Measurements of B( B ¯ 0 → Λ + c p ¯ ) and B( B − → Λ + c p ¯ π − ) and Studies of Λ + c π − Resonances
aa r X i v : . [ h e p - e x ] J a n B A B AR -PUB-08/016SLAC-PUB-13341arXiv:0807.4974 Measurements of B ( B → Λ + c p ) and B ( B − → Λ + c pπ − ) and Studies of Λ + c π − Resonances
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
We present an investigation of the decays B → Λ + c p and B − → Λ + c pπ − based on 383 × Υ (4 S ) → BB decays recorded with the B A B AR detector. We measure the branching fractions ofthese decays; their ratio is B ( B − → Λ + c pπ − ) / B ( B → Λ + c p ) = 15 . ± . ± .
3. The B − → Λ + c pπ − process exhibits an enhancement at the Λ + c p threshold and is a laboratory for searches for excitedcharm baryon states. We observe the resonant decays B − → Σ c (2455) p and B − → Σ c (2800) p butsee no evidence for B − → Σ c (2520) p . This is the first observation of the decay B − → Σ c (2800) p ;however, the mass of the observed excited Σ c state is (2846 ± ±
10) MeV /c , which is somewhatinconsistent with previous measurements. Finally, we examine the angular distribution of the B − → Σ c (2455) p decays and measure the spin of the Σ c (2455) baryon to be 1 /
2, as predicted by thequark model.
PACS numbers: 13.25.Hw, 13.60.Rj, 14.20.Lq
INTRODUCTION
Baryonic decays of B mesons, which contain a heavybottom quark and a light up or down quark, provide alaboratory for a range of particle physics investigations:trends in decay rates and baryon production mechanisms;searches for exotic states such as pentaquarks and glue-balls [1, 2]; searches for excited baryon resonances; ex-amination of the angular distributions of B -meson de-cay products to determine baryon spins; and measure-ments of radiative baryonic B decays that could be sen-sitive to new physics through flavor-changing neutral cur-rents [3, 4]. The latter measurements rely on improvingour theoretical understanding of baryonic B decays ingeneral [5, 6].The inclusive branching fraction for baryonic B decaysis (6 . ± . B decaymodes have been observed [8]. If we order the measureddecays by Q -value: Q = m B − X f m f , (1)where m f is the mass of each daughter in the final stateof the B decay, we find that for each type of baryonic B decay, the branching fractions decrease as the Q -valueincreases. The smallest measured branching fraction is ofthe order 10 − , which also corresponds to our experimen-tal sensitivity for measuring these branching fractions.Potentially interesting B -meson decays such as B → pp , B → ΛΛ , and B → Λ + c Λ − c have not yet been seen.Theoretical approaches to calculating baryonic B de-cays include pole models [9, 10], diquark models [11],and QCD sum rules [12, 13]. Recently, theoretical cal-culations have focused on pole models, where the B de- ∗ Deceased † Now at Temple University, Philadelphia, PA 19122, USA ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Universit`a di Perugia, Dipartimento di Fisica, Perugia,Italy ¶ Also with Universit`a di Roma La Sapienza, I-00185 Roma, Italy ∗∗ Now at University of South Alabama, Mobile, AL 36688, USA †† Also with Universit`a di Sassari, Sassari, Italy cay proceeds through an intermediate b -flavored baryonstate, which then decays weakly into one of the final statebaryons [14, 15]. However, it is not clear that the polemodel is reliable for baryon poles, and the predictionsgiven in the literature vary significantly. Perhaps themost satisfying theoretical interpretation of baryonic B decay rates is the qualitative one proposed by Hou andSoni in 2001 [16], who argue that B decays are favored ifthe baryon and antibaryon in the final-state configurationare close together in phase space. A consequence is thatdecay rates to two-body baryon-antibaryon final statesare suppressed relative to rates of three-body final statescontaining the same baryon-antibaryon system plus anadditional meson. In the three-body case, the baryon andantibaryon can be in the favored configuration—close to-gether in phase space—rather than back-to-back as inthe two-body case.In this paper, we investigate the decays B → Λ + c p and B − → Λ + c pπ − [17]. We investigate baryon production in B decays by comparing the two-body ( B → Λ + c p ) andthree-body ( B − → Λ + c pπ − ) decay rates directly. Thedynamics of the baryon-antibaryon ( Λ + c p ) system in thethree-body decay provide insight into baryon productionmechanisms. Additionally, the B − → Λ + c pπ − system is alaboratory for studying excited baryon states and is usedto measure the spin of the Σ c (2455) . This is the firstmeasurement of the spin of this state. B A B AR DETECTOR AND DATA SAMPLE
The measurements presented in this paper are based on383 × Υ (4 S ) → BB decays recorded with the B A B AR detector [18] at the PEP-II e + e − asymmetric-energy B Factory at the Stanford Linear Accelerator Center. Atthe interaction point, 9- GeV electrons collide with 3.1-GeV positrons at the Υ (4 S ) resonance with a center-of-mass energy of 10.58 GeV /c .Charged particle trajectories are measured by a five-layer silicon vertex tracker (SVT) and a 40-layer driftchamber (DCH) immersed in a 1 . E/ d x ) measurements in the SVT and DCHalong with Cherenkov radiation detection by an inter-nally reflecting ring-imaging detector (DRC).Exclusive B -meson decays are simulated with theMonte Carlo (MC) event generator EvtGen [19]. Back-ground continuum MC samples ( e + e − → qq , where q = u, d, s, c ) are simulated using Jetset7.4 [20] tomodel generic hadronization processes. Background MCsamples of e + e − → B + B − and B B are based on simu-lations of many exclusive B decays (also using EvtGen ).The large samples of simulated events are generated andpropagated through a detailed detector simulation usingthe
GEANT4 simulation package [21].
CANDIDATE SELECTION
We select candidates that are kinematically consistentwith B → Λ + c p and B − → Λ + c pπ − . For the decay mode B → Λ + c p , we reconstruct Λ + c candidates in the pK − π + , pK S , pK S π + π − , and Λπ + decay modes, requiring the in-variant mass of each Λ + c candidate to be within 10 MeV /c of the world average value [8]. For B − → Λ + c pπ − , we alsoreconstruct Λ + c candidates in the Λπ + π − π + decay mode,and require all of the Λ + c candidates to have an invariantmass within 12 MeV /c of the world average value.The p , K , and π candidates must be well-reconstructedin the DCH and are identified with likelihood-based par-ticle selectors using information from the SVT, DCH, andDRC.The K S candidates are reconstructed from two oppo-sitely charged pion candidates that come from a commonvertex; Λ candidates are formed by combining a protoncandidate with an oppositely charged pion candidate thatcomes from a common vertex. The invariant mass ofeach K S and Λ candidate must be within 10 MeV /c ofthe world average value [8] and the flight significance (de-fined as the flight distance from the Λ + c vertex in the x − y plane divided by the measurement uncertainty) must begreater than 2. The mass of each K S and Λ candidate isthen constrained to the world average value [8].A mass constraint is applied to all of the Λ + c candi-dates, and all Λ + c daughter tracks must come from a com-mon vertex. The Λ + c candidates are then combined withan antiproton to form a B → Λ + c p candidate, or withan antiproton and a pion to form a B − → Λ + c pπ − candi-date. The daughters of each B candidate must come froma common vertex, and the candidate with the largest χ probability in each event is selected.Additional background suppression is provided by in-formation about the topology of the events. A Fisherdiscriminant [22] is constructed based on the absolutevalue of the cosine of the angle of the B candidate mo-mentum vector with respect to the beam axis in the e + e − center-of-mass (CM) frame, the absolute value of the co-sine of the angle between the B candidate thrust axis [23]and the thrust axis of the rest of the event in the e + e − CM frame, and the moments L and L . The quantity L j is defined as P i p i | cos θ i | j , where θ i is the angle withrespect to the B candidate thrust axis of the i th chargedparticle or neutral cluster in the rest of the event and p i is its momentum. The optimal maximum value of theFisher discriminant is chosen separately for each Λ + c and B decay mode.Kinematic properties of B -meson pair production atthe Υ (4 S ) provide further background discrimination.We define a pair of observables, m m and m r , that areuncorrelated and exploit these constraints: m m = r(cid:16) q e + e − − ˆ q Λ + c p ( π − ) (cid:17) and m r = r(cid:16) q Λ + c p ( π − ) (cid:17) − m B . (2)The variable m m is based on the apparent recoil mass ofthe unreconstructed B meson in the event, where q e + e − is the four-momentum of the e + e − system and ˆ q Λ + c p ( π − ) is the four-momentum of the reconstructed B candidateafter applying a mass constraint. The variable m r is thedifference between the unconstrained mass of the recon-structed B candidate and m B , the world average valueof the mass of the B meson [8]. Signal events peak at m B in m m and 0 in m r . This set of variables was firstused in [24] and is chosen as an uncorrelated alternativeto ∆ E = E ∗ B − √ s and the energy-substituted mass m ES = q s − p ∗ B (where s = q e + e − and the asteriskdenotes the e + e − rest frame), which exhibit a ∼ B − → Λ + c pπ − .The event selection criteria are optimized based onstudies of sideband data (in the region 0 . < m r < .
20 GeV /c ) and simulated signal MC samples. The datain a signal region (approximately ± σ wide in m m and m r ) were blinded until the selection criteria were de-termined and the signal extraction procedure was spec-ified and validated. B candidates that satisfy m m > .
121 GeV /c and | m r | < .
10 GeV /c are used in themaximum likelihood fit. BACKGROUNDS
The primary source of background for B → Λ + c p can-didates is continuum e + e − → qq events. Backgroundsdue to decays such as B − → Λ + c pπ − , B → Λ + c pπ , and B − → Σ c p, Σ c → Λ + c π − are rejected by the criterion | m r | < .
10 GeV /c .Approximately equal amounts of continuum e + e − → qq and e + e − → BB events make up the backgroundfor B − → Λ + c pπ − events. Again, the requirement | m r | < .
10 GeV /c rejects most of the contributions fromsuch decays as B → Λ + c pπ + π − and B − → Λ + c pπ − π .Approximately 1% of the background in the fit regionis due to these four-body events, but they do not peakin m m and m r . A small peaking background is presentfrom B → Σ + c p, Σ + c → Λ + c π events, especially whenthe π has low momentum. Based on a branching frac-tion measurement of the isospin partner decay B ( B − → Σ c (2455) p ) = (3 . ± . ± . ± . × − [25], wherethe uncertainties are statistical, systematic, and the un-certainty due to B ( Λ + c → pK − π + ), respectively, we ex-pect 11 . ± . B − → Λ + c pπ − , Λ + c → pK − π + . A correction isapplied and a systematic uncertainty is assigned to com-pensate for these events. DETECTION EFFICIENCY
The detection efficiencies for B → Λ + c p and B − → Λ + c pπ − signal events are determined from signal MC sam-ples with 175 ,
000 to over 1 , ,
000 events in each sam-ple, depending on the Λ + c decay mode. To account forinaccuracies in the simulation of the detector, each MCevent is assigned a weight based on each daughter par-ticle’s momentum and angle. These weights are deter-mined from studies comparing large pure samples of pro-tons, kaons, and pions in MC samples and data. Smallcorrections (0 . − . K S and Λ ver-tices. These corrections depend on the K S and Λ daugh-ter trajectories’ transverse momentum and angle, and thedistance between the beam spot and the displaced vertex.The detection efficiency ( ε l ) for B → Λ + c p signalevents in each Λ + c decay mode ( l ) is determined fromthe number of signal events extracted from an extendedunbinned maximum likelihood fit to signal MC events.These events pass the same selection criteria as appliedto data. The fit is performed in two dimensions, m m and m r . The probability distribution function (PDF) forthe background consists of a threshold function [26] in m m multiplied by a first-order polynomial in m r ; this isthe same as the background PDF used in the fit to the B → Λ + c p data. The signal PDF consists of a Gaussianin m m multiplied by a modified asymmetric Gaussianwith a tail parameter in m r . The detection efficiencies ineach Λ + c decay mode are summarized in Table I.The detection efficiency for B − → Λ + c pπ − signalevents in each Λ + c decay mode varies considerably acrossthe Dalitz plane of the three-body decay. For reference,we quote the average efficiencies in Table I, but we ap-ply a more sophisticated treatment to these events. Weparameterize the physical Dalitz region using the vari-ables cos θ h and the Λ + c π − invariant mass, m Λ c π . Thehelicity angle θ h is defined as the angle between the π − and the p in the B − rest frame. The quantity cos θ h canbe expressed in terms of Lorentz-invariant products offour-vectors. We divide the kinematic region into rea-sonably sized bins that are uniform in cos θ h (0 . m Λ c π (60 −
200 MeV /c wide).This choice of variables is more conducive to rectangu- TABLE I: Detection efficiency for B → Λ + c p signal events,determined from signal Monte Carlo samples and separatedby Λ + c decay mode. The numbers correspond to the efficiencyfor B → Λ + c p ( B − → Λ + c pπ − ), Λ + c → f l , where f l is a givenfinal state. The efficiencies quoted for the B − → Λ + c pπ − decays are averaged across phase space.Efficiency for Λ + c → f l f l B → Λ + c p B − → Λ + c pπ − pK − π + .
9% 15 . pK S .
6% 14 . pK S π + π − .
6% 5 . Λπ + .
2% 11 . Λπ + π − π + – 4 . lar bins than the traditional set of Dalitz variables. The m Λ c π bins are narrower near the kinematic limits wherethe efficiency changes more rapidly and are centered onexpected resonances. For B − → Λ + c pπ − , Λ + c → pK − π + near cos θ h = 0, the efficiency varies from approximately13% at low m Λ c π , to 16% in the central m Λ c π region, to8% at high m Λ c π . The efficiency is fairly uniform withrespect to cos θ h , except at cos θ h ∼ m Λ c π ,where it drops to 7 . Λ + c decay modes ex-hibit similar variations in efficiency. SIGNAL EXTRACTION
To extract the number of signal events in data, a two-dimensional ( m m vs. m r ) extended unbinned maximumlikelihood fit is performed simultaneously across Λ + c de-cay modes. B → Λ + c p candidates and B − → Λ + c pπ − candidates are fit separately.The background PDF for each fit is a threshold func-tion [26] in m m multiplied by a first-order polynomial in m r . The shape parameter ( ~s bkg ) of the threshold func-tion is free but is common to all of the Λ + c decay modes.The slope a of the first-order polynomial is allowed tovary independently for each Λ + c decay mode.The signal PDF is a single Gaussian distribution in m m multiplied by a single Gaussian distribution in m r for B → Λ + c p and multiplied by a double Gaussian dis-tribution in m r for B − → Λ + c pπ − . A single Gaussian issufficient to describe the signal PDF for B → Λ + c p be-cause of the small number of expected signal events. Allof the shape parameters of the signal PDF ( ~s sig ) are freebut are shared among the Λ + c decay modes. Separate sig-nal ( N sig,l ) and background ( N bkg,l ) yields are extractedfor each Λ + c decay mode l .The total likelihood is the product of the likelihoods TABLE II: Signal yields from simultaneous fits (across Λ + c decay modes) to B → Λ + c p and B − → Λ + c pπ − candidates. N sig Mode B → Λ + c p B − → Λ + c pπ − pK − π + ±
11 991 ± pK S ± ± pK S π + π − ± ± Λπ + ± ± Λπ + π − π + – 88 ± for each Λ + c decay mode: L tot = Y l L l ( ~y l ; N sig,l , N bkg,l , ~s sig , ~s bkg , a l ) . (3)The symbol ~y represents the variables used in the 2-D fit, { m m , m r } .The full simultaneous fit is validated using independentsamples of signal MC events to simulate signal events andtoy MC samples (generated from the background MCsample distribution) to represent background events inthe fit region. For both B → Λ + c p and B − → Λ + c pπ − ,we perform fits to 100 combined MC samples and findthat the fit is robust and the results are unbiased.The results of the 2-D fits to data are shown in projec-tions of m m and m r for each Λ + c decay mode. Figure 1shows the result of the fit to B → Λ + c p candidates andFig. 2 shows the result of the fit to B − → Λ + c pπ − candi-dates. The signal yields from the fits are summarized inTable II. BRANCHING FRACTION MEASUREMENTS
For the three-body mode B − → Λ + c pπ − , the efficiencyvariation across the Dalitz plane requires a correctionfor each signal event in order to extract the branchingfraction for this mode. We use the s P lot method [27] tocalculate a weight for each event e based on the 2-D fitto the variables ~y . We have N s = 2 species (signal andbackground) for each Λ + c decay mode and define f j,k asthe signal ( j, k = 1) or background ( j, k = 2) PDF. The s P lot weights are calculated as s P n ( ~y e ) = P N s j =1 V nj f j ( ~y e ) P N s k =1 N k f k ( ~y e ) , (4)where s P n ( ~y e ) is the s P lot weight for species n , V isthe covariance matrix for signal and background yields, f j,k ( ~y e ) is the value of PDF f j,k for event e , and ~y e is the m m and m r value for event e . The elements of the inverse of the covariance matrix V are calculated as follows: V − nj = ∂ ( − ln L ) ∂N n ∂N j = N X e =1 f n ( ~y e ) f j ( ~y e ) (cid:16)P N s k =1 N k f k ( ~y e ) (cid:17) , (5)where the sum is over the N candidates. Note that inthe calculation of the covariance matrix, the data is refitto the same simultaneous PDF described above, exceptthat all fit parameters other than the yields are fixed tothe values from the original fit.We use these s P lot weights to generate a signal orbackground distribution for any quantity that is not cor-related with m m or m r . The s P lot formalism is easilyextended to incorporate an efficiency correction for eachcandidate. Each candidate is assigned a weight of 1 /ε ,where the efficiency ε for an event is determined by itslocation in the cos θ h vs. m Λ c π plane.The branching fraction for B → Λ + c p for Λ + c decaymode l is calculated as follows: B ( B → Λ + c p ) l = N sig,l N BB × ε l × R l × B ( Λ + c → pK − π + ) , (6)where N BB is the number of BB events in the data sam-ple and R l is the ratio of Λ + c branching fraction for decaymode l to B ( Λ + c → pK − π + ), taking care to include the K S → π + π − and Λ → pπ − branching fractions whereapplicable.In order to determine the branching fraction for B − → Λ + c pπ − , we take the product of the s P lot weight and effi-ciency weight for each candidate and sum over all of thecandidates in the fit region. We simplify the notation byusing s W i to denote the value of the signal s P lot weightfor event i and include a 1% correction for the peakingbackground due to B → Σ + c p, Σ + c → Λ + c π : B ( B − → Λ + c pπ − ) l = 0 . × (cid:18)P i s W i ε i (cid:19) l N BB × R l × B ( Λ + c → pK − π + ) . (7)The contribution from the peaking background is esti-mated using the Λ + c → pK − π + decay mode. Since theoverall branching fraction for the peaking backgroundcontribution is the same regardless of Λ + c decay mode,it is applied as a proportional correction. The measure-ments for B ( B → Λ + c p ) and B ( B − → Λ + c pπ − ) for each Λ + c decay mode are summarized in Table III.The BLUE (Best Linear Unbiased Estimate) techniqueis used as described in Ref. [28] to combine the corre-lated branching fraction measurements for different Λ + c decay modes. The purpose of the method is to obtainan estimate ˆ x that is a linear combination of t individual ) (GeV/c m m ) (GeV/c m m (g) ) (GeV/c r m-0.10 -0.05 0.00 0.05 0.10 ) (GeV/c r m-0.10 -0.05 0.00 0.05 0.10 ) E v e n t s / ( . G e V / c ) E v e n t s / ( . G e V / c FIG. 1: Projections of m m (left) and m r (right) in data for B → Λ + c p candidates, separated by Λ + c decay mode: ( a, b ) are Λ + c → pK − π + , ( c, d ) are Λ + c → pK S , ( e, f ) are Λ + c → pK S π + π − , and ( g, h ) are Λ + c → Λπ + . The m m projections ( a, c, e, g ) arefor | m r | < .
030 GeV /c and the m r projections ( b, d, f, h ) are for m m > .
27 GeV /c . The solid curves correspond to the PDFfrom the simultaneous 2-D fit to candidates for the four Λ + c decay modes, and the dashed curves represent the backgroundcomponent of the PDF. measurements ( x l ), is unbiased, and has the minimumpossible variance ˆ σ . The estimate ˆ x is defined byˆ x = X l α l x l . (8)The condition P l α l = 1 ensures that the method is un-biased. Each coefficient α l is a constant weight for mea-surement x l and is not necessarily positive. The set ofcoefficients α (a vector with t elements) is determined by α = E − UU T E − U , (9)where U is a t -component vector whose elements are all1 ( U T is its transpose) and E is the ( t × t ) error matrix.The diagonal elements of E are the individual variances, σ l . The off-diagonal elements are the covariances be-tween measurements ( rσ l σ l ′ , where r is the correlation between measurements l and l ′ ). The error matrices addlinearly, so we define E = E s tat + E s yst . E s tat includesthe uncertainties in the fit yields and the correlationsbetween yields from the simultaneous fit result. E s yst in-cludes the systematic uncertainties that are described inthe next section. Overall multiplicative constants ( N BB and B ( Λ + c → pK − π + )) that are common to all the mea-surements and their uncertainties are not included in theBLUE method.The solutions for α are B → Λ + c p : α T = (cid:16) .
757 0 .
128 0 .
019 0 . (cid:17) , (10) ) (GeV/c m m ) (GeV/c m m (i) ) (GeV/c r m-0.10 -0.05 0.00 0.05 0.10 ) (GeV/c r m-0.10 -0.05 0.00 0.05 0.10 ) E v e n t s / ( . G e V / c ) E v e n t s / ( . G e V / c FIG. 2: Projections of m m (left) and m r (right) in data for B − → Λ + c pπ − candidates, separated by Λ + c decay mode: ( a, b ) are Λ + c → pK − π + , ( c, d ) are Λ + c → pK S , ( e, f ) are Λ + c → pK S π + π − , ( g, h ) are Λ + c → Λπ + , and ( i, j ) are Λ + c → Λπ + π − π + . The m m projections ( a, c, e, g, i ) are for | m r | < .
030 GeV /c and the m r projections ( b, d, f, h, j ) are for m m > .
27 GeV /c . Thesolid curves correspond to the PDF from the simultaneous 2-D fit to candidates for the five Λ + c decay modes, and the dashedcurves represent the background component of the PDF. and B − → Λ + c pπ − : α T = (cid:16) .
913 0 . − .
003 0 .
029 0 . (cid:17) , (11)where α T is the transpose of α . The order of the co-efficients corresponds to the order of Λ + c decay modespresented in Table III.We calculate the best estimate ˆ x according to Eqn. 8and divide this quantity by N BB and B ( Λ + c → pK − π + ). We calculate the variance of ˆ x ˆ σ = α T E α . (12)Since the error matrices add linearly, we quote separatestatistical and systematic uncertainties. The statisti-cal and systematic uncertainties in N BB are added inquadrature with the statistical and systematic ˆ σ results,respectively. The combined branching fraction measure-0ments are thus B ( B → Λ + c p ) =(1 . ± . ± . ± . × − , B ( B − → Λ + c pπ − ) =(3 . ± . ± . ± . × − , (13)where the uncertainties are statistical, systematic, andthe uncertainty in B ( Λ + c → pK − π + ), respectively.We use the same procedure to determine the branchingratio B ( B − → Λ + c pπ − ) / B ( B → Λ + c p ): B ( B − → Λ + c pπ − ) B ( B → Λ + c p ) = 15 . ± . ± . . (14)In the branching ratio, many of the systematic uncer-tainties, including the dominant B ( Λ + c → pK − π + ) un-certainty, cancel. SYSTEMATIC UNCERTAINTIES IN THEBRANCHING FRACTIONS
The uncertainties in the B ( B → Λ + c p ) and B ( B − → Λ + c pπ − ) measurements are dominated by the uncertaintyin the Λ + c → pK − π + branching fraction, and then bythe uncertainties in the Λ + c branching ratios (comparedto Λ + c → pK − π + ) [8].The systematic uncertainties for each Λ + c decay modeare summarized in Tables IV and V. The systematicuncertainty in the number of BB events is 1 . B → Λ + c p , the uncertainty due to MCstatistics is (0 . − . B − → Λ + c pπ − , we calculatethe uncertainty due to MC statistics by independentlyvarying the number of reconstructed signal MC eventsin each cos θ h , m Λ c π bin according to a Poisson distribu-tion (ensuring that the data events in the same bin arecorrelated). The resulting uncertainty is (0 . − . τ + τ − candidates are selected, in which one τ candidatedecays to leptons and the other decays to more than onehadron plus a neutrino. Events are selected if one leptonand at least two charged hadrons are reconstructed. Theefficiency is then measured for reconstructing the thirdcharged particle for the hadronic decay. From this studythere is a (0 . − . .
21% to 1 .
18% dependingon the Λ + c decay mode. The systematic uncertaintiesdetermined in the two studies are added in quadrature. The systematic uncertainty for charged particle iden-tification is a measure of how well the corrections ap-plied to the events in the signal MC sample for theefficiency determination describe the B → Λ + c p and B − → Λ + c pπ − decay modes. The corrections are deter-mined from control MC and data samples (a Λ → pπ − sample for protons and D ∗ + → D π + , D → K − π + samples for pions and kaons). The efficiency as a func-tion of momentum and angle for the B → Λ + c p and B − → Λ + c pπ − signal MC samples and the control MCsamples agree to within (0 . − . Λ + c decay modes to ensurefit robustness. We allowed this parameter to vary inde-pendently among Λ + c decay modes and repeated the fitto data; the difference between the fit results is taken asa systematic uncertainty of (1 − Λ + c decay mode. A peaking background due to misre-constructed B → Σ + c p, Σ + c → Λ + c π events is presentat the level of 1 . .
5% to account for the uncertainty in B ( B → Σ + c p ).The nominal endpoint in the fit to m m is 5289 . /c ;we vary this by ± . /c , resulting in a systematicuncertainty of (0 . − . Λ + c p THRESHOLD ENHANCEMENT
The kinematic features and resonances in B − → Λ + c pπ − are investigated through examination of the 2-DDalitz plot ( m pπ vs. m Λ c π ) and its projections (the res-onances will be discussed in the next section). Using the s P lot formalism, we project the events in the { m m , m r } fit region using the signal s P lot weights and background s P lot weights along with the efficiency corrections. Thismethod allows us to project only the features of the signalevents, while taking the efficiency variations into account.Figure 3 shows the s P lot weights for m pπ vs. m Λ c π . Notethat the negative bins are suppressed in the 2-D Dalitzplot.We project the events in the fit region onto the m Λ c p axis with signal s P lot weights and efficiency correctionsto study the enhancement at threshold in the baryon-antibaryon mass distribution. This enhancement can beseen in B − → Λ + c pπ − decays as a peak in m Λ c p nearthe kinematic threshold, m Λ c p = 3224 . /c . We di-vide the normalized m Λ c p distribution by the expectationfrom three-body phase-space; the resulting distributionis shown in Figure 4. An enhancement is clearly visi-ble near threshold. The observation of this enhancementis consistent with baryon-antibaryon threshold enhance-ments as seen in other decay modes such as B → ppK ,1 TABLE III: Summary of the individual and combined branching fraction measurements for B → Λ + c p and B − → Λ + c pπ − .The uncertainties are statistical, systematic, and due to B ( Λ + c → pK − π + ), respectively.Mode B ( B → Λ + c p ) B ( B − → Λ + c pπ − ) Λ + c → pK − π + (2 . ± . ± . ± . × − (3 . ± . ± . ± . × − Λ + c → pK S (1 . ± . ± . ± . × − (3 . ± . ± . ± . × − Λ + c → pK S π + π − (4 . ± . ± . ± . × − (4 . ± . ± . ± . × − Λ + c → Λπ + (0 . ± . ± . ± . × − (3 . ± . ± . ± . × − Λ + c → Λπ + π − π + – (3 . ± . ± . ± . × − combined (1 . ± . ± . ± . × − (3 . ± . ± . ± . × − ) /c (GeV π c Λ m ) / c ( G e V π p2 m ) /c (GeV π c Λ m ) / c ( G e V π p2 m FIG. 3: Dalitz plot of m pπ vs. m Λ c π . Each event is efficiency-corrected and given a signal (left) or background (right) s P lot weight. Note that the density scales on the left- and right-hand plots are different, and negative bins are suppressed. B → Dpp ( π ), or in continuum e + e − → ppγ [1, 2]. RESONANT SUBSTRUCTURE OF B − → Λ + c pπ − We also project the events in the fit region onto the m Λ c π axis with signal s P lot weights and efficiency cor-rections to study resonances in m Λ c π . We perform 1-Dbinned χ fits to discriminate between resonant ( B − → Σ c p ) and nonresonant ( B − → Λ + c pπ − ) signal events.In each binned χ fit, the PDF is numerically integratedover each (variable-sized) bin and the following quantityis minimized: χ = n bins X i =1 (cid:18) R ( Y sig P sig + Y nr P nr ) dm i − Y i σ i (cid:19) , (15)where P sig is the resonant signal PDF, P nr is the nonres-onant signal PDF, Y sig is the expected yield of weightedresonant signal events, and Y nr is the expected yield ofweighted nonresonant signal events. We assume the am-plitude and phase of the non-resonant B − → Λ + c pπ − contribution is constant over the Dalitz plot, and does not interfere with the resonant contributions. The rangeof the integral over the quantity dm i takes into accountthe variable bin width, Y i is the number of weighteddata events, and σ i is the uncertainty in Y i . Variablebin widths are used to ensure that there are a sufficientnumber of signal events in each m Λ c π bin so that the es-timated uncertainty is valid. This is especially importantin the non-resonant sideband regions. Bin widths in thesignal regions are chosen to have sufficient granularitythroughout the resonant peaks.The Σ c (2455) and Σ c (2520) are well-established res-onances that decay to Λ + c π − . A third Σ c resonance, the Σ c (2800) , was reported by the Belle Collaboration in2005 [29] along with its isospin partners Σ c (2800) + and Σ c (2800) ++ . These resonances were observed in con-tinuum ( e + e − → cc ) Λ c π events. The Σ c (2800) reso-nance was fit with a D -wave Breit-Wigner distributionand the mass difference ∆ m = m Σ c (2800) − m Λ + c =(515 ± + 2 − ) MeV /c was measured, which correspondsto an absolute mass of (2802 + 4 − ) MeV /c [8]. The nat-ural width of the resonance is (61 + 28 − ) MeV [29]. Wesearch for evidence of all three resonances.2 TABLE IV: Summary of the contributions to the relative systematic uncertainty in B ( B → Λ + c p ) for each Λ + c decay mode.The total for each mode is determined by adding the uncertainty from each source in quadrature. The fractional statisticaluncertainty in the fit yield for each mode is provided for comparison.Source B → Λ + c p Systematic Uncertainty Λ + c → pK − π + Λ + c → pK S Λ + c → pK S π + π − Λ + c → Λπ + BB events 1 .
1% 1 .
1% 1 .
1% 1 . R l – 8 .
5% 11 .
8% 8 . .
4% 0 .
6% 0 .
6% 0 . .
7% 1 .
9% 2 .
8% 1 . .
1% 1 .
1% 1 . .
5% 2 .
1% 1 .
7% 1 . .
9% 7 .
0% 4 .
9% 24 . B ( B − → Λ + c pπ − ) for each Λ + c decay mode.The total for each mode is determined by adding the uncertainty from each source in quadrature. The fractional statisticaluncertainty in the fit yield for each mode is provided for comparison.Source B − → Λ + c pπ − Systematic Uncertainty Λ + c → pK − π + Λ + c → pK S Λ + c → pK S π + π − Λ + c → Λπ + Λ + c → Λπ + π − π + BB events 1 .
1% 1 .
1% 1 .
1% 1 .
1% 1 . R l – 8 .
5% 11 .
8% 8 .
9% 6 . .
6% 2 .
1% 3 .
1% 2 .
0% 3 . .
6% 2 .
3% 3 .
2% 2 .
1% 2 . .
1% 1 .
1% 1 .
1% 1 . .
8% 1 .
8% 2 .
5% 1 .
8% 3 . .
6% 3 .
2% 6 .
5% 2 .
5% 2 . .
4% 9 .
9% 14 .
5% 10 .
0% 8 . .
5% 9 .
1% 16 .
3% 11 .
4% 14 . ) (GeV/c p c Λ m ) / ( . G e V / c | A | FIG. 4: Projection of the amplitude squared ( | A | ) vs. m Λ c p for B − → Λ + c pπ − decays near threshold. Candidates areefficiency-corrected, weighted using the s P lot technique, andcorrected according to three-body phase space. A significant Σ c (2455) signal is seen near threshold;see Fig. 3 and Fig. 5. We construct a resonant signal PDFfrom a non-relativistic S -wave Breit-Wigner distributionconvolved with the sum of two Gaussian distributions (toform a “Voigtian” distribution). This quantity is multi-plied by a phase-space function. The mass and (constant)width of the resonance in the Breit-Wigner PDF are freein the fit. The resolution (described by the two Gaus-sians) is fixed; it is determined from a B − → Σ c (2455) p , Σ c (2455) → Λ + c π − , Λ + c → pK − π + signal MC sampleby comparing the measured Σ c (2455) mass to the true Σ c (2455) mass for each candidate. The two-body phase-space function goes to zero at the kinematic threshold for Λ c π : 2426 .
03 MeV /c . The non-resonant signal PDF is athreshold function [26]; the threshold is set to the kine-matic threshold for Λ c π . The shape parameter for thethreshold function is fixed from a fit to a non-resonant B − → Λ + c pπ − signal MC sample. The weighted datapoints are shown in Fig. 5 with the fit overlaid; the fitresults are summarized in Table VI. The average effi-ciency for Λ + c → pK − π + signal MC events in this regionis 14 . Σ c (2520) ; see Fig. 6. We perform a fit using a rela-tivistic D -wave Breit-Wigner distribution with a mass-dependent width to describe the resonant signal PDF,fixing the resonance mass and the width to the worldaverage values [8]: m R = (2518 . ± .
5) MeV /c andΓ R = (16 . ± .
1) MeV. The non-resonant signal PDFis a first-order polynomial. We obtain Y sig = 27 ± Λ + c → pK − π + signal MC events in this regionis 15 . m Λ c π distribution, we also observe an excited ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c (a) ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c (b) FIG. 5: (a) Projection of m Λ c π showing the Σ c (2455) reso-nance. Events are efficiency corrected and weighted using the s P lot technique, and the result of a binned χ fit to a Voigtiansignal plus a threshold function background is overlaid. Thevariable bin sizes range from 1 to 7 MeV /c . (b) The same fitresult and data is shown on a smaller vertical scale to showthe behavior of the PDF at threshold.TABLE VI: Fit results for B − → Σ c (2455) p . Y sig is theefficiency-corrected resonant signal yield in the fit range. Sys-tematic uncertainties from the fit to m m vs. m r are notincluded in the yield. The world average values from theParticle Data Group (PDG) of the mass and width of the Σ c (2455) are included for comparison [8].Fit Parameter Value PDG Value [8] Y sig ± m R ( GeV /c ) 2 . ± . . ± . R ( MeV) 2 . ± . . ± . ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c -20020406080100 ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c -20020406080100 FIG. 6: Projection of m Λ c π in the region of the Σ c (2520) resonance. Events are efficiency corrected and weighted usingthe s P lot technique, and the result of a binned χ fit to a rel-ativistic D -wave Breit-Wigner signal with a mass-dependentwidth plus a linear background is overlaid. The bin size is5 MeV /c . No significant signal is seen. Σ c state that is higher in mass than the Σ c (2520) . Weconstruct a resonant signal PDF from a relativistic Breit-Wigner distribution with a mass-dependent width:Γ( q ) = Γ R (cid:18) qq R (cid:19) L +1 (cid:18) m R m Λ c π (cid:19) B ′ L ( q, q R ) . (16)The quantity L is the angular momentum ( L = 0 , , S -wave, P -wave, D -wave, respectively), q is the momen-tum of the Λ + c (which is equal to the momentum of the π − ) in the excited Σ c rest frame, and q R is the valueof q when m Λ c π = m R . In Eqn. 16, B ′ L ( q, q R ) is theBlatt-Weisskopf barrier factor [8]: B ′ ( q, q R ) = 1 ,B ′ ( q, q R ) = s q R d q d ,B ′ ( q, q R ) = s ( q R d − + 9 q R d ( q d − + 9 q d , (17)where we define a constant impact parameter d = 1 fm(the approximate radius of a baryon), which correspondsto 5 . − . Blatt-Weisskopf barrier factors are weightsthat account for the fact that the maximum angular mo-mentum ( L ) in a strong decay is limited by the linearmomentum ( q ). Since the resonance is quite wide, we donot need to include a resolution function in the resonantsignal PDF. The two fit parameters ( m R and Γ R ) of the Σ c are free in the fit. The non-resonant signal PDF is afirst-order polynomial.From the 1-D binned χ fit, we obtain Y sig = 1449 ± Σ c state. We TABLE VII: Fit results for the excited Σ c resonance. Y sig isthe efficiency-corrected resonant signal yield in the fit range.Systematic uncertainties from the fit to m m vs. m r are notincluded in the yield. The world average values from theParticle Data Group (PDG) of the mass and width of the Σ c (2800) are included for comparison [8].Fit Parameter Value PDG Value [8] Y sig ± m R ( GeV /c ) 2 . ± .
008 2 . + 0 . − . Γ R ( MeV) 86 + 33 − + 28 − ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c ) (GeV/c π c Λ m ) E v e n t s / ( . G e V / c FIG. 7: Projection of m Λ c π showing an excited Σ c resonance.Events are efficiency corrected and weighted using the s P lot technique. The result of a binned χ fit to a relativistic D -wave Breit-Wigner signal with a mass-dependent width plusa linear background is overlaid. The variable bin sizes rangefrom 15 to 40 MeV /c . choose L = 2 for the nominal fit, but investigate L = 0 , Λ + c → pK − π + signalMC events in this region is 16 . χ from the fit is 37 with 31 degrees of freedom (DOF). Ifthe signal yield is fixed to zero and the mean and widthare fixed to the central values from the nominal fit, theresulting χ is 78 with 34 DOF. The significance can becalculated from ∆ χ = 40 .
9, which is equivalent to 5 . σ for the joint estimation of three parameters.The measured width of this state (86 + 33 − ±
12) MeVis consistent with the width of the Σ c (2800) measuredby Belle [29]. However, the measured mass of this ex-cited Σ c is (2846 ± ±
10) MeV /c , which is 40 MeV /c and 3 σ higher (assuming Gaussian statistics) than Belle’smeasured mass for the Σ c (2800) .We evaluate systematic uncertainties for the Σ c (2455) and the excited Σ c yields, masses, and widths by modify-ing the binning, the resonant signal PDF shape, and the5 TABLE VIII: Systematic uncertainties for Y sig , m R (inMeV /c ), and Γ R (in MeV) for the Σ c (2455) and excited Σ c resonances. Σ c (2455) excited Σ c Systematic Source Y sig Γ R Y sig m R Γ R Resonant Signal PDF – – 5 .
9% – ± .
2% – ± . ± . ± ± . ± . ± ± non-resonant signal PDF shape. Changing the variablebin sizes leads to the dominant systematic uncertainty inthe masses, widths, and yields of both resonances. Forthe Σ c (2455) , the bin width in the peak region was de-creased from the nominal 1 MeV /c to 0 . /c ; forthe excited Σ c , the bin width was varied from 10 to20 MeV /c compared to the nominal 15 MeV /c . For bothresonances, an S -wave and a P -wave relativistic Breit-Wigner (without a resolution function) was used insteadof the nominal resonant signal PDF. The (fixed) non-resonant threshold parameter for the Σ c (2455) was var-ied by ± σ . A second-order polynomial was used (in-stead of a first-order polynomial) for the excited Σ c non-resonant PDF. A summary of the systematic uncertain-ties for Y sig , m R , and Γ R are summarized in Table VIII.The significance is recalculated following each of thevariations used to evaluate the systematic uncertain-ties in the excited Σ c resonance parameters. The re-sulting significance (including systematics) is 5 . σ . Across-check is performed to make sure the Σ c (2800) sig-nal is not the result of interference with a ∆(1232) ++ ,for example (although no significant ∆(1232) ++ signalis seen in the m pπ distribution). The fit is performedagain in the Σ c (2800) mass region for candidates with m pπ > . /c . We obtain 1329 ±
230 resonant signalevents (compared to 1449 ±
284 events for the nominalfit) and a consistent mass and width.An additional cross-check is performed to investi-gate whether there are appropriate fractions of resonant Σ c (2800) events in different Λ + c decay modes. This isaccomplished by dividing the s P lot -weighted, efficiency-corrected data into two samples according to the Λ + c de-cay mode. Note that this cross-check neglects statisticalcorrelations from the combined m r vs. m m fit (less than15%) among the Λ + c decay modes. A binned χ fit to only Λ + c → pK − π + candidates gives Y sig = 776 ± ±
241 total non-resonant B − → Λ + c pπ − , Λ + c → pK − π + events ((12 ± χ fit toa combined sample of Λ + c → pK S , Λ + c → pK S π + π − , Λ + c → Λπ + , and Λ + c → Λπ + π − π + candidates gives Y sig = 530 ±
177 compared to 5956 ±
431 non-resonantevents ((9 ± m R and Γ R were fixed to their nominal values.) The fractionsare consistent in the two samples and the total (1306 ± B − → Λ + c pπ − Dalitz plot(Figure 3), and we do not obtain a statistically significantfit to two resonances.In order to measure the fraction of B − → Λ + c pπ − de-cays that proceed through intermediate Σ c resonances,we assume that the contribution from each Λ + c decaymode for events in the Σ c regions is equal to the measuredcontribution from each Λ + c decay mode in all (resonantand non-resonant) B − → Λ + c pπ − events. We set a 90%C.L. upper limit on B − → Σ c (2520) p that includes sys-tematic uncertainties and corresponds to 109 events. Themeasured fractions or upper limits of B − → Λ + c pπ − de-cays that proceed through an intermediate Σ c resonanceare B ( B − → Σ c (2455) p ) B ( B − → Λ + c pπ − ) = (12 . ± . ± . × − , B ( B − → Σ c (2800) p ) B ( B − → Λ + c pπ − ) = (11 . ± . ± . × − , B ( B − → Σ c (2520) p ) B ( B − → Λ + c pπ − ) < . × − (90% C.L.) . (18)Therefore approximately 1 / B − → Λ + c pπ − decaysproceed through a known intermediate Σ c resonance. MEASUREMENT OF THE Σ c (2455) SPIN
The Σ c (2455) is the lowest mass Σ c state. In thequark model, it is expected to have J P =
12 + , where J isthe spin and P is the parity. In this section, we providea quantitative evaluation of the spin-1 / / Σ c (2455) baryon.We determine the spin of the Σ c (2455) throughan angular analysis of the decay B − → Σ c (2455) p , Σ c (2455) → Λ + c π − . We define a helicity angle θ h as theangle between the momentum vector of the Λ + c and themomentum vector of the recoiling B -daughter p in therest frame of the Σ c (2455) . If we assume J ( Λ + c ) = 1 / / / Σ c (2455) are J ( Σ c ) = 12 : dNd cos θ h ∝ J ( Σ c ) = 32 : dNd cos θ h ∝ θ h . (19)These are the ideal distributions; the measured angulardistributions will be somewhat degraded due to nonuni-6form detector efficiencies, finite experimental resolutionfor measuring θ h , and background contamination. Weestimate the effects of inefficiencies and background con-tamination by performing parameterized MC studies toquantify the decrease in sensitivity to discriminate be-tween possible spin values.If we select from a ± σ signal region in m m and m r ,without s P lot weights or efficiency corrections, there are127 events in the Σ c (2455) signal region and 27 eventsin the Σ c (2455) background regions (2 . < m Λ c π < .
445 GeV /c and 2 . < m Λ c π < .
478 GeV /c ). Scal-ing the number of events in the background region bythe ratio of the total width of the background regionscompared to the width of the signal region, we expect7 . ± . θ h by comparing the measured value of cos θ h to the truevalue of cos θ h in B − → Λ + c pπ − , Λ + c → pK − π + events ina signal MC sample. The maximum root mean square ofthe measured value of cos θ h minus the true value of cos θ h in the Σ c (2455) signal region determines the helicityangle resolution σ (cos θ h ) < .
03. Therefore the finiteexperimental resolution is small compared to any featuresin the spin-1 / / L = P i w i ln( y i ),where y i is the probability density for observing event i .The weight w i for the MC studies is w i = ε i , where ε i is the efficiency for event i . We compute a log likelihoodfor each hypothesis:ln L (1 /
2) = X i w i ln 12ln L (3 /
2) = X i w i ln (cid:20) (cid:0) θ h,i (cid:1)(cid:21) . (20)The shape of the cos θ h distribution for backgroundevents is estimated from the shape of the helicity distri-bution for events in the background regions. The helicitydistribution for these events is illustrated in Fig. 8 as anon-parametric PDF (a histogram). This PDF is used togenerate the number of background events in the signalregion with a Poisson uncertainty (7 . ± . L that each generated distribu-tion is uniform in cos θ h (spin-1 /
2) or distributed as1 + 3 cos θ h (spin-3 / L =ln L (1 / − ln L (3 / L for events generated with each hypothesis. Thedashed histogram (negative values of ∆ ln L ) correspondsto samples generated according to the spin-3 / L )corresponds to samples generated according to the spin- π c Λ ) h θ cos( -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E v e n t s / ( . ) π c Λ ) h θ cos( -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E v e n t s / ( . ) FIG. 8: Helicity angle distribution for the combined sam-ple of background and non-resonant signal events, a non-parameteric PDF (line). The shaded region indicates thePoisson uncertainty in the distribution. / Σ c (2455) is shown in Figure 10. Thepoints are efficiency-corrected. Functions correspondingto the spin-1 / / L = +19 .
2. We indicatethe value of ∆ ln L in data with a vertical line in Figure 9.The observed value of ∆ ln L is consistent with the spin-1 / / > σ level.The ideal angular distributions for the Σ c (2455) stated in Eqn. 19 are also applicable for the excited Σ c resonance. Unlike the narrow Σ c (2455) resonance nearthreshold, the excited Σ c is much wider and therefore itsangular distribution is extremely contaminated by thenon-resonant signal events underneath the signal. Weperform a non-resonant sideband subtraction to extractthe helicity angle distribution of the excited Σ c , but arelimited by the number of signal events available. Anexamination of this distribution is somewhat consistentwith a J = 1 / Σ c .7 ln(L) ∆ -40 -30 -20 -10 0 10 20 30 40 E n t r i e s / . FIG. 9: Distribution of ∆ ln L = ln L (1 / − ln L (3 /
2) forsignal events generated with a uniform distribution in cos θ h (solid histogram, positive values) and a 1 + 3 cos θ h distribu-tion (dashed histogram, negative values). Background eventsare included, and all events are efficiency-corrected. We mea-sure ∆ ln L = +19 . / h θ cos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E v e n t s / ( . ) h θ cos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 E v e n t s / ( . ) FIG. 10: The helicity angle distribution for Σ c (2455) candi-dates in data. The points correspond to efficiency-corrected B − → Σ c (2455) p candidates. The curves for the spin-1 / / CONCLUSION
We have presented branching fraction measurementsfor the decays B → Λ + c p and B − → Λ + c pπ − : B ( B → Λ + c p ) =(1 . ± . ± . ± . × − , B ( B − → Λ + c pπ − ) =(3 . ± . ± . ± . × − , (21)where the uncertainties are statistical, systematic, anddue to the uncertainty in B ( Λ + c → pK − π + ), respectively.These measurements are based on 383 million BB eventsproduced by the SLAC B Factory and recorded by the B A B AR detector.If we combine the statistical and systematic uncertain-ties only, we obtain B ( B → Λ + c p ) = (1 . ± . × − ,which is consistent with a previous measurement by theBelle Collaboration of B ( B → Λ + c p ) = (2 . ± . × − [30]. Both measurements use the same value for B ( Λ + c → pK − π + ). However, our measurement for thethree-body mode, B ( B − → Λ + c pπ − ) = (3 . ± . × − ,is significantly larger (by about 4 σ ) than the previousmeasurement from Belle B ( B − → Λ + c pπ − ) = (2 . ± . × − [25]. The Belle Collaboration measurement uses sixcoarse regions across the B − → Λ + c pπ − Dalitz plane tocorrect for variations in efficiency; we use much finer re-gions and see significant variation near the edges of theDalitz plane. This difference in efficiency treatment mayaccount for some of the discrepancy between the two re-sults.One of the main motivations for studying baryonic B -meson decays is to gain knowledge about baryon-antibaryon production in meson decays. We have mea-sured the ratio of the two branching fractions, B ( B − → Λ + c pπ − ) B ( B → Λ + c p ) = 15 . ± . ± . . (22)In this quantity the 26% uncertainty in B ( Λ + c → pK − π + )cancels in the branching ratio.We have also measured the fractions of B − → Λ + c pπ − decays that proceed through a Σ c resonance: B ( B − → Σ c (2455) p ) B ( B − → Λ + c pπ − ) = (12 . ± . ± . × − , B ( B − → Σ c (2800) p ) B ( B − → Λ + c pπ − ) = (11 . ± . ± . × − . (23)Assuming no interference with direct decay to Λ + c pπ − ,about 1 / B − → Λ + c pπ − decays proceed through a Σ c resonance.The order of magnitude difference between the decayrates of B − → Λ + c pπ − and two-body decays such as8 B → Λ + c p , B − → Σ c (2455) p , and B − → Σ c (2800) p is consistent with the theoretical description [16] thatbaryonic B decays are favored when the baryon and an-tibaryon are close together in phase space. This inter-pretation is also supported by the observation of theenhancement in rate when m Λ c p is near threshold. Al-though the Λ + c p threshold enhancement alone could in-dicate a resonance below threshold, enhancements havebeen observed in other baryon-antibaryon systems andin decays such as e + e − → ppγ [1, 2]. Therefore the bodyof measurements indicates that we are observing a phe-nomenon that is common to baryon production from me-son decays, and possibly common to baryon productionin general.We have used the angular distribution of the decay B − → Σ c (2455) p to study the spin of the Σ c baryon.The helicity angle distribution is consistent with beinguniform, which indicates that the Σ c has J = 1 / Λ + c also has J = 1 / J = 3 / > σ level. This isconsistent with quark model expectations for the lowest Σ c baryon state.We also observe an excited Σ c state in B -meson de-cays to Λ + c pπ − . We measure the mass of this reso-nance to be (2846 ± ±
10) MeV /c and the width tobe (86 + 33 − ) MeV. It is possible that this observationis a confirmation of a triplet of Σ c (2800) states seen in Λ + c π − continuum production [29]. However, the neutral Σ c (2800) has a measured mass of (2802 + 4 − ) MeV /c andwidth of (61 + 28 − ) MeV. The widths of the Σ c (2800) andthe state observed in B decays are consistent, but themasses are 3 σ apart. If these are indeed the same state,then the discrepancy in measured masses needs to be re-solved.Another possible interpretation is that the excited Σ c resonance seen in this analysis is not the Σ c (2800) thatwas previously observed. A clear signal is evident for B − → Σ c (2455) p decays, but we do not see any evi-dence for the decay B − → Σ c (2520) p . The absence ofthe decay B − → Σ c (2520) p is in contrast to a claimed2 . σ signal from an analysis by the Belle Collaborationbased on 152 million BB events [25]. Also, an examina-tion of the B − → Λ + c pπ − Dalitz plot shows no evidencefor the decay B − → Λ + c ¯∆(1232) −− . The Σ c (2520) isa well-established state, and so is the ∆(1232) ++ . Bothare expected to have J = 3 /
2. The Belle Collaborationtentatively identified the Σ c (2800) as J = 3 / Σ c we observe is J = 1 /
2. It istherefore possible that B decays to higher-spin baryonsare suppressed, perhaps due to the same baryon produc-tion mechanisms that suppress two-body baryonic de-cays, and that the excited Σ c state that we have observedis a newly-observed spin-1 / B A B AR . The collaborating institutionswish to thank SLAC for its support and the kind hospi-tality extended to them. This work is supported by theUS Department of Energy and National Science Foun-dation, the Natural Sciences and Engineering ResearchCouncil (Canada), the Commissariat `a l’Energie Atom-ique and Institut National de Physique Nucl´eaire et dePhysique des Particules (France), the Bundesministeriumf¨ur Bildung und Forschung and Deutsche Forschungsge-meinschaft (Germany), the Istituto Nazionale di FisicaNucleare (Italy), the Foundation for Fundamental Re-search on Matter (The Netherlands), the Research Coun-cil of Norway, the Ministry of Education and Science ofthe Russian Federation, Ministerio de Educaci´on y Cien-cia (Spain), and the Science and Technology FacilitiesCouncil (United Kingdom). Individuals have receivedsupport from the Marie-Curie IEF program (EuropeanUnion) and the A. P. Sloan Foundation. [1] B. Aubert et al. ( B A B AR Collaboration), Phys. Rev.D , 051101 (2005).[2] B. Aubert et al. ( B A B AR Collaboration), Phys. Rev.D , 051101 (2006).[3] E. Barberio et al. (Heavy Flavor Averaging Group), hep-ex/0603003 (2006); B. Aubert et al. ( B A B AR Collabo-ration), Phys. Rev. Lett. , 171803 (2006); B. Aubert et al. ( B A B AR Collaboration), Phys. Rev. D , 052004(2005); P. Koppenburg et al. (Belle Collaboration), Phys.Rev. Lett. , 061803 (2004); K. Abe et al. (Belle Col-laboration), Phys. Lett. B , 151 (2001); S. Chen etal. (CLEO Collaboration), Phys. Rev. Lett. , 251807(2001).[4] M.-Z. Wang et al. (Belle Collaboration), Phys. Rev. D ,052004 (2007).[5] M. Misiak et al. , Phys. Rev. Lett. , 022002 (2007);T. Becher and M. Neubert, Phys. Rev. Lett. , 022003(2007).[6] C. Q. Geng and Y. K. Hsiao, Phys. Lett. B , 67(2005);H.-Y. Cheng and K.-C. Yang, Phys. Lett. B , 271(2002).[7] H. Albrecht et al. (ARGUS Collaboration), Z. Phys.C , 1 (1992).[8] W.-M. Yao et al. (Particle Data Group), J. Phys. G33 ,1 (2006) and 2007 partial update for the 2008 edition.[9] M. Jarfi et al. , Phys. Rev. D , 1599 (1991).[10] N. G. Deshpande et al. , Mod. Phys. Lett. A3 , 749 (1988).[11] P. Ball and H. G. Dosch, Z. Phys. C , 445 (1991).[12] L. J. Reinders et al. , Phys. Rep. , 1 (1985).[13] V. Chernyak and I. Zhitnitsky, Nucl. Phys. B , 137(1990).[14] H.-Y. Cheng and K.-C. Yang, Phys. Rev. D , 034008(2003).[15] H.-Y. Cheng and K.-C. Yang, Phys. Rev. D , 054028 (2002).[16] W.-S. Hou and A. Soni, Phys. Rev. Lett. , 4247 (2001).[17] Unless specifically stated otherwise, conjugate decaymodes are assumed throughout this paper.[18] B. Aubert et al. ( B A B AR Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A , 1 (2002).[19] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A , 152 (2001).[20] T. Sjostrand et al. , J. High Energy Phys. 05, (2006) 026.[21] S. Agostinelli et al. (GEANT4 Collaboration), Nucl. In-strum. Methods Phys. Res., Sect. A , 250 (2003).[22] R. A. Fisher, Annals Eugen. , 179 (1936).[23] S. Brandt et al. , Phys. Lett. , 57 (1964); E. Farhi,Phys. Rev. Lett. , 1587 (1977).[24] B. Aubert et al. ( B A B AR Collaboration), Phys. Rev. D , 111102(R) (2005).[25] N. Gabyshev et al. (Belle Collaboration), Phys. Rev.Lett. , 242001 (2006).[26] H. Albrecht et al. (ARGUS Collaboration), Z. Phys.C , 543 (1990).[27] M. Pivk and F. R. Le Diberder, Nucl. Instrum. MethodsPhys. Res., Sect. A , 356 (2005).[28] L. Lyons et al. , Nucl. Instrum. Methods Phys. Res., Sect.A , 110 (1988).[29] R. Mizuk et al. (Belle Collaboration), Phys. Rev. Lett. , 122002 (2005).[30] N. Gabyshev et al. (Belle Collaboration), Phys. Rev.Lett.90