Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |[subscript Vub]|

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Branching fraction and form-factor shape

measurements of exclusive charmless semileptonic

B decays, and determination of |[subscript Vub]|

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Citation

Lees, J. et al. “Branching Fraction and Form-factor Shape

Measurements of Exclusive Charmless Semileptonic B Decays, and

Determination of |V_{ub}|.” Physical Review D 86.9 (2012). © 2012

American Physical Society

As Published

http://dx.doi.org/10.1103/PhysRevD.86.092004

Publisher

American Physical Society

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Final published version

Citable link

http://hdl.handle.net/1721.1/76616

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Branching fraction and form-factor shape measurements of exclusive charmless

semileptonic

B decays, and determination of jV

_ub

j

J. P. Lees,1V. Poireau,1V. Tisserand,1J. Garra Tico,2E. Grauges,2A. Palano,3a,3bG. Eigen,4B. Stugu,4D. N. Brown,5 L. T. Kerth,5Yu. G. Kolomensky,5G. Lynch,5H. Koch,6T. Schroeder,6D. J. Asgeirsson,7C. Hearty,7T. S. Mattison,7 J. A. McKenna,7R. Y. So,7A. Khan,8V. E. Blinov,9A. R. Buzykaev,9V. P. Druzhinin,9V. B. Golubev,9E. A. Kravchenko,9

A. P. Onuchin,9S. I. Serednyakov,9Yu. I. Skovpen,9E. P. Solodov,9K. Yu. Todyshev,9A. N. Yushkov,9M. Bondioli,10 D. Kirkby,10A. J. Lankford,10M. Mandelkern,10H. Atmacan,11J. W. Gary,11F. Liu,11O. Long,11G. M. Vitug,11

C. Campagnari,12T. M. Hong,12D. Kovalskyi,12J. D. Richman,12C. A. West,12A. M. Eisner,13J. Kroseberg,13 W. S. Lockman,13A. J. Martinez,13B. A. Schumm,13A. Seiden,13D. S. Chao,14C. H. Cheng,14B. Echenard,14 K. T. Flood,14D. G. Hitlin,14P. Ongmongkolkul,14F. C. Porter,14A. Y. Rakitin,14R. Andreassen,15Z. Huard,15 B. T. Meadows,15M. D. Sokoloff,15L. Sun,15P. C. Bloom,16W. T. Ford,16A. Gaz,16U. Nauenberg,16J. G. Smith,16 S. R. Wagner,16R. Ayad,17,*W. H. Toki,17B. Spaan,18K. R. Schubert,19R. Schwierz,19D. Bernard,20M. Verderi,20 P. J. Clark,21S. Playfer,21D. Bettoni,22aC. Bozzi,22aR. Calabrese,22a,22bG. Cibinetto,22a,22bE. Fioravanti,22a,22b I. Garzia,22a,22bE. Luppi,22a,22bM. Munerato,22a,22bL. Piemontese,22aV. Santoro,22aR. Baldini-Ferroli,23A. Calcaterra,23

R. de Sangro,23G. Finocchiaro,23P. Patteri,23I. M. Peruzzi,23,†M. Piccolo,23M. Rama,23A. Zallo,23R. Contri,24a,24b E. Guido,24a,24bM. Lo Vetere,24a,24bM. R. Monge,24a,24bS. Passaggio,24aC. Patrignani,24a,24bE. Robutti,24aB. Bhuyan,25

V. Prasad,25C. L. Lee,26M. Morii,26A. J. Edwards,27A. Adametz,28U. Uwer,28H. M. Lacker,29T. Lueck,29 P. D. Dauncey,30U. Mallik,31C. Chen,32J. Cochran,32W. T. Meyer,32S. Prell,32A. E. Rubin,32A. V. Gritsan,33Z. J. Guo,33 N. Arnaud,34M. Davier,34D. Derkach,34G. Grosdidier,34F. Le Diberder,34A. M. Lutz,34B. Malaescu,34P. Roudeau,34 M. H. Schune,34A. Stocchi,34G. Wormser,34D. J. Lange,35D. M. Wright,35C. A. Chavez,36J. P. Coleman,36J. R. Fry,36

E. Gabathuler,36D. E. Hutchcroft,36D. J. Payne,36C. Touramanis,36A. J. Bevan,37F. Di Lodovico,37R. Sacco,37 M. Sigamani,37G. Cowan,38D. N. Brown,39C. L. Davis,39A. G. Denig,40M. Fritsch,40W. Gradl,40K. Griessinger,40

A. Hafner,40E. Prencipe,40R. J. Barlow,41,‡G. Jackson,41G. D. Lafferty,41E. Behn,42R. Cenci,42B. Hamilton,42 A. Jawahery,42D. A. Roberts,42C. Dallapiccola,43R. Cowan,44D. Dujmic,44G. Sciolla,44R. Cheaib,45D. Lindemann,45

P. M. Patel,45,§S. H. Robertson,45P. Biassoni,46a,46bN. Neri,46aF. Palombo,46a,46bS. Stracka,46a,46bL. Cremaldi,47 R. Godang,47,kR. Kroeger,47P. Sonnek,47D. J. Summers,47X. Nguyen,48M. Simard,48P. Taras,48G. De Nardo,49a,49b D. Monorchio,49a,49bG. Onorato,49a,49bC. Sciacca,49a,49bM. Martinelli,50G. Raven,50C. P. Jessop,51J. M. LoSecco,51 W. F. Wang,51K. Honscheid,52R. Kass,52J. Brau,53R. Frey,53N. B. Sinev,53D. Strom,53E. Torrence,53E. Feltresi,54a,54b

N. Gagliardi,54a,54bM. Margoni,54a,54bM. Morandin,54aM. Posocco,54aM. Rotondo,54aG. Simi,54aF. Simonetto,54a,54b R. Stroili,54a,54bS. Akar,55E. Ben-Haim,55M. Bomben,55G. R. Bonneaud,55H. Briand,55G. Calderini,55J. Chauveau,55 O. Hamon,55Ph. Leruste,55G. Marchiori,55J. Ocariz,55S. Sitt,55M. Biasini,56a,56bE. Manoni,56a,56bS. Pacetti,56a,56b

A. Rossi,56a,56bC. Angelini,57a,57bG. Batignani,57a,57bS. Bettarini,57a,57bM. Carpinelli,57a,57b,{G. Casarosa,57a,57b A. Cervelli,57a,57bF. Forti,57a,57bM. A. Giorgi,57a,57bA. Lusiani,57a,57cB. Oberhof,57a,57bE. Paoloni,57a,57bA. Perez,57a G. Rizzo,57a,57bJ. J. Walsh,57aD. Lopes Pegna,58J. Olsen,58A. J. S. Smith,58A. V. Telnov,58F. Anulli,59aR. Faccini,59a,59b

F. Ferrarotto,59aF. Ferroni,59a,59bM. Gaspero,59a,59bL. Li Gioi,59aM. A. Mazzoni,59aG. Piredda,59aC. Bu¨nger,60 O. Gru¨nberg,60T. Hartmann,60T. Leddig,60C. Voß,60R. Waldi,60T. Adye,61E. O. Olaiya,61F. F. Wilson,61S. Emery,62

G. Hamel de Monchenault,62G. Vasseur,62Ch. Ye`che,62D. Aston,63D. J. Bard,63R. Bartoldus,63J. F. Benitez,63 C. Cartaro,63M. R. Convery,63J. Dorfan,63G. P. Dubois-Felsmann,63W. Dunwoodie,63M. Ebert,63R. C. Field,63 M. Franco Sevilla,63B. G. Fulsom,63A. M. Gabareen,63M. T. Graham,63P. Grenier,63C. Hast,63W. R. Innes,63 M. H. Kelsey,63P. Kim,63M. L. Kocian,63D. W. G. S. Leith,63P. Lewis,63B. Lindquist,63S. Luitz,63V. Luth,63 H. L. Lynch,63D. B. MacFarlane,63D. R. Muller,63H. Neal,63S. Nelson,63M. Perl,63T. Pulliam,63B. N. Ratcliff,63 A. Roodman,63A. A. Salnikov,63R. H. Schindler,63A. Snyder,63D. Su,63M. K. Sullivan,63J. Va’vra,63A. P. Wagner,63 W. J. Wisniewski,63M. Wittgen,63D. H. Wright,63H. W. Wulsin,63C. C. Young,63V. Ziegler,63W. Park,64M. V. Purohit,64

R. M. White,64J. R. Wilson,64A. Randle-Conde,65S. J. Sekula,65M. Bellis,66P. R. Burchat,66T. S. Miyashita,66 E. M. T. Puccio,66M. S. Alam,67J. A. Ernst,67R. Gorodeisky,68N. Guttman,68D. R. Peimer,68A. Soffer,68P. Lund,69

S. M. Spanier,69J. L. Ritchie,70A. M. Ruland,70R. F. Schwitters,70B. C. Wray,70J. M. Izen,71X. C. Lou,71 F. Bianchi,72a,72bD. Gamba,72a,72bS. Zambito,72a,72bL. Lanceri,73a,73bL. Vitale,73a,73bF. Martinez-Vidal,74 A. Oyanguren,74P. Villanueva-Perez,74H. Ahmed,75J. Albert,75Sw. Banerjee,75F. U. Bernlochner,75H. H. F. Choi,75

G. J. King,75R. Kowalewski,75M. J. Lewczuk,75I. M. Nugent,75J. M. Roney,75R. J. Sobie,75N. Tasneem,75 T. J. Gershon,76P. F. Harrison,76T. E. Latham,76H. R. Band,77S. Dasu,77Y. Pan,77R. Prepost,77and S. L. Wu77

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(BABARCollaboration)

1_{Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite´ de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France}

2_{Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain}

3a_{INFN Sezione di Bari; I-70126 Bari, Italy}

3b

Dipartimento di Fisica, Universita` di Bari, I-70126 Bari, Italy

4_{University of Bergen, Institute of Physics, N-5007 Bergen, Norway}

5_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA}

6_{Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany}

7_{University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1}

8_{Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom}

9_{Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia}

10_{University of California at Irvine, Irvine, California 92697, USA}

11_{University of California at Riverside, Riverside, California 92521, USA}

12

University of California at Santa Barbara, Santa Barbara, California 93106, USA

13_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA}

14_{California Institute of Technology, Pasadena, California 91125, USA}

15_{University of Cincinnati, Cincinnati, Ohio 45221, USA}

16_{University of Colorado, Boulder, Colorado 80309, USA}

17_{Colorado State University, Fort Collins, Colorado 80523, USA}

18_{Technische Universita¨t Dortmund, Fakulta¨t Physik, D-44221 Dortmund, Germany}

19_{Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany}

20_{Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France}

21_{University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom}

22a_{INFN Sezione di Ferrara; I-44100 Ferrara, Italy}

22b_{Dipartimento di Fisica, Universita` di Ferrara, I-44100 Ferrara, Italy}

23_{INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy}

24a_{INFN Sezione di Genova; I-16146 Genova, Italy}

24b_{Dipartimento di Fisica, Universita` di Genova, I-16146 Genova, Italy}

25_{Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India}

26

Harvard University, Cambridge, Massachusetts 02138, USA

27_{Harvey Mudd College, Claremont, California 91711, USA}

28_{Universita¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany}

29_{Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, Newtonstr. 15, D-12489 Berlin, Germany}

30_{Imperial College London, London, SW7 2AZ, United Kingdom}

31_{University of Iowa, Iowa City, Iowa 52242, USA}

32_{Iowa State University, Ames, Iowa 50011-3160, USA}

33_{Johns Hopkins University, Baltimore, Maryland 21218, USA}

34_{Laboratoire de l’Acce´le´rateur Line´aire, IN2P3/CNRS et Universite´ Paris-Sud 11,}

Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France

35_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA}

36_{University of Liverpool, Liverpool L69 7ZE, United Kingdom}

37_{Queen Mary, University of London, London, E1 4NS, United Kingdom}

38_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom}

39_{University of Louisville, Louisville, Kentucky 40292, USA}

40_{Johannes Gutenberg-Universita¨t Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany}

41_{University of Manchester, Manchester M13 9PL, United Kingdom}

42_{University of Maryland, College Park, Maryland 20742, USA}

43_{University of Massachusetts, Amherst, Massachusetts 01003, USA}

44_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA}

45_{McGill University, Montre´al, Que´bec, Canada H3A 2T8}

46a_{INFN Sezione di Milano; I-20133 Milano, Italy}

46b_{Dipartimento di Fisica, Universita` di Milano, I-20133 Milano, Italy}

47_{University of Mississippi, University, Mississippi 38677, USA}

48_{Universite´ de Montre´al, Physique des Particules, Montre´al, Que´bec, Canada H3C 3J7}

49a

INFN Sezione di Napoli; I-80126 Napoli, Italy

49b_{Dipartimento di Scienze Fisiche, Universita` di Napoli Federico II, I-80126 Napoli, Italy}

50_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands}

51_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

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52_{Ohio State University, Columbus, Ohio 43210, USA}

53_{University of Oregon, Eugene, Oregon 97403, USA}

54a_{INFN Sezione di Padova; I-35131 Padova, Italy}

54b_{Dipartimento di Fisica, Universita` di Padova, I-35131 Padova, Italy}

55_{Laboratoire de Physique Nucle´aire et de Hautes Energies, IN2P3/CNRS,}

Universite´ Pierre et Marie Curie-Paris6, Universite´ Denis Diderot-Paris7, F-75252 Paris, France

56a_{INFN Sezione di Perugia; I-06100 Perugia, Italy}

56b_{Dipartimento di Fisica, Universita` di Perugia, I-06100 Perugia, Italy}

57a

INFN Sezione di Pisa; I-56127 Pisa, Italy

57b_{Dipartimento di Fisica, Universita` di Pisa; I-56127 Pisa, Italy}

57c_{Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy}

58_{Princeton University, Princeton, New Jersey 08544, USA}

59a_{INFN Sezione di Roma; I-00185 Roma, Italy}

59b_{Dipartimento di Fisica, Universita` di Roma La Sapienza, I-00185 Roma, Italy}

60_{Universita¨t Rostock, D-18051 Rostock, Germany}

61_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom}

62_{CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France}

63_{SLAC National Accelerator Laboratory, Stanford, California 94309 USA}

64_{University of South Carolina, Columbia, South Carolina 29208, USA}

65_{Southern Methodist University, Dallas, Texas 75275, USA}

66_{Stanford University, Stanford, California 94305-4060, USA}

67_{State University of New York, Albany, New York 12222, USA}

68_{Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel}

69_{University of Tennessee, Knoxville, Tennessee 37996, USA}

70

University of Texas at Austin, Austin, Texas 78712, USA

71_{University of Texas at Dallas, Richardson, Texas 75083, USA}

72a_{INFN Sezione di Torino; I-10125 Torino, Italy}

72b_{Dipartimento di Fisica Sperimentale, Universita` di Torino, I-10125 Torino, Italy}

73a_{INFN Sezione di Trieste; I-34127 Trieste, Italy}

73b_{Dipartimento di Fisica, Universita` di Trieste, I-34127 Trieste, Italy}

74_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain}

75_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6}

76_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom}

77_{University of Wisconsin, Madison, Wisconsin 53706, USA}

(Received 7 August 2012; published 5 November 2012)

We report the results of a study of the exclusive charmless semileptonic decays, B0_!_‘þ_,

Bþ! 0_‘þ_{, B}þ_{! !‘}þ_{, B}þ_{! ‘}þ_{, and B}þ_!0_‘þ_{(‘ ¼ e or ) undertaken with approximately}

462 106_B_{B pairs collected at the ð4SÞ resonance with the BABAR detector. The analysis uses events in}

which the signal B decays are reconstructed with a loose neutrino reconstruction technique. We obtain

partial branching fractions in several bins of q2, the square of the momentum transferred to the

lepton-neutrino pair, for B0_!_‘þ_{, B}þ_!0_‘þ_{, B}þ_{! !‘}þ_{, and B}þ_{! ‘}þ_{. From these distributions,}

we extract the form-factor shapes fþðq2Þ and the total branching fractions BðB0! ‘þÞ ¼ ð1:45

0:04stat 0:06systÞ 104 (combined and 0 decay channels assuming isospin symmetry),

BðBþ_{! !‘}þ_{Þ ¼ ð1:19 0:16}

stat 0:09systÞ 104 and BðBþ! ‘þÞ ¼ ð0:38 0:05stat0:05systÞ

104. We also measure BðBþ! 0‘þÞ ¼ ð0:24 0:08stat 0:03systÞ 104. We obtain values for

the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element jVubj by direct comparison

with three different QCD calculations in restricted q2_{ranges of B ! ‘}þ_{decays. From a simultaneous}

fit to the experimental data over the full q2_{range and the FNAL/MILC lattice QCD predictions, we obtain}

jVubj ¼ ð3:25 0:31Þ 103, where the error is the combined experimental and theoretical uncertainty.

DOI:10.1103/PhysRevD.86.092004 PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd

*_{Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.}

†_{Also with Universita` di Perugia, Dipartimento di Fisica, Perugia, Italy.}

‡_{Now at the University of Huddersfield, Huddersfield HD1 3DH, United Kingdom.}

§_Deceased.

k

Now at University of South Alabama, Mobile, AL 36688, USA.

{

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I. INTRODUCTION

A precise measurement of the

Cabibbo-Kobayashi-Maskawa (CKM) matrix [1] element jVubj will improve

our quantitative understanding of weak interactions and

CP violation in the Standard Model. The value of jVubj

can be determined by the measurement of the partial branching fractions of exclusive charmless semileptonic B decays since the rate for decays that involve a scalar meson is proportional to jVubfþðq2Þj2. Here, the form factor fþðq2Þ depends on q2, the square of the momentum transferred to the lepton-neutrino pair. Values of fþðq2Þ can be calculated at small q2(& 16 GeV2) using light cone sum rules (LCSR) [2–4] and at large q2(* 16 GeV2) from

unquenched lattice QCD (LQCD) [5,6]. Extraction

of the fþðq2Þ form-factor shapes from exclusive decays [7] such as B0 _!_‘þ_[₈_–₁₀_{], B}þ_!0_‘þ_[₈_], Bþ! !‘þ [11], and Bþ! ð0Þ‘þ [9] may be used to test these theoretical predictions [12]. Measurements of the branching fractions (BF) of all these decays will also improve our knowledge of the composition of charmless semileptonic decays. This input can be used to reduce the

large systematic uncertainty in jVubj due to the poorly

known b ! u‘ signal composition in inclusive semilep-tonic B decays. It will also help to constrain the size of the gluonic singlet contribution to form factors for the Bþ! ð0Þ‘þ decays [4,13].

In this paper, we present measurements of the partial

BFs BðB0 _!

‘þ; q2Þ in 12 bins of q2, BðBþ ! 0_‘þ_{; q}2_{Þ in 11 bins of q}2_,_BðBþ _{! !‘}þ_{; q}2_{Þ and} BðBþ ! ‘þ; q2_{Þ in 5 bins of q}2_{, as well as the BF}

BðBþ_!0

‘þÞ. From these distributions, we extract the total BFs for each of the five decay modes. Values of these BFs were previously reported in Refs. [8–11], and refer-ences therein. In this work, we carry out an untagged analysis (i.e. the second B meson is not explicitly recon-structed) with the loose neutrino reconstruction technique [14] whereby the selections on the variables required to reconstruct the neutrino are much looser than usual. This

results in a large candidate sample. Concerning the Bþ !

0‘þ and Bþ! !‘þ decay modes, this is the first

analysis using this technique.

We assume isospin symmetry to hold, and combine the

data of the Bþ! 0‘þ and B0! ‘þ channels

thereby leading to a large increase, of the order of 34%, in the effective number of B0 _!_‘þ_{events available}

for study. We refer to such events as B ! ‘þ decays.

The values of the BFs obtained in the present work are based on the use of the most recent BFs and form-factor shapes for all decay channels in our study. In particular, the subsequent improved treatment of the distributions that describe the combination of resonant and nonresonant b ! u‘ decays results in an increase of 3.5% in the total

BF value of the B0 _!_‘þ_{decays. This increase is}

significant in view of the total uncertainty of 5.1% obtained in the measurement of this BF.

We now optimize our selections over the entire fit region instead of the signal-enhanced region, as was done previ-ously [9]. The ensuing tighter selections produce a data set with a better signal to background ratio and higher purity in the B0 ! ‘þ and Bþ! ð0Þ‘þ decays.

As a result, we can now investigate the Bþ! ð0Þ‘þ

decays over their full q2_{ranges. The present analysis of the}

B0_!_‘þ_{decay channel makes use of the full BABAR}

data set compared to only a subset in Ref. [8]. As for the Bþ! !‘þ decay channel, it uses the unfolded values of the partial BFs and a selection procedure that is signifi-cantly different from the one in Ref. [11]. The unfolding process is used to obtain the distribution of the true values

of q2 by applying the inverse of the detector response

matrix to the distribution of the measured values of q2_. Each element of this matrix is constructed in Monte Carlo

(MC) simulation for each bin of q2 _{as the ratio of the}

number of true events to the total number of reconstructed events. The current work provides results for five decay channels using the same analysis method.

In this work, we compare the values of Bðq2_{Þ for the} B ! ‘þ mode to form-factor calculations [2,3,5,6] in restricted q2 _{ranges to obtain values of jV}

ubj. Values of jVubj with a smaller total uncertainty can also be obtained

from a simultaneous fit to the B ! ‘þ experimental

data over the full q2 range and the FNAL/MILC lattice

QCD predictions [6]. Such values were recently obtained

by BABAR [8] [jVubj ¼ ð2:95 0:31Þ 103] and Belle [10] [jVubj ¼ ð3:43 0:33Þ 103]. These results are consistent at the 2 level, when taking into account the correlations, but display a tension with respect to the value of jVubj measured [12] in inclusive semileptonic B decays, jVubj ¼ ð4:27 0:38Þ 103. This study attempts to re-solve the tension by analyzing the data using the most recent values of BFs and form factors.

II. DATA SAMPLE AND SIMULATION We use a sample of 462 106_B_{B pairs, corresponding} to an integrated luminosity of 416:1 fb1, collected at the

ð4SÞ resonance with the BABAR detector [15] at the

PEP-II asymmetric-energy eþe storage rings. A sample

of 43:9 fb1 collected approximately 40 MeV below the

ð4SÞ resonance (denoted ‘‘off-resonance data’’) is used to study contributions from eþe ! u u=d d=ss=cc=þ (continuum) events. Detailed MC simulations are used to optimize the signal selections, estimate the signal efficien-cies, obtain the shapes of the signal and background dis-tributions, and determine the systematic uncertainties associated with the BF values.

MC samples are generated for ð4SÞ ! B B events,

continuum events, and dedicated signal samples con-taining B0 _!_‘þ_{, B}þ_!0_‘þ_{, B}þ _{! !‘}þ_{, and}

Bþ! ð0Þ‘þ signal decays, separately. These signal

MC events are produced with the FLATQ2 generator [16]. The fþðq2Þ shape used in this generator is adjusted

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by reweighting the generated events. For the B ! ‘þ decays, the signal MC events are reweighted to reproduce

the Boyd-Grinstein-Lebed (BGL) parametrization [17],

where the parameters are taken from Ref. [9]. For the

Bþ! !‘þ decays, the events are reweighted to

repro-duce the Ball parametrization [18]. For the Bþ ! ð0Þ‘þ decays, the signal MC events are reweighted to reproduce

the Becirevic-Kaidalov (BK) parametrization [19], where

the parameter BK¼ 0:52 0:04 gave a reasonable fit

to the B0_!_‘þ_{and B}þ _{! ‘}þ_{data of Ref. [}₉_]. The BABAR detector’s acceptance and response are

simu-lated using the GEANT4 package [20].

III. EVENT RECONSTRUCTION AND CANDIDATE SELECTION

To reconstruct the decays B0 _!_‘þ_{, B}þ_!0_‘þ_, Bþ! !‘þ, and Bþ ! ð0Þ‘þ, we first reconstruct the final state meson. The ! meson is reconstructed in the

! ! þ0 decay channel. The meson is

recon-structed in the ! [ðÞ] and ! þ0

[ð3Þ] decay channels while the 0 is reconstructed in

the 0! þdecay channel, followed by the !

decay [0ðÞ]. The 0! 0_{decay channel suffers from} large backgrounds and we do not consider it in the present work.

Event reconstruction with the BABAR detector is de-scribed in detail elsewhere [15]. Electrons and muons are mainly identified by their characteristic signatures in the electromagnetic calorimeter and the muon detector, respec-tively, while charged hadrons are identified and recon-structed using the silicon vertex tracker, the drift chamber, and the Cherenkov detector. The photon and charged par-ticle tracking reconstruction efficiencies are corrected using various control samples. The average electron and muon reconstruction efficiencies are 93% and 70%, respectively, while the corresponding probabilities that a pion is identi-fied as a lepton are less than 0.2% and less than 1.5%, respectively.

The neutrino four-momentum, P¼ ðj ~pmissj; ~p missÞ, is inferred from the difference between the momentum of the colliding-beam particlesp~beams and the vector sum of the momenta of all the particles detected in the eventp~tot, such that p~miss¼ ~p

beams ~p

tot. All variables with an asterisk are given in the ð4SÞ frame. To evaluate Etot, the total energy of all detected particles, we assume zero mass for all neutral candidates, and we use the known masses for the charged particles identified in the event. If the particle is not identified, its mass is assumed to be that of a pion.

In this analysis, we calculate the momentum transfer squared as q2 _{¼ ðP}

B PmesonÞ2instead of q2¼ðP‘þPÞ2, where PB, Pmeson, and P‘ are the four-momenta of the B

meson, of the , !, , or 0 meson, and of the lepton,

respectively, evaluated in the ð4SÞ frame. With this choice, the value of q2is unaffected by any misreconstruc-tion of the neutrino. To maintain this advantage, PB must

be evaluated without any reference to the neutrino. It has an effective value since the magnitude of the three-momentump~B is determined from the center-of-mass en-ergy and the known B meson mass but the direction of the B meson cannot be measured. It can only be estimated.

To do this, we first combine the lepton with a , !, , or 0 meson to form the so-called Y pseudoparticle such that PY ¼ P‘þ Pmeson. The angle BY, between the Y and B momenta in the ð4SÞ frame, can be determined under the assumption that the only unobserved decay product is a neutrino, i.e., B ! Y. In this frame, the Y momentum,

the B momentum, and the angle BYdefine a cone with the

Y momentum as its axis and with a true B momentum lying somewhere on the surface of the cone. The B rest frame is

thus known up to an azimuthal angle c about the Y

mo-mentum. The value of q2 is then computed, as explained in Ref. [21], as the average of four q2 _{values corresponding to}

four possible angles,c,c þ =2,c þ ,c þ 3=2 rad,

where the angle c is chosen randomly. The four values of

q2 are weighted by the factor sin2B, B being the angle between the B direction and the beam direction in the ð4SÞ frame. This weight is needed since B B production follows a sin2

B distribution in the ð4SÞ frame. We require that

j cosBYj 1. We correct for the reconstruction effects on the measured values of q2 (the q2 resolution is

approxi-mately 0:6 GeV2_{) by applying an unregularized unfolding}

algorithm to the measured q2_{spectra [}₂₂_].

The selections of the candidate events are determined in MC simulation by maximizing the ratio S=pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðS þ BÞover the entire fit region, where S is the number of correctly reconstructed signal events and B is the total number of background events. The continuum background is sup-pressed by requiring the ratio of second to zeroth

Fox-Wolfram moments [23] to be smaller than 0.5. Radiative

Bhabha and two-photon processes are rejected by require-ments on the number of charged particle tracks and neutral calorimeter clusters [24]. To ensure all track momenta are well measured, their polar angles are required to lie be-tween 0.41 and 2.46 rad with respect to the electron beam direction (the acceptance of the detector). For all decays, we demand the momenta of the lepton and meson candi-dates to be topologically compatible with a real signal decay by requiring that a mass-constrained geometrical vertex fit [25] of the tracks associated with the two particles

gives a 2 probability greater than 1%. In the fit, the

external constraints such as reconstructed tracks are treated first, followed by all four-momenta conservation con-straints. Finally, at each vertex, the geometric constraints and the mass are combined. These combined constraints are applied consecutively.

To reduce the number of unwanted leptons and second-ary decays such as D ! X‘, J=c, , and kaon decays, the minimum transverse momentum is 50 MeV for all leptons and 30 MeV for all photons, and all electron (muon) tracks are required to have momenta greater than 0.5 (1.0) GeV in

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the laboratory frame. The momenta of the lepton and the meson are further restricted to enhance signal over back-ground. We require the following:

(i) for B ! ‘þ decays: j ~p_‘j > 2:2 GeV or j ~pj > 1:3 GeV or j ~p_‘j þ j ~pj > 2:8 GeV;

(ii) for Bþ! !‘þ decays: j ~p_‘j > 2:0 GeV or j ~p!j > 1:3 GeV or j ~p_‘j þ j ~p!j > 2:65 GeV;

(iii) for Bþ! ‘þ decays: j ~p_‘j > 2:1 GeV or j ~pj > 1:3 GeV or j ~p_‘j þ j ~pj > 2:8 GeV;

(iv) for Bþ! 0‘þ decays: j ~p_‘j > 2:0 GeV or j ~p 0j > 1:65 GeV or 0:69j ~p ‘j þ j ~p 0j > 2:4 GeV. These cuts primarily reject background and reduce the signal efficiencies by less than 5%.

To remove J=c ! þdecays, we reject any

combi-nation of two muons, including misidentified pions, if the two particles have an invariant mass consistent with the

J=c mass [3.07–3.13] GeV. We do not apply a specific

J=c veto for J=c ! eþe decays, since we find no

evidence for any remaining such events in our data set. We restrict the reconstructed masses of the meson to lie in the interval:

(i) for Bþ ! 0_‘þ_{decays: 0:115<m}

0<0:150GeV;

(ii) for Bþ! !‘þ decays: 0:760<m!<0:805GeV; (iii) for Bþ! ‘þ decays: 0:51 < m< 0:57 GeV; (iv) for Bþ! 0‘þ decays: 0:92 < m0 < 0:98 GeV.

Backgrounds are further reduced by q2_-dependent

se-lections on the cosine of the angle, costhrust, between the thrust axes [26] of the Y and of the rest of the event; on the polar angle, miss, associated with p~miss; on the invariant missing mass squared, m2miss¼ E2miss j ~pmissj2, divided by twice the missing energy (Emiss¼ Ebeams Etot); on the

cosine of the angle, cos‘, between the direction of the

virtual W boson (‘ and combined) boosted in the rest frame of the B meson and the direction of the lepton boosted in the rest frame of the W boson; and on L2, the momentum weighted Legendre monomial of order 2. The quantity m2

miss=2Emiss should be consistent with zero if a single neutrino is missing. The phrase ‘‘rest of the event’’ refers to all the particles left in the event after the lepton and the meson used to form the Y pseudoparticle are removed.

The q2_{-dependent selections are shown in the panels on} the left-hand side of Fig.1, and their effects are illustrated in the panels on the right-hand side of the same figure, for B0 _!_‘þ_{decays. A single vertical line indicates a} fixed cut; a set of two vertical lines represents a

q2-dependent cut. The position of the two lines

corre-sponds to the minimum and maximum values of the selec-tion, shown in the left-hand side panels. The functions

describing the q2 _{dependence are given in Tables} _VIII_,

IX,X,XI,XII, andXIIIof the Appendix for the five decays

under study. For Bþ! ‘þ decays, additional

back-ground is rejected by requiring that j cosVj < 0:95, where V is the helicity angle of the meson [16].

0

5

10

15

20

25 -1.0

-0.8

-0.6

-0.4

-0.2

-0.0

0

5

10

15

20

25

0.5

0.6

0.7

0.8

0.9

1.0

0

5

10

15

20

25

0.0

0.5

1.0

1.5

2.0

0

5

10

15

20

25

0.0

0.2

0.4

0.6

0.8

0

5

10

15

20

25

0

1

2

3

) 2 (GeV 2 q 0 5 10 15 20 25 cut valuel θ cos -1.0 -0.8 -0.6 -0.4 -0.2 -0.0 0 5 10 15 20 25 -1.0 -0.8 -0.6 -0.4 -0.2 -0.0 ) 2 (GeV _q2 0 5 10 15 20 25 cut value thrust θ cos 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 0.5 0.6 0.7 0.8 0.9 1.0 ) 2 (GeV 2 q 0 5 10 15 20 25

cut value (GeV)

miss /2E miss 2 m 0.0 0.5 1.0 1.5 2.0 0 5 10 15 20 25 0.0 0.5 1.0 1.5 2.0 ) 2 (GeV 2 q 0 5 10 15 20 25

cut value (rad)

miss θ 0.0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 0.0 0.2 0.4 0.6 0.8 ) 2 (GeV 2 q 0 5 10 15 20 25 L2 cut value 0 1 2 3 0 5 10 15 20 25 0 1 2 3 (rad) miss θ 0 1 2 3 E vents per 0 .05 ra d 0 2000 4000 (rad) miss θ 0 1 2 3 E vents per 0 .05 ra d 0 2000 4000 signal ν l π 0 B both B ν ul → → b same B ν ul → b both B B other B same B B other B continuum l θ cos -1.0 -0.5 0.0 0.5 1.0 E vents per 0 .05 0 2000 4000 l θ cos -1.0 -0.5 0.0 0.5 1.0 E vents per 0 .05 0 2000 4000 thrust θ cos 0.0 0.2 0.4 0.6 0.8 1.0 E vents per 0 .02 0 500 1000 1500 2000 thrust θ cos 0.0 0.2 0.4 0.6 0.8 1.0 E vents per 0 .02 0 500 1000 1500 2000 (GeV) miss /2E miss 2 m -2 -1 0 1 2 3

Events per 0.1 GeV

0 5000 10000 (GeV) miss /2E miss 2 m -2 -1 0 1 2 3

0 5000 10000 0 1 2 3 4 5 E vents per 0 .1 0 2000 4000 6000 8000 L2 0 1 2 3 4 5 E vents per 0 .1 0 2000 4000 6000 8000

FIG. 1 (color online). Left panels: Distributions of the

selec-tion values for the q2_{-dependent selections on the variables used}

in the analysis of B0_!_‘þ_{decays. The vertical axis}

repre-sents the selection value for a given q2_{value. We reject an event}

when its value is in the shaded region. Right panels: Corresponding distributions in the total fit region illustrating

the effects of the q2_{-dependent selections. The arrows indicate}

the rejected regions, as explained in the text. All the selections have been applied except for the one of interest. In each panel, the signal area is scaled to the area of the total background.

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The kinematic variables E ¼ ðPB Pbeams s=2Þ= ffiffiffi s p and mES ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs=2 þ ~pB ~pbeamsÞ2=E2beams ~p2B q are used in a fit to provide discrimination between signal and background decays. pffiffiffis is the center-of-mass energy of

the colliding particles. Here, PB¼ Pmesonþ P‘þ P

must be evaluated in the laboratory frame. We only retain

candidates with jEj < 1:0 GeV and mES> 5:19 GeV,

thereby removing from the fit a region with large back-grounds. Fewer than 6.6% (12.5%, 7.2%, 7.4%, 1.9%) of all ‘ (0_{‘, !‘, ‘,}0_{‘) events have more than one} candidate per event. For events with multiple candidates,

only the candidate with the largest value of cos‘ is

kept. The signal event reconstruction efficiency varies

between 6.1% and 8.5% for B0 _!_‘þ_{decays, between}

2.8% and 6.0% for Bþ! 0‘þ decays, between 1.0%

and 2.2% for Bþ! !‘þ decays, and between 0.9% and

2.6% for Bþ! ‘þ decays ( channel), depending on

the value of q2_{. The efficiency is 0.6% for both}

Bþ! ‘þ (þ0 _channel) _and _Bþ_!0_‘þ

decays. The efficiencies are given as a function of q2 _in

Tables XXIII, XXIV, XXV, XXVI, and XXVII of the

Appendix.

IV. BACKGROUNDS AND SIGNAL EXTRACTION Backgrounds can be broadly grouped into three main categories: decays arising from b ! u‘ transitions (other

than the signal), decays in other B B events (excluding

b ! u‘), and decays in continuum events. The ‘‘other

B B’’ background is the sum of different contributions,

where more than 75% are from B ! D=D=D decays.

For the B0 _!_‘þ_{, B}þ_!0_‘þ_{and combined}

B ! ‘þ modes, for which there is a large number of

candidate events, each of the first two categories of back-ground is further split into a backback-ground category where the pion and the lepton come from the decay of the same B meson (‘‘same-B’’ category), and a background category where the pion and the lepton come from the decay of different B mesons (‘‘both-B’’ category).

We use the E-mES histograms, obtained from the MC

simulation, as two-dimensional probability density func-tions (PDFs) in an extended binned maximum-likelihood fit [27] to the data to extract the yields of the signal and backgrounds as a function of q2_{. This fit method} incorpo-rates the statistical uncertainty from the finite MC sample size into the fit uncertainty. The E-mES plane is

subdi-vided into 34 bins for each bin of q2 _{in the fits to the}

‘þ, 0_‘þ_{, and ‘}þ_{candidate data where we have a} reasonably large number of events, and into 19 bins in the fits to the !‘þ, ‘þ, and 0‘ decay data. The E-mES

distributions for the B0_!_‘þ_{decay channel are}

shown in Fig. 2. The binning used in this case is also

displayed in the figure. We use variable bin sizes because we want to have a large number of small bin sizes in the signal-enhanced region to better define this specific region.

The signal-enhanced region is the region of the E-mES

plane with a large proportion of signal events. It is delim-ited in our work by the boundaries 0:16 < E <

0:20 GeV and mES> 5:268 GeV (see Fig. 2). To allow

the fit to converge quickly we cannot have too many bins in

the overall E-mES plane. Hence the bins outside the

signal-enhanced region will have a larger size. The actual size is dictated by the need to have a good description of the smooth backgrounds. The parameters of the fit are the scaling factors of the MC PDFs, i.e., the factors used to

adjust the number of events in a PDF to minimize the 2

value of the fit.

Given the sufficient number of events for the B0!

‘þ and combined B ! ‘þ decay modes, the data

samples can be subdivided into 12 bins of q2for the signal and two bins for each of the five background categories. The use of two bins for each background component allows the fit to adjust for inaccuracies in the modeling of the shape of the background q2 _{spectra. The boundaries of the} two background bins of q2_{for the B}0_!_‘þ_{and B !}

‘þ decays are ½0–18–26:4 GeV2 _{for the b ! u‘}

same-B category, ½0–22–26:4 GeV2 _{for the b ! u‘}

both-B category, ½0–10–26:4 GeV2 _{for the other B}_B

same-B category, ½0–14–26:4 GeV2 _{for the other B}_B

both-B category, and ½0–22–26:4 GeV2_{for the continuum}

category. In each case, the q2 ranges of the two bins are chosen to contain a similar number of events. In the fit to the data, we determine for each bin of q2, the signal yield, the b ! u‘, the other B B, and the continuum background yields in each bin of E-mES.

Note, however, that the scaling factors obtained for each background are constrained to have the same value over their ranges of q2 _{defined above. We thus have a total} of 22 parameters and ð12 34 22Þ degrees of freedom in the fit to the B0 _!_‘þ_{data and to the combined}

B ! ‘þ data. The limited number of events for the

other signal modes reduces the number of parameters,

and hence the number of q2 _{bins that can be used for}

the fits to converge. Table Ishows the number of bins of

q2 _{used for each signal mode as a function of the fit}

category.

TABLE I. Categories and number of fit parameters for each

decay mode.

Categories Decay mode

‘ 0_{‘ !‘} _‘ðÞ 0_‘ðÞ ‘ ‘ ( & 3) ‘ð3Þ Signal 12 11 5 5 1 b ! u‘ same B 2 1 1 fixed fixed b ! u‘ both B 2 1 Other B B same B 2 1 1 1 1 Other B B both B 2 1 Continuum 2 1 1 1 fixed

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As an initial estimate in the fit, the MC continuum back-ground yield and q2_{-dependent shape are first normalized to} match the yield and q2_{-dependent shape of the off-resonance} data control sample. This results in a large statistical uncer-tainty due to the small number of events in the off-resonance data. To improve the statistical precision, the continuum background is allowed to vary in the fit to the data for the ‘, !‘, and ‘ðÞ modes where we have a relatively large number of events. The fit result is compatible with the measured distribution of off-resonance data. Whenever a background is not varied in the fit, it is fixed to the MC prediction, except for the continuum background, which is fixed to its normalized yield and q2-dependent shape using

the off-resonance data. The background parameters, which are free in the fit, typically require an adjustment of less than 10% with respect to the MC predictions. The initial agree-ment between MC and data is already good before we do any fit. After the fit, the agreement becomes excellent, as can be

seen in Fig. 3 for a number of variables of interest. The

values of the scaling factors, obtained in this work, are

presented in Table XIV of the Appendix for each decay

channel. The full correlation matrices of the fitted scaling factors are given in TablesXV,XVI,XVII,XVIII,XIX,XX,

XXI, andXXIIof the Appendix.

We refit the data on several different subsets obtained by dividing the final data set based on time period, electron

0 10 20 30 40 50 60 70 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 signal ν l -π → 0 B 0 2 4 6 8 10 12 14 16 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 Continuum 0 5 10 15 20 25 30 35 40 45 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 same B ν ul → b 0 5 10 15 20 25 30 35 40 45 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 same B B Other B 0 1 2 3 4 5 6 7 8 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 both B ν ul → b 0 5 10 15 20 25 30 35 40 E (GeV) ∆ -1.0 -0.5 0.0 0.5 1.0 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 both B B Other B

FIG. 2 (color online). E-mES MC distributions, summed over all bins of q2, for the six categories of events used in the signal

extraction fit, after all the selections have been applied, in the case of the B0_!_‘þ_{decay channel. Also shown is the binning used}

for this decay mode.

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or muon candidates, by modifying the q2, E, or mES binnings, and by varying the event selections. We obtain consistent results for all subsets. We have also used MC simulation to verify that the nonresonant decay contribu-tions to the resonance yields are negligible. For example, we find that there are 30 nonresonant þ0_{‘ events}

out of a total yield of 1861 233 events for the Bþ !

!‘þ decay channel.

For illustrative purposes only, we show in Figs.4–6E and mES fit projections in the signal-enhanced region for

the B0 _!_‘þ_{, B}þ_!0_‘þ_{and combined B}0 _!

‘þ and Bþ! 0_‘þ_{decays, respectively, in two} ranges of q2 _{corresponding to the sum of eight bins below}

and four bins above q2 ¼ 16 GeV2, respectively. More

detailed E and mES fit projections in each q2 bin are

shown in Figs.13and14of the Appendix for the combined

B ! ‘þ decays. The data and the fit results are in

good agreement. Fit projections for Bþ ! !‘þ and

Bþ! ð0Þ‘þ decays, over their q2 _{ranges of} investiga-tion, are shown in Fig.7. TableIIgives the fitted yields in

the full q2 range studied for the signal and each

back-ground category as well as the 2 _{values and degrees of}

freedom for the overall fit region. The yield values in the

Bþ! ‘þ column are the result of the fit to the

com-bined and 3 modes.

V. SYSTEMATIC UNCERTAINTIES

Systematic uncertainties on the values of the partial

branching fractions, Bðq2_{Þ, and their correlations}

among the q2 bins have been investigated. These

uncer-tainties are estimated from the variations of the resulting

partial BF values (or total BF values for Bþ! 0‘þ

decays) when the data are reanalyzed by reweighting dif-ferent simulation parameters such as BFs and form factors. For each parameter, we use the full MC data set to produce

Events per 0.05 0 2000 4000 6000 Events per 0.05 0 2000 4000 6000 πlν signal 0 B both B ν ul →→ b same B ν ul → b both B B other B same B B other B continuum data π θ cos -1 -0.5 0 0.5 1 0.5 1 1.5

0 2000 4000

0 2000 4000 (GeV) π T p 0 1 2 3 0.5 1 1.5

0 2000 4000 6000

0 2000 4000 6000 lepton (GeV) T p 0 1 2 3 0.5 1 1.5

0 2000 4000 6000 8000

0 2000 4000 6000 8000 (GeV) lepton p 1 2 3 4 0.5 1 1.5 Events per 0.05 0 1000 2000 3000 Events per 0.05 0 1000 2000 3000 BY θ cos -1 0 1 0.5 1 1.5 Events per 0.02 0 500 1000 1500 2000 Events per 0.02 0 500 1000 1500 2000 thrust θ cos 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5

FIG. 3 (color online). Comparison of the on-resonance data and MC simulation, for B0_!_‘þ_{decays, after all analysis cuts and}

MC simulation corrections have been applied. The Y signal candidates related distributions are generated from events in the E and

mESplane with the signal-enhanced region removed. The ratios of data/MC events are presented below each panel. The general level of

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new E-mES distributions (‘‘MC event samples’’) by re-weighting the parameter randomly over a complete Gaussian distribution whose standard deviation is given by the uncer-tainty on the parameter under study. One hundred such samples are produced for each parameter. Each MC event sample is analyzed the same way as real data to determine values of Bðq2_{Þ (or total BF values for B}þ_!0_‘þ decays). The contribution of the parameter to the systematic uncertainty is given by the rms value of the distribution of these Bðq2_{Þ values over the 100 samples.}

The systematic uncertainties due to the imperfect de-scription of the detector in the simulation are computed by using the uncertainties determined from control samples. These include the tracking efficiency of all charged particle tracks, the particle identification ef-ficiencies of signal candidate tracks, the calorimeter

efficiencies (varied separately for photons and K0

L), and

the energy deposited in the calorimeter by K0

L mesons as

well as their production spectrum. The reconstruction of these neutral particles affects the analysis through the neutrino reconstruction used to obtain the values of E and mES.

The uncertainties due to the generator-level inputs to the simulation are given by the uncertainties in the BFs of the background b ! u‘ and b ! c‘ pro-cesses, in the BFs of the secondary decays producing

leptons, and in the BFs of the ð4SÞ ! B B decays

[12]. The B ! X‘ form-factor uncertainties, where X ¼

ð; ;!;ð0Þ

;D;D;DÞ, are given by recent calculations or

(GeV)

ES

m

5.20 5.22 5.24 5.26 5.28

0 500 1000 (GeV) ES m 5.20 5.22 5.24 5.26 5.28

0 500 1000 signal ν l π 0 B both B ν ul →→ b same B ν ul → b both B B other B same B B other B continuum data a) 2 < 16 GeV 2 0 < q E (GeV) ∆ -1 -0.5 0 0.5 1

0 500 1000 E (GeV) ∆ -1 -0.5 0 0.5 1

0 500 1000 c) E (GeV) ∆ -1 -0.5 0 0.5 1 0 200 400 600 E (GeV) ∆ -1 -0.5 0 0.5 1 0 200 400 600 d) (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 200 400 600 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 200 400 600 b) 2 < 26.4 GeV 2 16 < q

FIG. 4 (color online). Projections of the data and fit results

for the B0_!_‘þ_{decays, in the signal-enhanced region:}

(a,b) mES with 0:16 < E < 0:20 GeV; and (c,d) E

with mES > 5:268 GeV. The distributions (a,c) and (b,d)

are projections for q2 _{< 16 GeV}2 _{and for q}2 _{> 16 GeV}2_,

respectively.

(GeV)

ES

m

5.20 5.22 5.24 5.26 5.28

0 100 200 300 400 (GeV) ES m 5.20 5.22 5.24 5.26 5.28

0 100 200 300 400 signal ν l 0 π + B both B ν ul →→ b same B ν ul → b both B B other B same B B other B continuum data a) 2 < 16 GeV 2 0 < q E (GeV) ∆ -1 -0.5 0 0.5 1

0 200 400 E (GeV) ∆ -1 -0.5 0 0.5 1

0 200 400 c) E (GeV) ∆ -1 -0.5 0 0.5 1 0 100 200 E (GeV) ∆ -1 -0.5 0 0.5 1 0 100 200 d) (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 50 100 150 200 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 50 100 150 200 b) 2 < 26.4 GeV 2 16 < q

FIG. 5 (color online). Projections of the data and fit results

for the Bþ ! 0_‘þ_{decays, in the signal-enhanced region:}

(a,b) mES with 0:16 < E < 0:20 GeV; and (c,d) E

with mES > 5:268 GeV. The distributions (a,c) and (b,d)

are projections for q2 _{< 16 GeV}2 _{and for q}2 _{> 16 GeV}2_,

respectively.

(GeV)

ES

m

5.20 5.22 5.24 5.26 5.28

0 500 1000 1500 (GeV) ES m 5.20 5.22 5.24 5.26 5.28

0 500 1000 1500 signal ν l π B cross feed both B ν ul → → b same B ν ul → b both B B other B same B B other B continuum data a) 2 < 16 GeV 2 0 < q E (GeV) ∆ -1 -0.5 0 0.5 1

0 500 1000 1500 E (GeV) ∆ -1 -0.5 0 0.5 1

0 500 1000 1500 c) E (GeV) ∆ -1 -0.5 0 0.5 1 0 200 400 600 800 E (GeV) ∆ -1 -0.5 0 0.5 1 0 200 400 600 800 _d) (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 200 400 600 800 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 200 400 600 800 b) 2 < 26.4 GeV 2 16 < q

FIG. 6 (color online). Projections of the data and fit results for

the combined B0_!_‘þ_{and B}þ_!0_‘þ_{decays, in the}

signal-enhanced region: (a,b) mES with 0:16 < E <

0:20 GeV; and (c,d) E with mES> 5:268 GeV. The

distribu-tions (a,c) and (b,d) are projecdistribu-tions for q2_{< 16 GeV}2 _{and for}

q2_{> 16 GeV}2_{, respectively.}

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measurements [12]. The uncertainties in the heavy quark parameters used in the simulation of nonresonant b ! u‘ events are given in Ref. [28]. The uncertainty due to final state radiation (FSR) corrections calculated by PHOTOS [29] is given by 20% [30] of the difference in the values of the BF obtained with PHOTOS switched on and with PHOTOS switched off. The uncertainty due to the model-ing of the continuum is obtained by comparmodel-ing the shape of its q2 _{distribution to that of the off-resonance data control} sample. When the continuum is fixed in the fit, the uncer-tainty in the total yield is used instead. The unceruncer-tainty in that case is given by the comparison of the MC total yield to the one measured off resonance. Finally, the uncertainty due to B counting has been established to be 0.6% in BABAR.

Additional details on the various sources of systematic uncertainties considered in this analysis are presented

in Ref. [8]. The individual sources are, to a good

approximation, uncorrelated. Their associated contributions to the uncertainties can therefore be added in quadrature to yield the total systematic uncertainties for each decay mode. The list of all the systematic uncertainties, as well as their values for the partial and total BFs, are given in

Tables XXIII, XXIV, XXV, XXVI, and XXVII of the

Appendix. The term ‘‘Signal MC stat error’’ in these tables incorporates the systematic uncertainty due to the unfolding procedure. The correlation matrices obtained in the measurement of the partial BFs are presented in

Tables XXVIII, XXIX, XXX, XXXI, XXXII, XXXIII,

XXXIV, andXXXV. Condensed versions of all the uncer-tainties, together with signal yields and partial BFs in

selected q2 ranges, are given in Table III for the B0!

‘þ and Bþ! 0_‘þ_{decays, and in Table}_IV_{for the}

combined B ! ‘þ decays, as well as for the Bþ!

!‘þ and Bþ! ð0Þ‘þ decays. The values given for

the Bþ! ‘þ decays are those obtained from the

(GeV)

ES

m

5.20 5.22 5.24 5.26 5.28

0 100 200 300 400 (GeV) ES m 5.20 5.22 5.24 5.26 5.28

0 100 200 300 400 signal ν l ω + B ν ul →→ b B other B continuum data a) 2 < 20.2 GeV 2 0 < q E (GeV) ∆ -1 -0.5 0 0.5 1

0 100 200 300 400 E (GeV) ∆ -1 -0.5 0 0.5 1

0 100 200 300 400 _d) E (GeV) ∆ -1 -0.5 0 0.5 1 0 100 200 300 400 E (GeV) ∆ -1 -0.5 0 0.5 1 0 100 200 300 400 e) (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 100 200 300 400 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 100 200 300 400 _B+ ηlν signal ν ul →→ b B other B continuum data b) 2 < 22.4 GeV 2 0 < q E (GeV) ∆ -1 -0.5 0 0.5 1 0 20 40 60 80 E (GeV) ∆ -1 -0.5 0 0.5 1 0 20 40 60 80 _f) (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 20 40 60 80 (GeV) ES m 5.20 5.22 5.24 5.26 5.28 0 20 40 60 80 _B+ η’lν signal ν ul →→ b B other B continuum data c) 2 < 18.7 GeV 2 0 < q

FIG. 7 (color online). Projections of the data and fit results for the Bþ! !‘þ and Bþ! ð0Þ‘þ decays, in the signal-enhanced

region: (a,b,c) mESwith 0:16 < E < 0:20 GeV; and (d,e,f) E with mES> 5:268 GeV. The distributions (a,d), (b,e), and (c,f) are

projections for the Bþ! !‘þ, combined Bþ! ‘þ, and Bþ! 0‘þ decays, respectively.

TABLE II. Fitted yields in the full q2 _{range investigated for the signal and each background category, total fitted yield and}

experimental data events, and values of 2_{for the overall fit region.}

Decay mode ‘þ 0_‘þ _‘þ _!‘þ _‘þ 0_‘þ

Signal 9297 316 3204 170 12448 361 1861 233 867 101 141 49

b ! u‘ 15689 664 7810 334 23284 796 3246 293 2411 (fixed) 242 (fixed)

Other B B 44248 656 10795 307 55350 777 8778 246 11167 187 2984 87

Continuum 9159 459 4173 236 13283 537 2776 270 2505 155 493 (fixed)

Fitted yield 78393 507 25982 228 104365 531 16661 172 16950 153 3860 71

Data events 78387 280 25977 161 104364 323 16662 129 16901 130 3857 62

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combined fit to the distributions of the ! and !

þ0 _{channels. The ranges of q}2 _{delimited by the}

numbers 12, 16 are ranges used in theoretical predictions. We also give the results for the fully allowed kinematical range of q2_.

VI. BRANCHING FRACTION RESULTS

The total BF for the Bþ! 0‘þ decays and the

partial BFs for the other four decay modes are calculated using the unfolded signal yields, the signal efficien-cies given by the simulation, and the branching

frac-tionsBðð4SÞ ! B0_B0_{Þ ¼ 0:484 0:006 and Bðð4SÞ!}

BþBÞ¼0:5160:006 [12]. The values of the total BF

obtained in this work are compared in Table V to those

reported recently.

The BFs for the Bþ! 0‘þ and Bþ! ‘þ decays are consistent with those presented in our earlier work [9] even though there are significant differences between the two analyses. We now use updated BFs and form-factor shapes; we have tightened various selections; we have

subdivided the data in five signal bins for the

Bþ! ‘þ decays compared to the previous three bins;

and we have also investigated the full kinematically

al-lowed ranges of q2 whereas this range was earlier

re-stricted to less than 16 GeV2 _{due to the very large}

backgrounds at high q2_{. Thus, the present BF values}

supersede the earlier ones [9]. It should be noted that

the total BF value for the Bþ! 0‘þ decays has a

TABLE III. Values of signal yields, Bðq2_{Þ and their relative uncertainties (%) for B}0_!_‘þ_{and B}þ_!0_‘þ_decays.

Decay mode ‘þ 0_‘þ q2_{range (GeV}2₎ _q2_{< 12} _q2_{< 16} _q2_{> 16} _{0 < q}2_{< 26:4} _q2_{< 12} _q2_{< 16} _q2_{> 16} _{0 < q}2_{< 26:4} Unfolded yield 5604.1 6982.4 2314.2 9296.5 2231.7 2666.7 537.3 3204.1 Bðq2_{Þ (10}4₎ _0.83 _1.07 _0.40 _1.47 _0.46 _0.61 _0.16 _0.77 Statistical error 4.3 3.8 6.7 3.5 6.6 5.3 17.8 5.7 Detector effects 3.4 3.5 3.2 2.8 2.9 2.8 3.0 2.6 Continuum bkg 0.4 0.4 1.4 0.4 1.2 0.8 7.1 1.1 b ! u‘ bkg 1.6 1.4 2.1 1.3 1.7 1.5 5.9 1.9 b ! c‘ bkg 0.6 0.5 0.6 0.5 0.6 0.4 1.0 0.4 Other effects 2.2 2.1 2.1 2.1 2.1 2.1 2.5 2.0 Total uncertainty 6.2 5.8 8.1 5.1 7.9 6.5 20.4 6.9

TABLE IV. Values of signal yields, Bðq2_{Þ and their relative uncertainties (%) for combined B ! ‘}þ_{, B}þ_{! !‘}þ_{, combined}

Bþ! ‘þ ( and 3 decay channels) and Bþ! 0‘þ decays.

Decay mode Combined ‘þ !‘þ ‘þ 0‘þ

q2_{range (GeV}2₎ _q2_{< 12} _q2_{< 16} _q2_{> 16} _{0 < q}2_{< 26:4} _{0 < q}2_{< 20:2} _{0 < q}2_{< 22:4} _{0 < q}2_{< 18:7} Unfolded yield 7805.4 9618.9 2829.0 12447.9 1860.8 867.3 141.1 Bðq2_{Þ (10}4₎ _0.83 _1.08 _0.37 _1.45 _1.19 _0.38 _0.24 Statistical error 3.6 3.2 5.8 3.0 13.0 13.7 34.9 Detector effects 3.7 3.8 3.5 3.1 3.9 9.8 7.7 Continuum bkg 0.4 0.6 3.3 0.6 3.2 5.8 b ! u‘ bkg 1.6 1.4 4.0 1.4 5.1 8.4 4.9 b ! c‘ bkg 0.4 0.4 0.4 0.3 1.0 2.1 3.3 Other effects 1.8 1.7 1.5 1.6 1.8 1.8 2.4 Total uncertainty 5.8 5.5 8.7 4.9 15.0 19.0 36.7

TABLE V. Values of the total branching fractions obtained in

this analysis and previous results. The two uncertainties are

statistical and systematic, respectively. All BF values are 104.

Decay mode This analysis Previous results Ref.

B ! ‘þ 1:45 0:04 0:06 1:41 0:05 0:07 [8] B0_!_‘þ_{1:47 0:05 0:06 1:44 0:06 0:07} _[₈_] 1:42 0:05 0:07 [9] 1:49 0:04 0:07 [10] Bþ! 0_‘þ_{0:77 0:04 0:03 0:76 0:06 0:06} _[₈_] Bþ! !‘þ 1:19 0:16 0:09 1:21 0:14 0:10 [11] Bþ! ‘þ 0:38 0:05 0:05 0:36 0:05 0:04 [9] Bþ! 0‘þ 0:24 0:08 0:03 0:24 0:08 0:03 [9]