Measurements of B --> {pi, eta, eta'} l nu Branching Fractions and Determination of |Vub| with Semileptonically Tagged B Mesons
aa r X i v : . [ h e p - e x ] M a y B A B AR -PUB-08/013SLAC-PUB-13215 Measurements of B → { π, η, η ′ } ℓν ℓ Branching Fractions and Determination of | V ub | withSemileptonically Tagged B Mesons
B. Aubert, M. Bona, Y. Karyotakis, J. P. Lees, V. Poireau, E. Prencipe, X. Prudent, V. Tisserand, J. Garra Tico, E. Grauges, L. Lopez ab , A. Palano ab , M. Pappagallo ab , G. Eigen, B. Stugu, L. Sun, G. S. Abrams, M. Battaglia, D. N. Brown, R. N. Cahn, R. G. Jacobsen, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, G. Lynch, I. L. Osipenkov, M. T. Ronan, ∗ K. Tackmann, T. Tanabe, C. M. Hawkes, N. Soni, A. T. Watson, H. Koch, T. Schroeder, D. Walker, D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom, C. Hearty, T. S. Mattison, J. A. McKenna, M. Barrett, A. Khan, L. Teodorescu, V. E. Blinov, A. D. Bukin, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todyshev, M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, D. P. Stoker, S. Abachi, C. Buchanan, J. W. Gary, F. Liu, O. Long, B. C. Shen, ∗ G. M. Vitug, Z. Yasin, L. Zhang, V. Sharma, C. Campagnari, T. M. Hong, D. Kovalskyi, M. A. Mazur, J. D. Richman, T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, T. Schalk, B. A. Schumm, A. Seiden, L. Wang, M. G. Wilson, L. O. Winstrom, C. H. Cheng, D. A. Doll, B. Echenard, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter, R. Andreassen, G. Mancinelli, B. T. Meadows, K. Mishra, M. D. Sokoloff, F. Blanc, P. C. Bloom, W. T. Ford, A. Gaz, J. F. Hirschauer, A. Kreisel, M. Nagel, U. Nauenberg, J. G. Smith, K. A. Ulmer, S. R. Wagner, R. Ayad, † A. Soffer, ‡ W. H. Toki, R. J. Wilson, D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, M. Karbach, J. Merkel, A. Petzold, B. Spaan, K. Wacker, M. J. Kobel, W. F. Mader, R. Nogowski, K. R. Schubert, R. Schwierz, J. E. Sundermann, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, Ch. Thiebaux, M. Verderi, P. J. Clark, W. Gradl, S. Playfer, J. E. Watson, M. Andreotti ab , D. Bettoni a , C. Bozzi a , R. Calabrese ab , A. Cecchi ab , G. Cibinetto ab , P. Franchini ab , E. Luppi ab , M. Negrini ab , A. Petrella ab , L. Piemontese a , V. Santoro ab , R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Pacetti, P. Patteri, I. M. Peruzzi, § M. Piccolo, M. Rama, A. Zallo, A. Buzzo a , R. Contri ab , M. Lo Vetere ab , M. M. Macri a , M. R. Monge ab , S. Passaggio a , C. Patrignani ab , E. Robutti a , A. Santroni ab , S. Tosi ab , K. S. Chaisanguanthum, M. Morii, R. S. Dubitzky, J. Marks, S. Schenk, U. Uwer, V. Klose, H. M. Lacker, G. De Nardo ab , L. Lista a , D. Monorchio ab , G. Onorato ab , C. Sciacca ab , D. J. Bard, P. D. Dauncey, J. A. Nash, W. Panduro Vazquez, M. Tibbetts, P. K. Behera, X. Chai, M. J. Charles, U. Mallik, J. Cochran, H. B. Crawley, L. Dong, W. T. Meyer, S. Prell, E. I. Rosenberg, A. E. Rubin, Y. Y. Gao, A. V. Gritsan, Z. J. Guo, C. K. Lae, A. G. Denig, M. Fritsch, G. Schott, N. Arnaud, J. B´equilleux, A. D’Orazio, M. Davier, J. Firmino da Costa, G. Grosdidier, A. H¨ocker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, ¶ A. Stocchi, G. Wormser, D. J. Lange, D. M. Wright, I. Bingham, J. P. Burke, C. A. Chavez, J. R. Fry, E. Gabathuler, R. Gamet, D. E. Hutchcroft, D. J. Payne, C. Touramanis, A. J. Bevan, K. A. George, F. Di Lodovico, R. Sacco, M. Sigamani, G. Cowan, H. U. Flaecher, D. A. Hopkins, S. Paramesvaran, F. Salvatore, A. C. Wren, D. N. Brown, C. L. Davis, K. E. Alwyn, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, J. I. Yi, J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, J. M. Tuggle, C. Dallapiccola, S. S. Hertzbach, X. Li, E. Salvati, S. Saremi, R. Cowan, D. Dujmic, P. H. Fisher, K. Koeneke, G. Sciolla, M. Spitznagel, F. Taylor, R. K. Yamamoto, M. Zhao, S. E. Mclachlin, ∗ P. M. Patel, S. H. Robertson, A. Lazzaro ab , V. Lombardo a , F. Palombo ab , J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, ∗∗ R. Kroeger, D. A. Sanders, D. J. Summers, H. W. Zhao, M. Simard, P. Taras, F. B. Viaud, H. Nicholson, M. A. Baak, G. Raven, H. L. Snoek, C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, W. F. Wang, G. Benelli, L. A. Corwin, K. Honscheid, H. Kagan, R. Kass, J. P. Morris, A. M. Rahimi, J. J. Regensburger, S. J. Sekula, Q. K. Wong, N. L. Blount, J. Brau, R. Frey, O. Igonkina, J. A. Kolb, M. Lu, R. Rahmat, N. B. Sinev, D. Strom, J. Strube, E. Torrence, G. Castelli ab , N. Gagliardi ab , M. Margoni ab , M. Morandin a , M. Posocco a , M. Rotondo a , F. Simonetto ab , R. Stroili ab , C. Voci ab , P. del Amo Sanchez, E. Ben-Haim, H. Briand, G. Calderini, J. Chauveau, P. David, L. Del Buono, O. Hamon, Ph. Leruste, J. Ocariz, A. Perez, J. Prendki, L. Gladney, M. Biasini ab , R. Covarelli ab , E. Manoni ab , C. Angelini ab , G. Batignani ab , S. Bettarini ab , M. Carpinelli ab , †† A. Cervelli ab , F. Forti ab , M. A. Giorgi ab , A. Lusiani ac , G. Marchiori ab , M. Morganti ab , N. Neri ab , E. Paoloni ab , G. Rizzo ab , J. J. Walsh a , J. Biesiada, D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, A. V. Telnov, F. Anulli a , E. Baracchini ab , G. Cavoto a , D. del Re ab , E. Di Marco ab , R. Faccini ab , F. Ferrarotto a , F. Ferroni ab , M. Gaspero ab , P. D. Jackson a , L. Li Gioi a , M. A. Mazzoni a , S. Morganti a , G. Piredda a , F. Polci ab , F. Renga ab , C. Voena a , M. Ebert, T. Hartmann, H. Schr¨oder, R. Waldi, T. Adye, B. Franek, E. O. Olaiya, W. Roethel, F. F. Wilson, S. Emery, M. Escalier, L. Esteve, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault, W. Kozanecki, G. Vasseur, Ch. Y`eche, M. Zito, X. R. Chen, H. Liu, W. Park, M. V. Purohit, R. M. White, J. R. Wilson, M. T. Allen, D. Aston, R. Bartoldus, P. Bechtle, J. F. Benitez, R. Cenci, J. P. Coleman, M. R. Convery, J. C. Dingfelder, J. Dorfan, G. P. Dubois-Felsmann, W. Dunwoodie, R. C. Field, A. M. Gabareen, S. J. Gowdy, M. T. Graham, P. Grenier, C. Hast, W. R. Innes, J. Kaminski, M. H. Kelsey, H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, S. Li, B. Lindquist, S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane, H. Marsiske, R. Messner, D. R. Muller, H. Neal, S. Nelson, C. P. O’Grady, I. Ofte, A. Perazzo, M. Perl, B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, D. Su, M. K. Sullivan, K. Suzuki, S. K. Swain, J. M. Thompson, J. Va’vra, A. P. Wagner, M. Weaver, C. A. West, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, A. K. Yarritu, K. Yi, C. C. Young, V. Ziegler, P. R. Burchat, A. J. Edwards, S. A. Majewski, T. S. Miyashita, B. A. Petersen, L. Wilden, S. Ahmed, M. S. Alam, R. Bula, J. A. Ernst, B. Pan, M. A. Saeed, S. B. Zain, S. M. Spanier, B. J. Wogsland, R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, R. F. Schwitters, B. W. Drummond, J. M. Izen, X. C. Lou, F. Bianchi ab , D. Gamba ab , M. Pelliccioni ab , M. Bomben ab , L. Bosisio ab , C. Cartaro ab , G. Della Ricca ab , L. Lanceri ab , L. Vitale ab , V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, A. Oyanguren, J. Albert, Sw. Banerjee, B. Bhuyan, H. H. F. Choi, K. Hamano, R. Kowalewski, M. J. Lewczuk, I. M. Nugent, J. M. Roney, R. J. Sobie, T. J. Gershon, P. F. Harrison, J. Ilic, T. E. Latham, G. B. Mohanty, H. R. Band, X. Chen, S. Dasu, K. T. Flood, Y. Pan, M. Pierini, R. Prepost, C. O. Vuosalo, and S. L. Wu (The B A B AR Collaboration) Laboratoire de Physique des Particules, IN2P3/CNRS et Universit´e de Savoie, F-74941 Annecy-Le-Vieux, France Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain INFN Sezione di Bari a ; Dipartmento di Fisica, Universit`a di Bari b , I-70126 Bari, Italy University of Bergen, Institute of Physics, N-5007 Bergen, Norway Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA University of Birmingham, Birmingham, B15 2TT, United Kingdom Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany University of Bristol, Bristol BS8 1TL, United Kingdom University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia University of California at Irvine, Irvine, California 92697, USA University of California at Los Angeles, Los Angeles, California 90024, USA University of California at Riverside, Riverside, California 92521, USA University of California at San Diego, La Jolla, California 92093, USA University of California at Santa Barbara, Santa Barbara, California 93106, USA University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA California Institute of Technology, Pasadena, California 91125, USA University of Cincinnati, Cincinnati, Ohio 45221, USA University of Colorado, Boulder, Colorado 80309, USA Colorado State University, Fort Collins, Colorado 80523, USA Technische Universit¨at Dortmund, Fakult¨at Physik, D-44221 Dortmund, Germany Technische Universit¨at Dresden, Institut f¨ur Kern- und Teilchenphysik, D-01062 Dresden, Germany Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom INFN Sezione di Ferrara a ; Dipartimento di Fisica, Universit`a di Ferrara b , I-44100 Ferrara, Italy INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy INFN Sezione di Genova a ; Dipartimento di Fisica, Universit`a di Genova b , I-16146 Genova, Italy Harvard University, Cambridge, Massachusetts 02138, USA Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany Humboldt-Universit¨at zu Berlin, Institut f¨ur Physik, Newtonstr. 15, D-12489 Berlin, Germany INFN Sezione di Napoli a ; Dipartimento di Scienze Fisiche,Universit`a di Napoli Federico II b , I-80126 Napoli, Italy Imperial College London, London, SW7 2AZ, United Kingdom University of Iowa, Iowa City, Iowa 52242, USA Iowa State University, Ames, Iowa 50011-3160, USA Johns Hopkins University, Baltimore, Maryland 21218, USA Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11,Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France Lawrence Livermore National Laboratory, Livermore, California 94550, USA University of Liverpool, Liverpool L69 7ZE, United Kingdom Queen Mary, University of London, E1 4NS, United Kingdom University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom University of Louisville, Louisville, Kentucky 40292, USA University of Manchester, Manchester M13 9PL, United Kingdom University of Maryland, College Park, Maryland 20742, USA University of Massachusetts, Amherst, Massachusetts 01003, USA Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8 INFN Sezione di Milano a ; Dipartimento di Fisica, Universit`a di Milano b , I-20133 Milano, Italy University of Mississippi, University, Mississippi 38677, USA Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7 Mount Holyoke College, South Hadley, Massachusetts 01075, USA NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands University of Notre Dame, Notre Dame, Indiana 46556, USA Ohio State University, Columbus, Ohio 43210, USA University of Oregon, Eugene, Oregon 97403, USA INFN Sezione di Padova a ; Dipartimento di Fisica, Universit`a di Padova b , I-35131 Padova, Italy Laboratoire de Physique Nucl´eaire et de Hautes Energies,IN2P3/CNRS, Universit´e Pierre et Marie Curie-Paris6,Universit´e Denis Diderot-Paris7, F-75252 Paris, France University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA INFN Sezione di Perugia a ; Dipartimento di Fisica, Universit`a di Perugia b , I-06100 Perugia, Italy INFN Sezione di Pisa a ; Dipartimento di Fisica,Universit`a di Pisa b ; Scuola Normale Superiore di Pisa c , I-56127 Pisa, Italy Princeton University, Princeton, New Jersey 08544, USA INFN Sezione di Roma a ; Dipartimento di Fisica,Universit`a di Roma La Sapienza b , I-00185 Roma, Italy Universit¨at Rostock, D-18051 Rostock, Germany Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France University of South Carolina, Columbia, South Carolina 29208, USA Stanford Linear Accelerator Center, Stanford, California 94309, USA Stanford University, Stanford, California 94305-4060, USA State University of New York, Albany, New York 12222, USA University of Tennessee, Knoxville, Tennessee 37996, USA University of Texas at Austin, Austin, Texas 78712, USA University of Texas at Dallas, Richardson, Texas 75083, USA INFN Sezione di Torino a ; Dipartimento di Fisica Sperimentale, Universit`a di Torino b , I-10125 Torino, Italy INFN Sezione di Trieste a ; Dipartimento di Fisica, Universit`a di Trieste b , I-34127 Trieste, Italy IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain University of Victoria, Victoria, British Columbia, Canada V8W 3P6 Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom University of Wisconsin, Madison, Wisconsin 53706, USA (Dated: November 5, 2018)We report measurements of branching fractions for the decays B → P ℓν ℓ , where P are thepseudoscalar charmless mesons π − , π , η and η ′ , based on 348 fb − of data collected with the B A B AR detector, using B and B + mesons found in the recoil of a second B meson decaying as B → D ( ∗ ) ℓν ℓ . Assuming isospin symmetry, we combine pionic branching fractions to obtain B ( B → π − ℓ + ν ℓ ) = (1 . ± . (stat) ± . (syst) ) × − ; we find 3 . σ evidence of the decay B + → ηℓ + ν ℓ andmeasure its branching fraction to be (0 . ± . (stat) ± . (syst) ) × − , and determine B ( B + → η ′ ℓ + ν ℓ ) < . × − to 90% confidence level. Using partial branching fractions for the pionic decaysin ranges of the momentum transfer and a recent form factor calculation, we obtain the magnitude ofthe Cabibbo-Kobayashi-Maskawa matrix element | V ub | = (4 . ± . (stat) ± . (syst)+0 . − . ) × − . PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd, 14.40.Aq
The determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix [1] element | V ub | provides acritical constraint on the Unitarity Triangle; the decay b → uℓν ℓ is a theoretically and experimentally robustmeans of measuring | V ub | . In the measurements describedin this Letter, we reconstruct the b → uℓν ℓ decay exclu-sively, measuring branching fractions for the processes B → π − ℓ + ν ℓ [2] and B + → π ℓ + ν ℓ . These are selectedin the recoil of the semileptonic decay B → D ( ∗ ) ℓν ℓ ,which provides a measurement complementary to otherstudies [3, 4]; this measurement is significantly more pre-cise than previous measurements of its kind [3, 5]. Addi-tionally, branching fractions for the decays B + → ηℓ + ν ℓ and B + → η ′ ℓ + ν ℓ are measured, which provide potentialadditional means of determining | V ub | as well as a probeinto the dynamics of the η – η ′ meson system [6].We use a sample of 383 million BB pairs, correspond-ing to an integrated luminosity of 348 fb − recorded onthe Υ(4 S ) resonance by the B A B AR detector at the PEP-IIasymmetric-energy e + e − storage rings. The B A B AR de-tector provides neutral and charged particle reconstruc-tion and charged particle identification, and is describedin detail elsewhere [7]. We also use a detailed MonteCarlo simulation (MC) [8] to estimate signal efficiencyand signal and background distributions.We tag B mesons decaying as B → D ( ∗ ) ℓν ℓ through thefull hadronic reconstruction of D ± and D mesons; D mesons are reconstructed through K − π + , K − π + π + π − , K − π + π and K S π + π − decays, and D + mesons through K − π + π + and K S π + decays; K S candidates are recon-structed as K S → π + π − ; and neutral pions are recon-structed as π → γγ with the requirement 115 ≤ m γγ ≤
150 MeV /c . Masses of D candidates are required to bewithin 2 . σ of their nominal value, where the mass resolu-tion σ ranges between 5 . . /c , depending onthe decay channel; we also use a “sideband” sample of D candidates with reconstructed mass in a range (typically4 σ to 7 σ ) off the appropriate nominal mass. We requirecharged daughters of the D candidate to originate froma common vertex. We reconstruct D ∗ + mesons as D π + and D + π and D ∗ mesons as D π and D γ . The massdifference between the D ∗ candidate and its D daughtermust be within 3 . σ of its nominal value; the resolution σ of this difference ranges between 0 . . /c ,depending on the decay mode.Candidate D ( ∗ ) mesons are paired with tracks identi- fied as leptons with absolute momentum | ~p ℓ | ≥ . /c [9]. If a D candidate (its daughter kaon) is charged, itis required have charge opposite to (same as) that of thecorresponding lepton. The Y ≡ D ∗ ℓ system is requiredto have invariant mass m Y ≥ /c and originatefrom a common vertex. Photons consistent with origi-nating from bremsstrahlung from this lepton or the de-cay D ( ∗ ) → Dγ ( γ ) are added to the Y system. Assumingthat the B → Y ν decay hypothesis is correct, the angle θ BY between the directions of the (measured) Y and itsparent B is described bycos θ BY = 2 E B E Y − m B − m Y | ~p B || ~p Y | , (1)where E B , m B and | ~p B | ( E Y , m Y and | ~p Y | ) are the en-ergy, mass and absolute momentum of the B meson ( Y system); for the B meson, these are inferred from ini-tial beam energies. If the B → Y ν hypothesis is cor-rect, we have | cos θ BY | ≤ θ BY is strongly correlated with our discriminatingvariable cos φ B , we impose the loose requirement that | cos θ BY | ≤ BB events, we rejectevents for which the ratio of the second and zeroth Fox-Wolfram moments [10] is greater than 0 .
5. We also rejectevents containing lepton pairs kinematically and geomet-rically consistent with having originated from the decayof a
J/ψ meson. We reject D ( ∗ ) ℓ candidates for whichthe event contains any K S → π + π − candidates not over-lapping this D ( ∗ ) ℓ system. We require exactly one addi-tional lepton with absolute momentum | ~p ℓ | ≥ . /c in the event. If the two leptons are an e + e − pair, werequire them not to be consistent with originating from γ → e + e − conversion. This second lepton is paired withremaining tracks (assumed to be pions), neutral pionsand photons in the event to form B → P ℓν ℓ candidates,where P is one of the mesons π ± , π , η or η ′ . For B → π ± ℓν ℓ candidates, the lepton and pion are requiredto have opposite charge. B → π ℓν ℓ candidates are sub-ject to the additional requirement | ~p π | + | ~p ℓ | ≥ . /c ,where | ~p π | is the absolute momentum of this π can-didate. For B → ηℓν ℓ candidates, η mesons are recon-structed through decays to γγ , π + π − π and π π π , withinvariant mass requirements 500 ≤ m γγ ≤ ≤ m πππ ≤
560 MeV /c . Charged pions from η → π + π − π decays are required to come from a common vertex; the π candidates are required to have absolute laboratoryframe momentum greater than 280 MeV /c (180 MeV /c )when coming from π + π − π ( π π π ) candidates. The η ′ meson in B → η ′ ℓν ℓ decays is reconstructed throughits decay η ′ → ηπ + π − with the η candidate selected asabove; the additional pions are required to originate froma common vertex, and the ηπ + π − system is required tohave invariant mass between 920 and 970 MeV /c . For B ± decays ( P = π , η , η ′ ), the leptons in an event arerequired to have opposite charge.We define the X as a charmless meson π ± , π , η or η ′ and corresponding lepton (including photons consis-tent with having originated from bremsstrahlung fromit); θ BX is defined analogously to θ BY ; we require | cos θ BX | ≤
5. For each D ( ∗ ) ℓ - P ℓ candidate, we re-quire that there be no additional tracks in the event and,for hypothesized B B ( B + B − ) events, at most 140 MeV(70 MeV) of neutral energy (i.e., photon candidates) notassociated with the D ( ∗ ) ℓ or P ℓ candidates. In the casethat more than one D ( ∗ ) ℓ - P ℓ pair fulfills all requirementsfor a given event and P mode, the candidate is chosen bysmallest | cos θ BY | , then by largest absolute P momen-tum. Signal events containing accepted D ( ∗ ) ℓ - P ℓ candi-dates have, on average, between 1 .
15 and 1 .
39 of them,depending on P .Signal yield is extracted independently for each P ;while we implicitly allow an event to be reconstructed inmultiple P modes, we find the induced pairwise statisticalcorrelations between our measured branching fractions tobe negligible. The signal yield is extracted through thequantity cos φ B , where φ B is the angle between the di-rection of either B and the plane containing the X and Y momenta:cos φ B = cos θ BY + 2 cos γ cos θ BY cos θ BX + cos θ BX sin γ ,(2)where γ is the angle between the X and Y momenta. Forcorrectly reconstructed signal events, we have cos φ B ≤ B → P ℓν ℓ decay, q is defined as the squaredinvariant mass of the lepton-neutrino system, and is cal-culated in the approximation that the B is at rest, i.e., q = ( m B − E P ) − | ~p P | , where E P and ~p P are, respec-tively, the energy and momentum of the P meson. Thedata are divided into three bins: q <
8, 8 ≤ q < q ≥
16 GeV /c , in each of which the yield is ex-tracted separately, except in the B + → η ′ ℓ + ν ℓ mode, inwhich, due to a lower reconstruction efficiency, the yieldis measured in a q <
16 GeV /c bin and over the full q range. The data is described as a sum of three contri-butions, dN/d cos φ B = N sig P sig + N bg P bg + N cmb P cmb ,where these N i and P i are the yield and probability den-sity functions (PDF) of: signal (“sig”), background withcorrectly reconstructed D , ± mesons (“bg”) and back-grounds with combinatoric D , ± candidates (“cmb”). B φ cos e v e n t s / . B φ cos e v e n t s / . (a) B φ cos e v e n t s / . B φ cos e v e n t s / . (b) B φ cos e v e n t s / . B φ cos e v e n t s / . (c) B φ cos e v e n t s / B φ cos e v e n t s / (d) FIG. 1: Distributions of cos φ B for B → π − ℓ + ν ℓ (a), B + → π ℓ + ν ℓ (b), B + → ηℓ + ν ℓ (c) and B + → η ′ ℓ + ν ℓ (d) candidates;filled and hollow circles represent D mass peak and sidebanddata, respectively. The curves are stacked fit results for “cmb”(dotted), “bg” (dashed) and “sig” (solid) PDFs, as defined inthe text. The fits are performed in bins of q but are hereshown in the full q range. The signal PDF, P sig , is modeled as a threshold func-tion (constant between zero and unity, vanishing else-where) with finite resolution and an exponential tail (fourparameters). The correct D background PDF, P bg , ismodeled as an exponential with a nonnegative constantterm (two parameters); the combinatoric D background, P cmb , is modeled by a second order polynomial (two pa-rameters). These eight PDF shape parameters and the P i are determined via simultaneous unbinned maximumlikelihood fit (see Figure 1) of dN/d cos φ B to the data, P sig to MC signal events, P bg to MC background events(with correctly identified D , ± mesons) and P cmb to thesideband sample. The combinatoric yield N cmb is furtherconstrained, up to statistical accuracy, by the number ofevents in the sideband sample. Total signal yields arefound to be 150 ±
22, 134 ±
20, 55 ±
15 and 0 . ± . π ± ℓν ℓ , π ℓν ℓ , ηℓν ℓ and η ′ ℓν ℓ respectively.The B → D ( ∗ ) ℓν ℓ reconstruction efficiency is deter-mined via an analogous cos φ B study on “double tag”events, i.e., events reconstructed as BB with both B mesons decaying as B → D ( ∗ ) ℓν ℓ . The B → P ℓν ℓ re-construction efficiency for each q bin is determined fromthe MC signal sample, as are bin-to-bin migrations due tothe finite q resolution, which are small ( < B , are found, in units of 10 − ,to be 1 .
4, 1 .
8, 1 . .
22 for B → π ± ℓν ℓ , B → π ℓν ℓ , B → ηℓν ℓ and B → η ′ ℓν ℓ respectively.Systematic uncertainties associated with physics mod-eling are evaluated by determining the change in the mea-sured branching fraction after varying independently inMC within current knowledge: B → { ρ, ω } ℓν ℓ branchingfractions, B → π ± , ℓν ℓ branching fractions, B → η ( ′ ) ℓν ℓ branching fractions, the total B charmless semileptonicdecay branching fraction, the B charmless semileptonicdecay spectrum [11], B → P ℓν ℓ form factors (comparingthe model by Ball and Zwicky [12] to that of Scora andIsgur [13]) and several B → Dℓν ℓ branching fractions;the largest is found to have an effect four times smallerthan the statistical uncertainty. We also apply uncer-tainties derived from those on η and η ′ decay branchingfractions.We estimate the systematic uncertainty associatedwith the accuracy of BB background simulation by com-paring the cos φ B distributions in signal-depleted dataand MC samples. From study of 37 fb − of e + e − colli-sions 40 MeV below the Υ(4 S ) resonance, we determinethat there is no contribution from non- BB events to thesignal; the precision to which this can be determined isalso taken as a systemic uncertainty.Final state radiation in B → π − ℓ + ν ℓ decays is deter-mined, from simulation, to cause q bin migrations nogreater than 1 . .
59% (1 . B B ( B + B − ) decays associated with the as-sumption that double tag events can be used to estimatethe single tag efficiency reliably.As double tag events are used to determine the D ( ∗ ) ℓν ℓ reconstruction efficiency, detector simulation uncertain-ties are applied only to particles on the P ℓ side: 0 . π , 2% (3%) per electron (muon).There is a 1 .
1% systematic uncertainty from counting BB pairs [14], and a 1 .
4% systematic uncertainty fromthe Υ(4 S ) → B B fraction [15]. Measured branchingfractions and associated uncertainties are given in TableI. Quoted statistical uncertainties are due to the finitesize of data and MC samples. We combine B → π − ℓ + ν ℓ and B + → π ℓ + ν ℓ branching fractions using the isospinrelation Γ( B → π − ℓ + ν ℓ ) = 2Γ( B + → π ℓ + ν ℓ ) and thelifetime ratio τ B + /τ B = 1 . ± .
009 [15]. The signifi-cance of the B + → ηℓ + ν ℓ signal is 3 . σ .A Bayesian 90% confidence limit B ( B + → η ′ ℓ + ν ℓ ) < . × − is determined, assuming a flat prior in thephysical (nonnegative branching fraction) region, via theintegral of the likelihood function from the signal extrac-tion, smeared by a Gaussian resolution function withvarying width representing all other sources of uncer-tainty. We also determine the partial branching fraction∆ B ( B + → η ′ ℓ + ν ℓ ) < . × − for q <
16 GeV /c and the ratio B ( B + → η ′ ℓ + ν ℓ ) / B ( B + → ηℓ + ν ℓ ) < . η - η ′ system[6]. These are in disagreement with a recently publishedresult [16].Extraction of | V ub | from the measured B → πℓν ℓ branching fractions ∆ B proceeds through the relation | V ub | = p ∆ B / ( τ B ∆ ζ ), with τ B = 1 . ± .
009 ps − the B meson lifetime [15] and ∆ ζ the calculated reduced(i.e., appropriately normalized) decay rate over the cor-responding q range, which depends on the decay formfactor f π + . Several form factor calculations are available,including one using light-cone sum rules [12] and variouslattice QCD methods [17, 18, 19]. Results are given inTable II. The branching fractions B ( B → η ( ′ ) ℓν ℓ ) willprovide additional means of determining | V ub | as accu-rate calculations of f η ( ′ ) + become available.In conclusion, we have measured the branching frac-tions for B → P ℓν ℓ , where P are charmless pseudoscalarmesons, as a function of the squared momentum transfer q . We report the total branching fractions, the thirdwith a significance of 3 . σ : B ( B → π − ℓ + ν ℓ ) = (1 . ± . ± . × − , (3) B ( B + → π ℓ + ν ℓ ) = (0 . ± . ± . × − , (4) B ( B + → ηℓ + ν ℓ ) = (0 . ± . ± . × − , (5)with the first uncertainty statistical and the second sys-tematic, and, to 90% confidence level, B ( B + → η ′ ℓ + ν ℓ ) < . × − . (6)We combine the pionic branching fractions to obtain B ( B → π − ℓ + ν ℓ ) = (1 . ± . ± . × − , amongthe most precise measurements of this branching fractionavailable. We use the partial branching fractions to ex-tract | V ub | , using a variety of form factor calculations,and obtain values ranging from 3 . × − to 4 . × − .The pionic branching fraction measurements represent aroughly 30% improvement over a previous B A B AR mea-surement in this channel [3], and is statistically indepen-dent of similar measurements in other channels [3, 4].We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, andfor the substantial dedicated effort from the comput-ing organizations that support B A B AR . The collaborat-ing institutions wish to thank SLAC for its support andkind hospitality. This work is supported by DOE andNSF (USA), NSERC (Canada), CEA and CNRS-IN2P3(France), BMBF and DFG (Germany), INFN (Italy),FOM (The Netherlands), NFR (Norway), MES (Russia),MEC (Spain), and STFC (United Kingdom). Individualshave received support from the Marie Curie EIF (Euro-pean Union) and the A. P. Sloan Foundation. ∗ Deceased
TABLE I: Partial and total branching fractions, in units of 10 − , for each decay channel; the first uncertainty given is statistical,the second is systematic. Ranges for q are given in GeV /c . In the bottom row is the result from combining B → π − ℓ + ν and B + → π ℓ + ν branching fractions. q < ≤ q < q ≥ q <
16 total B → π − ℓ + ν . ± . ± .
03 0 . ± . ± .
02 0 . ± . ± .
03 0 . ± . ± .
05 1 . ± . ± . B + → π ℓ + ν . ± . ± .
02 0 . ± . ± .
03 0 . ± . ± .
03 0 . ± . ± .
05 0 . ± . ± . B + → ηℓ + ν . ± . ± .
01 0 . ± . ± .
01 0 . ± . +0 . − . . ± . ± .
02 0 . ± . ± . B + → η ′ ℓ + ν - - - − . ± . +0 . − . . ± . +0 . − . B → π − ℓ + ν (combined) 0 . ± . ± .
03 0 . ± . ± .
03 0 . ± . ± .
04 1 . ± . +0 . − . . ± . ± . | V ub | derived using branching fractionsmeasured in this Letter and various form factor calculations.Range for q is stated in GeV /c , reduced decay rate in ps − .The given uncertainties on | V ub | are, respectively, statistical,systematic and due to uncertainties in form factor calculation. q ∆ ζ | V ub | (10 − )Ball & Zwicky [12] <
16 5 . ± .
43 3 . ± . ± . +0 . − . Gulez et al. [17] >
16 2 . ± .
57 3 . ± . ± . +0 . − . Okamoto et al. [18] >
16 1 . ± .
50 4 . ± . ± . +0 . − . Abada et al. [19] >
16 1 . ± .
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