Measurement of the $B \to \pi \ell \nu$ Branching Fraction and Determination of $|V_{ub}|$ with Tagged B Mesons

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arXiv:hep-ex/0607089v2 21 Nov 2006

SLAC-PUB-11966 hep-ex/0607089

Measurement of the B → πℓν Branching Fraction and Determination of |V

ub

|

with Tagged B Mesons

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,17J. D. Richman,17T. 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,21J. 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 _{D. J. Bard,}32 _{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,36G. Schott,36N. Arnaud,37M. Davier,37 G. Grosdidier,37A. H¨ocker,37F. Le Diberder,37V. 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_{R. K. Yamamoto,}46 _{H. Kim,}47

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S. E. Mclachlin,47_{P. M. Patel,}47_{S. H. Robertson,}47_{A. Lazzaro,}48 _{V. Lombardo,}48_{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,61G. Calderini,61 M. Carpinelli,61 R. Cenci,61F. Forti,61 M. A. Giorgi,61

A. Lusiani,61 _{G. Marchiori,}61_{M. A. Mazur,}61 _{M. Morganti,}61_{N. Neri,}61 _{E. Paoloni,}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}

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17_{University of California at Santa Barbara, Santa Barbara, California 93106, USA}

18_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, 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} 28_{Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy} 29_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’Accélérateur Linéaire, IN2P3-CNRS et Université 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_{Université de Montréal, Physique des Particules, Montréal, Québec, 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} 76_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}

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

(Dated: October 25, 2018)

We report a measurement of the B → πℓν branching fraction based on 211 fb−1_{of data collected}

with the BA_BARdetector. We use samples of B0_{and B}+_{mesons tagged by a second B meson}

recon-structed in a semileptonic or hadronic decay, and combine the results assuming isospin symmetry to obtain B(B0 _{→ π}−_ℓ+_{ν) = (1.33 ± 0.17}

stat± 0.11syst) × 10−4. We determine the magnitude of

the Cabibbo-Kobayashi-Maskawa matrix element |Vub| by combining the partial branching fractions

measured in ranges of the momentum transfer squared and theoretical calculations of the form fac-tor. Using a recent lattice QCD calculation, we find |Vub| = (4.5 ± 0.5stat± 0.3syst+0.7−0.5FF) × 10

−3_,

where the last error is due to the normalization of the form factor. PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd

The magnitude of the Cabibbo-Kobayashi-Maskawa matrix [1] element Vub is a critical constraint on the Uni-tarity Triangle. Our knowledge of |Vub| comes from mea-surements of the b → uℓν decay rate, where the hadronic system in the final state can be reconstructed either in-clusively or exin-clusively. The precisions are limited by the uncertainties in the non-perturbative QCD calculations that are used to extract |Vub| from the measured decay rates. It is therefore crucial to pursue both the inclusive and exclusive approaches, which rely on different theo-retical methods, and to test their consistency.

The rate of the exclusive decay B → πℓν (ℓ = e or µ) is related to |Vub| through the form factor f+(q2), where q2 _{is the momentum transfer squared. Measurements} of the B → πℓν branching fraction have been reported by CLEO [2], BA_BAR _{[3], and Belle [4]. In this Letter,}

we report a measurement in which B → πℓν decays are searched for in Υ (4S) → BB events that are identified by reconstruction of the second B meson (Btag). The tech-nique, which was also used in [4], allows us to constrain the kinematics, reduce the combinatorics, and determine the charge of the signal B. The result is an improved sig-nal purity at the expense of the efficiency compared with the traditional measurements in which only the signal B meson is reconstructed. We perform two analyses in which Btagis reconstructed in semileptonic and hadronic decays, respectively, and combine the measured partial branching fractions ∆B in ranges of q2 _{with the recent} form-factor calculations [5, 6, 7, 8] to determine |Vub|.

The measurement uses a sample of approximately 232 million BB pairs, corresponding to an integrated lumi-nosity of 211 fb−1, recorded near the Υ (4S) resonance with the BA_BAR_{detector [9] at the PEP-II}

asymmetric-energy e+e− _{storage rings. We use a detailed Monte} Carlo (MC) simulation to estimate the signal efficiency and the signal and background distributions.

In the first analysis, we reconstruct Btagin the semilep-tonic decay B → D(∗)_{ℓν. We reconstruct D}0 _mesons in K−_π+_{, K}−_π+_π+_π−_{, K}−_π+_π0_{, and K}0

Sπ

+_π− _decays, and D+ _{mesons in K}−_π+_π+ _{decays [10]. The D mass} resolution (σ) is between 4.6 and 12.9 MeV depending on the decay channel. The mass of the D candidate

is required to be within 2.6σ and 3.0σ of the expected value for the B0_{and B}+ _{channels, respectively. We also} use a sideband sample, in which the D candidate mass is more than 3σ away from the nominal value, for sub-tracting the combinatoric background. We reconstruct D∗+ _{mesons in D}0_π+ _{and D}+_π0 _{decays. The mass} dif-ference between the D∗ _{and D is required to be within} 3 MeV of the expected value [11]. The reconstructed D and D∗_{candidates are paired with a charged lepton with} a center-of-mass (c.m.) momentum |pℓ| > 0.8 GeV to form a Y = D(∗)_{ℓ system. If the D decay contains a} charged kaon, the lepton must have the same charge as the kaon. The lepton and the D meson are required to originate from a common vertex. Assuming that only a massless neutrino escaped detection, we calculate the cosine of the angle between the B and Y momenta as cos θBY = (2EBEY−m2B−m2Y)/(2|pB||pY|), where mB, mY, EB, EY, pB, pY refer to the masses, c.m. energies, and momenta of the B and Y , respectively. For back-ground events, cos θBY does not correspond to the cosine of a physical angle and can extend outside ±1. We apply a loose selection of | cos θBY| < 5 at this stage.

After identifying the Btag meson, we require the re-maining particles in the event to be consistent with a B → πℓν decay. Charged tracks that are not identi-fied as a lepton or a kaon are considered charged pion candidates. Neutral pion candidates are formed from pairs of photon candidates with invariant mass between 115 and 150 MeV. For the B0 _{channel, the lepton must} have |pℓ| > 0.8 GeV, and its charge must be oppo-site to that of the charged pion. The lepton charge must be opposite to that of the Btag for the B+ chan-nel. We reject the lepton candidate if, when combined with an oppositely-charged track, it is consistent with a J/ψ → ℓ+_ℓ−_{decay or a photon conversion. Once the} sig-nal B candidate is identified, we require that the event contain no other charged particles and small total c.m. energy Eres of the residual neutral particles. In mea-suring Eres, we remove the neutral candidates that are consistent with coming from a D∗ _{→ Dπ}0 _{or Dγ} de-cay, bremsstrahlung from an electron, or beam-related background. We require Eres< 70 MeV for the B0

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chan-nel and Eres < 250 MeV for the B+ channel, the latter being relaxed to allow for additional photons from de-cays of D∗0 _{and higher resonances. We calculate the} cosine of the angle between the B and πℓ momenta as cos θBπℓ = (2EBEπℓ − mB2 − m2πℓ)/(2|pB||pπℓ|), where mπℓ, Eπℓ, pπℓ are the mass, c.m. energy, and momentum of the πℓ system, respectively. We require | cos θBπℓ| < 5. Ignoring the small c.m. momentum of the B meson, the invariant mass squared of the lepton-neutrino system in a B → πℓν decay can be inferred as q2 _{= (m}

B − Eπ)2− |pπ|2, where Eπ and pπ are the c.m. energy and momentum of the pion. We divide the data into three bins: q2_{< 8 GeV}2_{, 8 < q}2_{< 16 GeV}2_{, and q}2_{> 16 GeV}2_. We use simulated B → πℓν events to estimate and to correct for the small (< 8%) migration between the q2 bins due to resolution, which is approximately 0.8 GeV2 at q2_{= 8 GeV}2 _{and improves with increasing q}2_.

Having identified the two B mesons that decayed semileptonically, conservation of the total momentum de-termines the angle φBbetween the direction of the B mo-menta and the plane defined by the Y and πℓ momo-menta:

cos2φB= cos2_θ

BY + cos2θBπℓ+ 2 cos θBYcos θBπℓcos γ

sin2γ ,

(1) where γ is the angle between the Y and πℓ momenta. The variable cos2_φ

B satisfies cos2φB ≤ 1 for correctly reconstructed signal events, and is broadly distributed for the background (see Fig. 1). We use the cos2_φ

B dis-tributions to extract the signal yield in the data in each q2_{bin. We did not require stringent cuts on cos θ}

BY and cos θBπℓbecause they are incorporated in cos2φB.

We express the data distribution as a sum of three contributions: dN/d cos2φB = NsigPsig + NbkgPbkg + NcmbPcmb, where Nc and Pc are the number of events and the probability density function (PDF) for each cat-egory c, defined as the signal (sig), background with correctly-reconstructed D mesons (bkg), and other back-grounds (cmb). The events in the D mass sideband are also used in the fit to constrain the NcmbPcmb term. The PDF shapes are determined from the MC simula-tion. The signal PDF is a combination of a smeared step function and an exponential tail. The background PDFs are either an exponential plus constant or a sec-ond order polynomial. The two data samples (D mass peak and sideband) and the MC samples are used in an unbinned maximum likelihood fit that determines Nsig, Nbkg, Ncmb, and the PDF parameters simultaneously. Figure 1 shows the fit results summed over the q2 _bins. We find the signal yields and their statistical errors to be 57+13₋₁₂ events and 92+26₋₂₄ events for the B0 _{and B}+ channels, respectively.

We use simulated B → πℓν events to estimate the signal efficiencies. Control samples are used to derive corrections for the data-MC differences in the Btag re-construction, charged and neutral particle

reconstruc-B φ 2 cos 0 5 10 15 20 Events/0.5 0 10 20 30 40 B φ 2 cos 0 5 10 15 20 Events/0.5 0 10 20 30 40 _a) B φ 2 cos 0 5 10 15 20 Events/0.5 0 20 40 60 80 B φ 2 cos 0 5 10 15 20 Events/0.5 0 20 40 60 80 b)

FIG. 1: Distributions of cos2_φ

Bof the a) B0→ π−ℓ+νand b)

B+_{→ π}0_ℓ+_ν_{candidates. The points with error bars and the}

shaded histograms are the data in the D mass peak and side-band, respectively. The curves are the fit results representing the total (solid), background (dashed), and ‘cmb’ (dotted) components defined in the text. The fits were performed in bins of q2_{, but the results shown are for the complete q}2_range.

tion, and lepton identification. The largest uncertainty comes from the Btag reconstruction efficiency, which is determined from a sample of events in which two non-overlapping Btag candidates are reconstructed. The effi-ciency correction factors for the Btag reconstruction are found to be 1.00 ± 0.07 and 0.99 ± 0.02 for the B0 _and B+_{channels, respectively. The average signal efficiencies} after the correction are 1.1 × 10−3 _{for the B}0 _channel and 3.0 × 10−3_{for the B}+ _{channel. The latter is larger} mainly because of the higher efficiency of reconstructing a D0_{meson compared with a D}+ _{or D}∗+ _meson.

The measured branching fractions are summarized in Table I. The largest sources of systematic error [12] are: the Btag reconstruction efficiency (discussed above), the shape of the background cos2_φ

B distribution (studied with control samples that fail the signal selection crite-ria), and the branching fractions of the B semileptonic decays other than B → πℓν (varied within the current knowledge [11]).

In the second analysis, we reconstruct the Btagmeson in a set of purely hadronic final states B → D(∗)_{X. We} reconstruct D0_{mesons in K}−_π+_{, K}−_π+_π0_{, K}−_π+_π+_π−_, and K0

Sπ

+_π− _{decays, and D}+ _{mesons in K}−_π+_π+_, K−_π+_π+_π0_{, K}0 Sπ +_{, K}0 Sπ +_π0_{, and K}0 Sπ +_π+_π− _decays. The D∗ _{mesons are reconstructed in D}0_π+_{, D}0_π0_{, and} D0_{γ decays. The hadronic system X has a total charge} ±1 and is composed of n1π±+n2K±+n3π0+n4KS0where n1+n2< 6, n3< 3 and n4< 3. The total reconstruction efficiency for a B0 _(B+_{) meson is 0.3% (0.5%).}

We separate correctly-reconstructed Btagmesons from the background using two kinematic variables: the beam-energy substituted mass mES = ps/4 − |pB|2 and the energy difference ∆E = EB−√s/2, where√s is the c.m. energy of the e+_e− _{system. We select signal candidates} in mode-dependent ∆E windows around zero. We apply a loose selection 5.2 < mES < 5.3 GeV and fit the mES distribution at a later stage to extract the signal yield.

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TABLE I: Partial and total branching fractions, in units of 10−4_{, measured with the semileptonic and hadronic tag analyses.}

The q2 _{ranges are in GeV}2_{. The errors are statistical and systematic. The combined results are expressed as B}0 _{→ π}−

ℓ+ν branching fractions. q2<8 8 < q2 <16 q2>16 q2<16 Total B0 _{Semileptonic 0.50 ± 0.16 ± 0.05 0.33 ± 0.14 ± 0.04 0.29 ± 0.15 ± 0.04 0.83 ± 0.22 ± 0.08 1.12 ± 0.25 ± 0.10} Hadronic 0.09 ± 0.10 ± 0.02 0.33 ± 0.15 ± 0.05 0.65 ± 0.20 ± 0.13 0.42 ± 0.18 ± 0.05 1.07 ± 0.27 ± 0.15 Average 0.38 ± 0.12 ± 0.04 0.33 ± 0.10 ± 0.03 0.47 ± 0.13 ± 0.06 0.72 ± 0.16 ± 0.06 1.19 ± 0.20 ± 0.10 B+ _{Semileptonic 0.18 ± 0.08 ± 0.02 0.45 ± 0.13 ± 0.05 0.10 ± 0.12 ± 0.04 0.63 ± 0.16 ± 0.06 0.73 ± 0.18 ± 0.08} Hadronic 0.16 ± 0.11 ± 0.03 0.39 ± 0.16 ± 0.06 0.26 ± 0.12 ± 0.06 0.56 ± 0.19 ± 0.08 0.82 ± 0.22 ± 0.11 Average 0.18 ± 0.07 ± 0.02 0.43 ± 0.10 ± 0.04 0.22 ± 0.09 ± 0.05 0.61 ± 0.12 ± 0.05 0.82 ± 0.15 ± 0.09 Combined 0.36 ± 0.09 ± 0.03 0.52 ± 0.10 ± 0.04 0.46 ± 0.10 ± 0.06 0.87 ± 0.13 ± 0.06 1.33 ± 0.17 ± 0.11

After reconstructing the Btag, we look for the signa-ture of a B → πℓν decay in the recoiling system. The selection criteria for the pion and lepton candidates are similar to the first analysis, except a) the minimum |pℓ| for electrons is 0.5 GeV, and b) the π0 _{mass window is} 110–160 MeV. We require Eres < 450 MeV for the B0 channel to reduce the B0_{→ ρ}−_ℓ+_{ν background, and no} requirement is made for the B+ _channel.

The full reconstruction of Btag allows us to determine the neutrino four-momentum precisely from the missing four-momentum pmiss = pΥ(4S)− pB_tag − pπ− pℓ. The missing mass squared m2

misspeaks near zero for the signal and extends above zero for the background (see Fig. 2). We require |m2

miss| < 0.3 GeV2 for the B0 channel and −0.5 < m2

miss < 0.7 GeV2 for the B+ channel, with the latter being broader and asymmetric due to the resolu-tion of the π0 _{energy measurement.}

Precise knowledge of pmiss allows us to calculate q2 with small uncertainties. We divide the signal candi-dates into the same three q2_{bins as before, and subtract} the small bin-to-bin migration as background. In each q2 _{bin, we obtain the number of correctly-tagged events} by an unbinned maximum likelihood fit to the mES dis-tribution. The PDF for the signal is determined from MC simulation as a Gaussian function joined to an ex-ponential tail. For the background, we use a threshold function of the form x√1 − x2_{exp(−ξ(1 − x}2_{)), where} x = 2mES/√s and the parameter ξ is allowed to float in the fit. Fig. 2 shows the m2

miss distribution obtained by splitting the data samples in bins of m2

missand repeating the mESfit.

The signal side of the correctly-tagged events may not be a B → πℓν decay. Contributions from this type of background are estimated with the MC simula-tion, as indicated by shaded histograms in Fig. 2, which are scaled to match the data in the sideband region 1 < m2

miss< 4 GeV

2_{. After background subtraction, we} find signal yields of 31 ± 7 events and 26 ± 7 events for the B0 _{and B}+ _{channels, respectively, where the errors} are statistical.

Instead of estimating the absolute signal efficiency, we

) 2 (GeV miss 2 m -1 0 1 2 3 2 Events/0.275 GeV 0 20 40 60 80 -1 0 1 2 3 0 20 40 60 80 a) ) 2 (GeV miss 2 m -1 0 1 2 3 2 Events/0.275 GeV 0 20 40 60 80 -1 0 1 2 3 0 20 40 60 80 b) FIG. 2: Distributions of m2

miss of the a) B0 → π−ℓ+ν and

b) B+ _{→ π}0_ℓ+_ν _{candidates. The points with error bars are}

the data. The histograms represent, from the lightest to the darkest, the MC simulation of the B → πℓν signal, b → uℓν, b → cℓν, and other backgrounds. The arrows indicate the regions in which the signals are extracted.

normalize the signal yield to the number of inclusive B semileptonic decays, B → Xℓν, in the recoil of Btag. The reconstruction efficiencies of the Btag and of the lepton cancel to first order in the ratio between the yields of the signal and normalization samples. The inclusive branch-ing fraction B(B → Xℓν) is taken as 10.73 ± 0.28% [11]. The yield of the normalization sample is extracted by a fit to the mES distribution. The component of the back-ground that peaks in the mES distribution is estimated from the MC simulation and subtracted. Efficiency dif-ferences between the signal and normalization samples are estimated with the MC simulation, and the corre-sponding corrections are applied to the result.

The measured branching fractions are summarized in Table I. The largest source of systematic error is the lim-ited statistics of the signal MC sample. Other significant sources include the modeling of the signal PDF (studied with alternative fitting methods), photon-energy mea-surement, π0 _{reconstruction, muon identification, and} the branching fractions of non-signal B → Xuℓν decays. We take weighted averages of the measured partial branching fractions in each q2_{bin. The results for the B}0 and B+ _{channels are consistent with the isospin relation} Γ(B0 _{→ π}−_ℓ+_{ν) = 2Γ(B}+ _{→ π}0_ℓ+_{ν) and the lifetime}

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TABLE II: Values of |Vub| derived using the form factor

cal-culations. The first two errors on |Vub| come from the

sta-tistical and systematic uncertainties of the partial branching fractions. The third errors correspond to the uncertainties on ∆ζ due to the form-factor calculations, and are taken from Refs. 5, 6, 7, 8. q2 _(GeV2_{) ∆ζ (ps}−1₎ _|V ub| (10−3) Ball-Zwicky [5] <16 5.44 ± 1.43 3.2 ± 0.2 ± 0.1+0.5 −0.4 Gulez et al. [6] >16 1.46 ± 0.35 4.5 ± 0.5 ± 0.3+0.7 −0.5 Okamoto et al. [7] > 16 1.83 ± 0.50 4.0 ± 0.5 ± 0.3+0.7 −0.5 Abada et al. [8] >16 1.80 ± 0.86 4.1 ± 0.5 ± 0.3+1.6 −0.7

ratio τB+/τB0 = 1.081 ± 0.015 [11], with χ2 = 5.2 for 3 degrees of freedom. Assuming isospin symmetry, we combine the B0_{and B}+ _{channels and express the results} as the B0 _{branching fraction in the last row of Table I.} The overall χ2 _{is 10.2 for 9 degrees of freedom.}

We extract |Vub| from the partial branching fractions ∆B using |Vub| =p∆B/(τB0∆ζ), where τB0 = (1.536 ± 0.014) ps [11] is the B0 _{lifetime and ∆ζ = ∆Γ/|V}

ub|2 is the normalized partial decay rate predicted by the form-factor calculations. We use the light-cone sum rules cal-culation [5] for q2_{< 16 GeV}2

and the lattice QCD calcu-lations [6, 7, 8] for q2_{> 16 GeV}2

. The results are shown in Table II.

In conclusion, we have measured the B → πℓν branch-ing fraction as a function of q2 _{using tagged B meson} samples, and have extracted |Vub|. The measured total branching fraction, B(B0_{→ π}−_ℓ+_{ν) = (1.33 ± 0.17}

stat± 0.11syst) × 10−4, has the smallest systematic uncertainty among the existing measurements [2, 3, 4] thanks to the superior signal purity, and the overall precision is com-parable to the best. Using theoretical calculations of the form factor, we obtain values of |Vub| ranging between 3.2 × 10−3 _{and 4.5 × 10}−3_{. As an example, the recently} published unquenched lattice QCD calculation [6] gives |Vub| = (4.5 ± 0.5stat± 0.3syst+0.7−0.5FF) × 10−3. Improve-ment will be possible with additional data combined with more precise form-factor calculations.

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 comput-ing organizations that support BA_BAR_{. The}

collaborat-ing 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), MEC (Spain), and PPARC (United Kingdom). Individuals 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

‡ _{Also with Universit`}_{a della Basilicata, Potenza, Italy}

[1] M. Kobayahi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).

[2] S. B. Athar et al. (CLEO Collaboration), Phys. Rev. D68_{, 072003 (2003).}

[3] B. Aubert et al. (BA_BARCollaboration), Phys. Rev. D72, 051102 (2005).

[4] T. Hokuue et al. (Belle Collaboration), hep-ex/0604024. [5] P. Ball and R. Zwicky, Phys. Rev. D71, 014015 (2005). [6] E. Gulez et al. (HPQCD Collaboration), Phys. Rev. D73,

074502 (2006).

[7] M. Okamoto et al., hep-lat/0409116.

[8] A. Abada et al., Nucl. Phys. B619, 565 (2001).

[9] B. Aubert et al. (BA_BAR _{Collaboration), Nucl. Inst. &} Meth. A479, 1 (2002).

[10] Charge conjugate states are implied throughout this Let-ter.

[11] S. Eidelman et al. (Particle Data Group), Phys. Lett. B592, 1 (2004).

[12] See EPAPS Document No. E-PRLTAO-97-050647 for two tables containing (i) the systematic errors of the mea-sured partial branching fractions (B → πℓν) and (ii) the error matrices. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.

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Electronic Physics Auxiliary Publication Service (EPAPS)

This is an EPAPS attachment to B. Aubert et al. (BA_BAR_{Collaboration), Phys. Rev. Lett. 97, 211801 (2006)}

[arXiv:hep-ex/0607089]. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.

TABLE I: Fractional systematic errors (in %) of the measured partial branching fractions. The q2 _{bins are defined as 1:}

q2 < 8 GeV2_{, 2: 8 < q}2

< 16 GeV2_{, and 3: q}2

> 16 GeV2_{. The + and × symbols indicate if the error is additive (+) or}

multiplicative (×).

Btag B0 semilep. B+ semilep. B0hadronic B+ hadronic

bin 1 2 3 1 2 3 1 2 3 1 2 3 B→ πℓν form factor × 1.0 0.5 1.1 0.9 0.5 4.5 0.3 0.2 0.1 0.3 0.2 2.2 B→ Xcℓνbackground + 1.9 2.9 3.8 2.0 3.5 7.7 0.2 0.2 0.2 2.6 2.6 2.6 B→ Xuℓνbackground + 0.8 1.7 6.9 1.2 1.7 12.1 4.2 4.2 4.2 1.7 1.7 1.7 B(B → Xℓν) × not applicable 2.6 2.6 2.6 2.6 2.6 2.6 B(Υ (4S) → B0_B0₎ _× _1.6 _1.6 _{1.6 1.6} _1.6 _1.6 _{not applicable} Final-state radiation × 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 Btag efficiency × 7.3 7.3 7.3 4.3 2.5 12.9 0.7 0.7 0.7 1.4 1.4 1.4 q2 _resolution _× _1.6 _1.3 _{1.2 1.2} _{4.5 18.0} _negligible Fit method + 1.4 2.1 5.7 4.8 6.2 32.8 5.7 5.7 5.7 2.7 2.7 2.7 Lepton identification × 1.6 1.9 1.9 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Charged track reconstruction × 1.6 1.6 1.6 0.8 0.8 0.8 1.1 1.1 1.1 1.4 1.4 1.4 Neutral energy reconstruction × negligible 3.2 3.0 6.3 1.2 1.2 1.2 3.7 3.7 3.7 Number of BB events × 1.1 1.1 1.1 1.1 1.1 1.1 not applicable

MC statistics × 5.2 5.1 4.6 4.7 4.2 6.8 18.3 11.8 17.6 19.8 14.7 23.0 Total 10.0 10.4 13.6 9.7 10.9 43.5 20.1 14.4 19.4 21.0 16.3 24.1

TABLE II: Values and errors (in unit of 10−4_{) of the combined partial branching fractions. The errors are separated into}

statis-tical, multiplicative systematic, and non-multiplicative systematic components, and the covariance matrices for the systematic components are given. The q2 _{bins are defined as 1: q}2

<8 GeV2_{, 2: 8 < q}2 <16 GeV2_{, and 3: q}2 >16 GeV2_. bin 1 2 3 Value 0.355 0.518 0.457 Statistical error 0.086 0.097 0.104 Multiplicative systematic error 0.028 0.038 0.052

Covariance 1 1.000 0.593 0.471

2 0.593 1.000 0.504 3 0.471 0.504 1.000 Non-multiplicative systematic error 0.008 0.017 0.021

Covariance 1 1.000 0.986 0.791

2 0.986 1.000 0.881 3 0.791 0.881 1.000