror are shown in Table II. Erer-rors due to charged

track-TABLE I: Signal yields, efficiencies and branching fractions for B+_→K∗+_K+_K−_{, B}+ _→K∗+_π+_K−_{, B}+_→K∗+_K+_π−_and B+_→K∗+_π+_π−_{, measured using K}0 Sπ +_h+ 1h −

2 events. The first error is statistical and in the case of the measured branching fractions the second error is systematic. These efficiencies have taken into account that B(K∗+ _→K0

π+

) = 2/3, assuming isospin symmetry, as well as B(K0 _→K0

S) and B(K 0 S →π

+_π−_{) [7]. The branching fraction upper limits at a 90% C.L. are} shown for B+ _→

K∗+_π+

K− _{and B}+ _→

K∗+_K+

π−_{. Asymmetries are reported (first error is statistical and the second is} systematic) only for the channels with statistically significant yields.

Mode Signal Events Efficiency Measured Branching Fraction Upper Limit Asymmetry (AK∗hh)

Yield (%) (× 10−6_{) (× 10}−6₎ B+_→ K∗+_K+ K− _{288 ± 26 3.4 36.2 ± 3.3 ± 3.6 – 0.11 ± 0.08 ± 0.03} B+_→ K∗+_π+ K− _{20.1 ± 24.7 3.5 2.5 ± 3.1 ± 5.3 11.8 –} B+_→ K∗+_K+ π− _{9.7 ± 17.1 3.5 1.2 ± 2.1 ± 2.0 6.1 –} B+_→K∗+_π+_π− _{583 ± 46 3.3 75.3 ± 6.0 ± 8.1 – 0.07 ± 0.07 ± 0.04}

ing efficiency and K0

S reconstruction efficiency were as-signed by comparing control channels in MC events and data. The error in the efficiency was due to limited MC statistics, generated for each of the decays B+

→ K∗+_K+_K−_{, B}+ _{→ K}∗+_π+_K−_{, B}+ _{→ K}∗+_K+_π− _and

B+ _{→ K}∗+_π+_π−_{. Using a sample of e}+_e− _{→ µ}+_µ−

decays, the uncertainty in the number of BB events was calculated to be 1.1%. To calculate errors due to the fit procedure, a large number of MC samples were used, containing the amounts of signal and continuum events measured in data, and the estimated number of B-background events. The differences between the gen-erated and fitted values using these samples were used to ascertain the sizes of any biases. Biases of +4.2, +10.7, +5.1 and +6.4% were observed in the fitted sig-nal yields of B+ → K∗+_K+_K−_{, B}+ → K∗+_π+_K−_, B+ → K∗+_K+_π− _{and B}+ → K∗+_π+_π−_{, respectively,}

that were a consequence of small correlations between fit variables. These biases were applied as corrections to ob-tain the final signal yields and half of the correction was added as a systematic uncertainty. The uncertainty of the B-background contribution to the fit was estimated by varying the known branching fractions within their errors. Each background was varied individually and the effect on the fitted signal yield was added in quadrature as a contribution to the uncertainty. For the mK∗ fit range there was also the possibility of B-background con-tributions from nonresonant and higher K∗+_resonances

which was modeled in the data fit using a LASS param-eterization [12, 13]. The contribution from this back-ground was estimated by extrapolating a Kπ invariant mass projection fitted in a higher-mass region (0.992 < mK∗ < 1.6 GeV/c2), into the signal region. This esti-mated background was modeled in the final data fit, and half of the contribution to the signal was added as a sys-tematic error contribution. The extrapolation assumed there were no integrated interference effects between the Kπ background and the K∗+_{(892) signal. The}

uncer-tainty due to reconstructing the wrong B+ _{→ K}∗+_h+ 1h−2

signal candidate as a consequence of K/π

misidentifica-tion, for example B+

→ K∗+_K+_K− _{events being}

re-constructed as B+

→ K∗+_π+_K− _{candidates was}

deter-mined using MC events and added as a systematic. The uncertainty due to PDF modeling was estimated from the calibration channel B+ _{→ ¯D}0_{(→ K}∗+_π−_)π+ _and

by varying the PDFs according to the precision of the parameters obtained from the calibration channel fit to data. In order to take correlations between parameters into account, the full correlation matrix was used when varying parameters. All PDF parameters that were orig-inally fixed in the fit were then varied in turn, and each difference from the nominal fit was combined in quadra-ture and taken as a systematic contribution.

TABLE II: Summary of systematic uncertainty contributions to the branching fraction measurements B+ _{→ K}∗+_h+

1h − 2. Multiplicative errors are shown as a percentage of the branch-ing fraction and additive errors are shown in events. The fi-nal column shows the total systematic error on the branching fraction.

Error K∗+K+K− K∗+π+K− K∗+K+π− K∗+π+π− source error(%) error(%) error(%) error (%) Multiplicative errors (%) Tracking 2.4 2.4 2.4 2.4 K0 S Efficiency 1.2 1.2 1.2 1.2 Efficiency 5.3 9.4 8.2 5.6 No. of BB 1.1 1.1 1.1 1.1 Tot. mult.(%) 6.0 9.8 8.7 6.3

Additive errors (events)

Fit Bias 6.0 1.1 0.3 18.7 B-background 6.9 33.4 1.3 37.9 K(892)∗+_{bkg 19.5 12.0 4.5 25.6} Signal mis-id 0.0 14.2 15.5 0.0 PDF params. 8.4 19.4 3.0 14.0 Tot. add. 23.1 42.9 16.5 51.4 (events) Total (10−6_{) 3.6 5.3 2.0 8.1}

For the decays B+

→ K∗+_h+

1h−2, interference effects

(nonreso-nant and K0∗+(1430)) integrate to zero if the acceptance

of the detector and analysis is uniform; the same is true of the interference between the K∗+_{(892) and D-wave}

final states (K2∗+(1430)). Studies of MC events showed

the efficiency variations were small enough to make these interference effects insignificant. The integrated inter-ference between K∗+_{(892) and other P-wave amplitudes}

such as K∗+

1 (1410) is in principle nonzero, but in

prac-tice is negligible due to the small branching fraction of K∗+

1 (1410) → K 0

Sπ

+

(6.6 ± 1.3% [7]) and the fact that the Kπ mass lineshapes have little overlap.

The CP -violating charge asymmetries for the decays B+

→ K∗+_K+_K−_{and B}+

→ K∗+_π+_π−_{were measured}

to be AK∗KK= 0.11 ± 0.08 ± 0.03 and AK∗ππ = 0.07 ±

0.07±0.04, respectively, where the first errors are statisti-cal and the second errors are systematic. The background asymmetries ABkgK∗KK and A

Bkg

K∗ππ, which were expected

to be consistent with zero, were measured to be 0.00 ± 0.02 and 0.01 ± 0.01, respectively. As a further study, the asymmetry ADπ for B+ → ¯D0(→ K∗+π−)π+, also

expected to be consistent with zero, was measured to be −0.01 ± 0.02 with a corresponding background asymme-try ABkgDπ of −0.01 ± 0.06 (statistical errors only).

The systematic error on AK∗h1h2 was calculated by considering contributions due to track finding, fit bi-ases, B-background uncertainties and particle interac-tion asymmetries. The error due to fit biases was found to be negligible. Uncertainties due to charged tracking efficiency were assigned by comparing control channels in MC simulation and data. The contribution from B-background was calculated by varying the number of expected events within errors and by assuming a CP -violating asymmetry of ± 0.2, as there are no available measurements for these decays. The CP asymmetry as-sumed for the individual B-backgrounds was chosen to be greater than any asymmetry observed for charged B decays. The interaction asymmetry of matter and anti-matter with the detector was studied using background measurements ABkgK∗KK and A

Bkg

K∗ππ, where no effect was

observed and the statistical precision of the measurement was added as a systematic contribution.

In summary, we have analyzed K0

Sπ

+_h+

1h−2 final states

to obtain the first branching fraction measurements for the decays B+

→ K∗+_K+_K− _{and B}+

→ K∗+_π+_π−_,

and no evidence for new physics was found, placing upper limits on the branching fractions B+

→ K∗+_π+_K− _and

B+

→ K∗+_K+_π−_.

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 support BA_BAR_{. The collaborating}

institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), 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). Indi-viduals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

∗ _{Also at Laboratoire de Physique Corpusculaire,} Clermont-Ferrand, France

† _{Also with Universit`a di Perugia, Dipartimento di Fisica,} Perugia, Italy

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[8] R. A. Fisher, Ann. Eugenics 7, 179 (1936); G. Cowan, Statistical Data Analysis, 51 (Oxford University Press, 1998).

[9] The Heavy Flavor Averaging Group (HFAG),

http://www.slac.stanford.edu/xorg/hfag/rare/winter06/ charmless/index.html.

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