Search for $B^+ \to \phi \pi^+$ and $B^0 \to \phi \pi^0$ Decays

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arXiv:hep-ex/0605037v2 9 Jul 2006

Abstract

A search has been made for the decays B+_{→ φπ}+_{and B}0_{→ φπ}0_{in a}

data sample of approximately 232 ×106

B ¯B pairs recorded at the Υ(4S) resonance with the BaBar detector at the PEP-II B-meson Factory at SLAC. No significant signals have been observed, and therefore upper limits have been set on the branching fractions: B(B+ _{→ φπ}+_{) < 2.4 ×}

10−7_{and B(B}0

→ φπ0

) < 2.8 × 10−7_{at 90% probability.}

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arXiv:hep-ex/0605037v2 9 Jul 2006

B B

SLAC-PUB-11854 hep-ex/0605037

Search for B

+

_→

_φπ

+

_{and B}

0

_→

_φπ

0

_Decays

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

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

Y. S. Zhu,4 _{G. Eigen,}5 _{I. Ofte,}5_{B. Stugu,}5 _{G. S. Abrams,}6 _{M. Battaglia,}6_{D. N. Brown,}6 _{J. Button-Shafer,}6

R. N. Cahn,6 _{E. Charles,}6_{C. T. Day,}6 _{M. S. Gill,}6 _{Y. Groysman,}6_{R. G. Jacobsen,}6 _{J. A. Kadyk,}6_{L. T. Kerth,}6

Yu. G. Kolomensky,6_{G. Kukartsev,}6 _{G. Lynch,}6 _{L. M. Mir,}6 _{P. J. Oddone,}6 _{T. J. Orimoto,}6_{M. Pripstein,}6

N. A. Roe,6 _{M. T. Ronan,}6_{W. A. Wenzel,}6_{M. Barrett,}7_{K. E. Ford,}7_{T. J. Harrison,}7_{A. J. Hart,}7 _{C. M. Hawkes,}7

S. E. Morgan,7 _{A. T. Watson,}7 _{K. Goetzen,}8 _{T. Held,}8 _{H. Koch,}8 _{B. Lewandowski,}8 _{M. Pelizaeus,}8 _{K. Peters,}8

T. Schroeder,8_{M. Steinke,}8_{J. T. Boyd,}9 _{J. P. Burke,}9_{W. N. Cottingham,}9_{D. Walker,}9_{T. Cuhadar-Donszelmann,}10

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

M. Saleem,11 _{L. Teodorescu,}11_{V. E. Blinov,}12 _{A. D. Bukin,}12 _{V. P. Druzhinin,}12 _{V. B. Golubev,}12 _{A. P. Onuchin,}12

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

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

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

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

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

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

G. Nesom,18 _{T. Schalk,}18 _{B. A. Schumm,}18 _{A. Seiden,}18 _{P. Spradlin,}18 _{D. C. Williams,}18 _{M. G. Wilson,}18

J. Albert,19 _{E. Chen,}19 _{A. Dvoretskii,}19 _{D. G. Hitlin,}19 _{I. Narsky,}19_{T. Piatenko,}19 _{F. C. Porter,}19 _{A. Ryd,}19

A. Samuel,19 _{R. Andreassen,}20 _{G. Mancinelli,}20 _{B. T. Meadows,}20_{M. D. Sokoloff,}20 _{F. Blanc,}21 _{P. C. Bloom,}21

S. Chen,21 _{W. T. Ford,}21 _{J. F. Hirschauer,}21_{A. Kreisel,}21_{U. Nauenberg,}21_{A. Olivas,}21_{W. O. Ruddick,}21

J. G. Smith,21_{K. A. Ulmer,}21 _{S. R. Wagner,}21_{J. Zhang,}21 _{A. Chen,}22 _{E. A. Eckhart,}22_{A. Soffer,}22_{W. H. Toki,}22

R. J. Wilson,22 _{F. Winklmeier,}22_{Q. Zeng,}22 _{D. D. Altenburg,}23_{E. Feltresi,}23 _{A. Hauke,}23_{H. Jasper,}23 _{B. Spaan,}23

T. Brandt,24 _{V. Klose,}24 _{H. M. Lacker,}24 _{W. F. Mader,}24 _{R. Nogowski,}24 _{A. Petzold,}24 _{J. Schubert,}24

K. R. Schubert,24 _{R. Schwierz,}24_{J. E. Sundermann,}24 _{A. Volk,}24_{D. Bernard,}25 _{G. R. Bonneaud,}25 _{P. Grenier,}25, ∗

E. Latour,25_{Ch. Thiebaux,}25 _{M. Verderi,}25 _{D. J. Bard,}26 _{P. J. Clark,}26 _{W. Gradl,}26 _{F. Muheim,}26 _{S. Playfer,}26

A. I. Robertson,26 _{Y. Xie,}26 _{M. Andreotti,}27 _{D. Bettoni,}27_{C. Bozzi,}27 _{R. Calabrese,}27 _{G. Cibinetto,}27 _{E. Luppi,}27

M. Negrini,27 _{A. Petrella,}27 _{L. Piemontese,}27 _{E. Prencipe,}27 _{F. Anulli,}28 _{R. Baldini-Ferroli,}28 _{A. Calcaterra,}28

R. de Sangro,28_{G. Finocchiaro,}28 _{S. Pacetti,}28 _{P. Patteri,}28_{I. M. Peruzzi,}28, † _{M. Piccolo,}28 _{M. Rama,}28

A. Zallo,28_{A. Buzzo,}29_{R. Capra,}29_{R. Contri,}29_{M. Lo Vetere,}29 _{M. M. Macri,}29_{M. R. Monge,}29 _{S. Passaggio,}29

C. Patrignani,29 _{E. Robutti,}29 _{A. Santroni,}29_{S. Tosi,}29 _{G. Brandenburg,}30 _{K. S. Chaisanguanthum,}30 _{M. Morii,}30

J. Wu,30 _{R. S. Dubitzky,}31 _{J. Marks,}31 _{S. Schenk,}31_{U. Uwer,}31 _{W. Bhimji,}32_{D. A. Bowerman,}32_{P. D. Dauncey,}32

U. Egede,32 _{R. L. Flack,}32_{J. R. Gaillard,}32 _{J .A. Nash,}32 _{M. B. Nikolich,}32_{W. Panduro Vazquez,}32 _{X. Chai,}33

M. J. Charles,33_{U. Mallik,}33 _{N. T. Meyer,}33 _{V. Ziegler,}33_{J. Cochran,}34 _{H. B. Crawley,}34_{L. Dong,}34_{V. Eyges,}34

W. T. Meyer,34_{S. Prell,}34 _{E. I. Rosenberg,}34 _{A. E. Rubin,}34 _{A. V. Gritsan,}35 _{M. Fritsch,}36 _{G. Schott,}36

N. Arnaud,37 _{M. Davier,}37 _{G. Grosdidier,}37_{A. H¨}_ocker,37 _{F. Le Diberder,}37 _{V. Lepeltier,}37 _{A. M. Lutz,}37

A. Oyanguren,37_{S. Pruvot,}37_{S. Rodier,}37 _{P. Roudeau,}37 _{M. H. Schune,}37 _{A. Stocchi,}37 _{W. F. Wang,}37

G. Wormser,37 _{C. H. Cheng,}38 _{D. J. Lange,}38 _{D. M. Wright,}38 _{C. A. Chavez,}39 _{I. J. Forster,}39 _{J. R. Fry,}39

E. Gabathuler,39 _{R. Gamet,}39 _{K. A. George,}39 _{D. E. Hutchcroft,}39 _{D. J. Payne,}39 _{K. C. Schofield,}39

C. Touramanis,39 _{A. J. Bevan,}40 _{F. Di Lodovico,}40 _{W. Menges,}40 _{R. Sacco,}40 _{C. L. Brown,}41_{G. Cowan,}41

H. U. Flaecher,41 _{D. A. Hopkins,}41_{P. S. Jackson,}41_{T. R. McMahon,}41_{S. Ricciardi,}41_{F. Salvatore,}41_{D. N. Brown,}42

C. L. Davis,42 _{J. Allison,}43 _{N. R. Barlow,}43 _{R. J. Barlow,}43 _{Y. M. Chia,}43 _{C. L. Edgar,}43_{M. P. Kelly,}43

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

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

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2 F. Taylor,46_{R. K. Yamamoto,}46 _{H. Kim,}47 _{P. M. Patel,}47 _{C. T. Potter,}47 _{S. H. Robertson,}47 _{A. Lazzaro,}48

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

J. Reidy,49_{D. A. Sanders,}49_{D. J. Summers,}49 _{H. W. Zhao,}49 _{S. Brunet,}50_{D. Cˆot´e,}50 _{M. Simard,}50_{P. Taras,}50

F. B. Viaud,50_{H. Nicholson,}51 _{N. Cavallo,}52, ‡_{G. De Nardo,}52 _{D. del Re,}52 _{F. Fabozzi,}52, ‡ _{C. Gatto,}52 _{L. Lista,}52

D. Monorchio,52 _{P. Paolucci,}52_{D. Piccolo,}52 _{C. Sciacca,}52 _{M. Baak,}53 _{H. Bulten,}53 _{G. Raven,}53_{H. L. Snoek,}53

C. P. Jessop,54 _{J. M. LoSecco,}54 _{T. Allmendinger,}55_{G. Benelli,}55 _{K. K. Gan,}55 _{K. Honscheid,}55 _{D. Hufnagel,}55

P. D. Jackson,55 _{H. Kagan,}55 _{R. Kass,}55_{T. Pulliam,}55 _{A. M. Rahimi,}55 _{R. Ter-Antonyan,}55 _{Q. K. Wong,}55

N. L. Blount,56 _{J. Brau,}56 _{R. Frey,}56 _{O. Igonkina,}56_{M. Lu,}56 _{R. Rahmat,}56 _{N. B. Sinev,}56 _{D. Strom,}56

J. Strube,56 _{E. Torrence,}56_{F. Galeazzi,}57_{A. Gaz,}57_{M. Margoni,}57 _{M. Morandin,}57_{A. Pompili,}57 _{M. Posocco,}57

M. Rotondo,57 _{F. Simonetto,}57 _{R. Stroili,}57 _{C. Voci,}57_{M. Benayoun,}58_{J. Chauveau,}58_{P. David,}58_{L. Del Buono,}58

Ch. de la Vaissi`ere,58 _{O. Hamon,}58_{B. L. Hartfiel,}58_{M. J. J. John,}58 _{Ph. Leruste,}58 _{J. Malcl`es,}58 _{J. Ocariz,}58

L. Roos,58 _{G. Therin,}58 _{P. K. Behera,}59 _{L. Gladney,}59 _{J. Panetta,}59_{M. Biasini,}60 _{R. Covarelli,}60 _{M. Pioppi,}60

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

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

J. Walsh,61 _{M. Haire,}62_{D. Judd,}62_{D. E. Wagoner,}62_{J. Biesiada,}63_{N. Danielson,}63_{P. Elmer,}63_{Y. P. Lau,}63_{C. Lu,}63

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

F. Ferrarotto,64 _{F. Ferroni,}64_{M. Gaspero,}64 _{L. Li Gioi,}64 _{M. A. Mazzoni,}64_{S. Morganti,}64_{G. Piredda,}64_{F. Polci,}64

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

E. O. Olaiya,66_{F. F. Wilson,}66 _{S. Emery,}67_{A. Gaidot,}67 _{S. F. Ganzhur,}67 _{G. Hamel de Monchenault,}67

W. Kozanecki,67 _{M. Legendre,}67 _{B. Mayer,}67_{G. Vasseur,}67 _{Ch. Y`eche,}67_{M. Zito,}67 _{W. Park,}68_{M. V. Purohit,}68

A. W. Weidemann,68 _{J. R. Wilson,}68 _{M. T. Allen,}69 _{D. Aston,}69 _{R. Bartoldus,}69 _{P. Bechtle,}69_{N. Berger,}69

A. M. Boyarski,69 _{R. Claus,}69_{J. P. Coleman,}69_{M. R. Convery,}69_{M. Cristinziani,}69 _{J. C. Dingfelder,}69 _{D. Dong,}69

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

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

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

R. Messner,69 _{D. R. Muller,}69 _{C. P. O’Grady,}69 _{V. E. Ozcan,}69 _{A. Perazzo,}69 _{M. Perl,}69_{B. N. Ratcliff,}69

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

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

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

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

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

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

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

M. Bomben,76 _{L. Bosisio,}76 _{C. Cartaro,}76_{F. Cossutti,}76 _{G. Della Ricca,}76 _{S. Dittongo,}76 _{S. Grancagnolo,}76

L. Lanceri,76 _{L. Vitale,}76 _{V. Azzolini,}77 _{F. Martinez-Vidal,}77 _{Sw. Banerjee,}78 _{B. Bhuyan,}78 _{C. M. Brown,}78

D. Fortin,78 _{K. Hamano,}78 _{R. Kowalewski,}78 _{I. M. Nugent,}78 _{J. M. Roney,}78 _{R. J. Sobie,}78 _{J. J. Back,}79

P. F. Harrison,79_{T. E. Latham,}79 _{G. B. Mohanty,}79 _{H. R. Band,}80 _{X. Chen,}80 _{B. Cheng,}80 _{S. Dasu,}80 _{M. Datta,}80

A. M. Eichenbaum,80 _{K. T. Flood,}80 _{J. J. Hollar,}80_{J. R. Johnson,}80_{P. E. Kutter,}80 _{H. Li,}80_{R. Liu,}80 _{B. Mellado,}80

A. Mihalyi,80_{A. K. Mohapatra,}80_{Y. Pan,}80_{M. Pierini,}80_{R. Prepost,}80 _{P. Tan,}80_{S. L. Wu,}80_{Z. Yu,}80_{and H. Neal}81

(The BA_BAR _{Collaboration)}

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

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

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

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

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

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

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

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

18_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA} 19_{California Institute of Technology, Pasadena, California 91125, USA}

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

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

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

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

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

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

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

36_Universit¨_{at Karlsruhe, Institut f¨}_{ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany} 37_{Laboratoire de l’Accélérateur Linéaire, IN2P3-CNRS et Université Paris-Sud 11,}

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

38_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA} 39_{University of Liverpool, Liverpool L69 7ZE, United Kingdom} 40_{Queen Mary, University of London, E1 4NS, United Kingdom}

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

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

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

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

50_{Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7} 51_{Mount Holyoke College, South Hadley, Massachusetts 01075, USA}

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

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

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

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

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

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

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

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

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

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

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

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

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

75_Universit`_{a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy} 76_Universit`_{a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy}

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4 78_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6}

79_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom} 80_{University of Wisconsin, Madison, Wisconsin 53706, USA}

81_{Yale University, New Haven, Connecticut 06511, USA}

(Dated: November 10, 2018) A search has been made for the decays B+

→ φπ+

and B0

→ φπ0

in a data sample of approxi-mately 232 ×106

B ¯B pairs recorded at the Υ (4S) resonance with the BABAR_{detector at the PEP-II} B-meson Factory at SLAC. No significant signals have been observed, and therefore upper limits have been set on the branching fractions: B(B+

→ φπ+

) < 2.4×10−7_{and B(B}0

→ φπ0

) < 2.8×10−7

at 90% probability.

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

The measurements of B → φK and B → φπ decay rates are important because they are sensitive to con-tributions beyond the Standard Model (SM). In partic-ular, the latter is strongly suppressed in the SM, and a measurement of B(B → φπ) >_{∼ 10}−7 _{would be evidence}

for new physics, for example supersymmetric contribu-tions [1]. The study of the processes B+

→ φπ+ _{[2] and}

B0

→ φπ0 _{is also important to understand the}

theoret-ical uncertainties associated with measurements of CP asymmetries in B0

→ φK0

decays. The B → φπ decay amplitudes are related to the sub-leading terms of the B0

→ φK0 _{decay amplitude [3] and can therefore}

pro-vide stringent bounds on possible contributions to the time-dependent CP asymmetry in B0

→ φK0 _[4],

an-other probe of new physics effects in B decays.

In Fig. 1 we show the leading order Feynman diagram for the B → φπ decay and a sub-leading diagram for B → φK decay. + W t , c , u b d, s u, d

B

φ

,K

π

FIG. 1: Feynman diagram for B → φπ and B → φK.

Previous searches for these decay modes have been re-ported by BA_BAR _{and CLEO [5, 6, 7]. The results}

pre-sented here are based on data collected with the BA_BAR

detector [8] at the PEP-II asymmetric-energy e+_e−

col-lider [9] located at the Stanford Linear Accelerator Cen-ter. An integrated luminosity of 211 fb−1, corresponding to (231.8±2.6)×106_{BB pairs, was recorded at the Υ (4S)}

resonance (center-of-mass energy√s = 10.58 GeV). Charged particles from the e+_e− _{interactions are}

de-tected, and their momenta measured, by a combination of five layers of double-sided silicon microstrip detectors

(SVT) and a 40-layer drift chamber (DCH), both op-erating in the 1.5-T magnetic field of a superconduct-ing solenoid. Photons and electrons are identified with a CsI(Tl) electromagnetic calorimeter (EMC). Further charged particle identification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring imaging Cherenkov detec-tor (DIRC) covering the central region.

Monte Carlo simulation is used to evaluate background contamination and selection efficiency. Signal and back-ground Monte Carlo samples are generated with EvtGen [10]. The detector response is simulated with GEANT4 [11] and all simulated events are reconstructed in the same manner as data.

We reconstruct B meson candidates through the de-cays φπ+ _{or φπ}0

, with φ → K+_K− _{and π}0

→ γγ. All kaon candidate tracks in the reconstructed decay chains must satisfy a set of loose kaon identification criteria based on the response of the DIRC and the dE/dx mea-surements in the DCH and SVT. In both decay modes, all the tracks coming from the fully reconstructed B are required to originate from the interaction point. A pair of oppositely-charged kaon candidates is considered as a φ candidate if its invariant mass is within 15 MeV/c2 _of

the nominal φ mass value (1019.5 MeV/c2 _{[12]). This is}

about three times the observed width in the K+_K−

in-variant mass spectrum. A pair of energy deposits in the EMC, each of which is isolated from any charged track and has the lateral shower shape expected for photons, is considered as a π0 _{candidate if both the deposits}

ex-ceed 40 MeV in the laboratory frame and the associated invariant mass of the pair is between 110 MeV/c2 _and

160 MeV/c2_{(about three times the observed width in the}

γγ invariant mass spectrum). B meson candidates are made by combining φ candidates with a charged track or a π0 _{candidate. We do not apply any particle}

identi-fication criteria on the track which comes directly from B meson decay (primary track) at this stage, so for the charged mode we reconstruct B+

→ φh+ _(h+ _{= π, K)}

events. This allows us to study the B+

→ φK+ _signal,

which is the largest background coming from B decays. Two kinematic variables are used to discriminate be-tween signal B decays and combinatorial background:

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the invariant mass of the reconstructed B meson can-didate, mB and mmiss = p(qe+_e−− ˜qB)

2_{, where q} e+_e− is the four momentum of the initial e+_e− _{system and}

˜

qB is the mass-constrained four momentum of the

re-constructed B meson candidate. By construction, the linear correlation between mmissand mB vanishes.

Com-pared to the kinematic variables ∆E = E∗ B− 1 2 √_{s and} mES = q 1 4s − p∗2B (where s = q 2

e+_e− and the asterisk denotes the e+_e− _{rest frame), which were used in the}

previous BA_BAR_{analysis of these modes [6], the present}

combination of variables has less correlation and bet-ter background suppression. The distribution of mB

peaks at the nominal B mass value [12], with a width of about 20 MeV/c2 _{for φπ}+_{, and about 40 MeV/c}2 _for

φπ0_{, with a low-side tail due to energy leakage from}

the EMC. The resolution on mmiss is about 5 MeV/c2,

dominated by the beam-energy spread. We require mB

to be within 150 MeV/c2 _{of the nominal B mass and}

5.11 GeV/c2 _{< m}

miss < 5.31 GeV/c2. The region

mmiss < 5.2 GeV/c2 is used for background

character-ization.

The dominant background comes from combinatorial e+_e− _{→ q¯q (q = u, d, s, c) continuum events. They tend}

to be jet-like in the center-of-mass (CM) frame, while B decays tend to be spherical. To exploit this characteristic for discriminating against continuum background, we use the ratio L2/L0, where Li is defined as

Li=

X

k

|pk|| cos(θk)|i, (1)

where pkis the momentum of particle k, and θkis the

an-gle between pkand the thrust axis of the reconstructed B

meson evaluated in the CM frame. The sum runs over the charged and neutral particles of the event not assigned to the B meson. We require L2/L0 < 0.55, which

sup-presses the continuum background by more than a factor of 3, while retaining about 90% of the signal. We require | cos θ∗

B| < 0.9, where θ∗B is the angle between the B

candidate momentum and the e+_{momentum in the CM}

frame. For B candidates the probability density function of θ∗

B is proportional to sin 2

θ∗

B, whereas for continuum

events it is nearly uniform after acceptance. We select events for which one B is reconstructed as B+

→ φh+

or B0

→ φπ0 _{and the other B is only partially}

recon-structed [13]. We define ∆t to be the difference between the proper decay times of the B mesons and σ∆t the

un-certainty associated with it. We require, in the case of B0

→ φπ0

only, |∆t| < 20 ps and σ∆t < 2.5 ps. These

requirements on ∆t and σ∆tretain about 92% of the

sig-nal, while removing about 15% of the continuum events. The r.m.s. ∆t resolution is 1.1 ps for the events that satisfy these requirements. After the application of these selection criteria on Monte Carlo simulated events, the efficiencies for φπ+ _{and φπ}0

signal are (37.1 ± 0.1)% and (29.5 ± 0.8)% respectively. The average candidate

mul-tiplicity in events with at least one candidate is ∼ 1.005 for both decay modes. If more than one B candidate is reconstructed in an event, we choose the one with the φ → K+_K−_{invariant mass closest to the nominal φ mass}

value [12], for B+_{→ φπ}+ _{decays. For B}0_{→ φπ}0_decays,

we choose the candidate with the π0_{→ γγ invariant mass}

closest to the nominal π0_{mass value [12]. These criteria}

produce no bias in the shape of the other event variables used in the maximum likelihood fit described below. We select 10990 and 2732 events in the φh+_{and φπ}0_analyses

respectively.

A possible background to the φ → K+_K− _decays

comes from the S-wave production of the K+_K−_system

(B → (K+_K−₎

S−waveπ decays) with contributions

com-ing predominantly from resonances such as f0(980) and

a0(980). Using samples of simulated decays of B mesons

equivalent to nearly five times the size of the data sample, we found that all the other B decay modes give negligible sources of background. To discriminate against S-wave background in the maximum likelihood fit, we use the helicity of the K+_K− _{system, in terms of the cosine of}

the angle θH between the K+ candidate and the

par-ent B meson flight direction in the K+_K− _{rest frame.}

The helicity probability density function is proportional to cos2_θ

H for the signal, and is uniformly distributed for

the S-wave background. Further discrimination is pro-vided by the K+_K− _{invariant mass distribution, m}

KK,

which peaks at the φ mass for the signal, while it peaks at lower values for the S-wave background.

In the case of charged B decays, we exploit the Cherenkov angle θc measured in the DIRC for the

pri-mary track, in order to determine simultaneously the yields of B+

→ φπ+ _{and B}+

→ φK+ _{decays and the}

yields of the two corresponding B+

→ (K+_K−₎

S−waveh+

(h = π, K) background components.

Signal and background yields Ni, where i denotes

sig-nal, continuum, and S-wave background, are extracted using an extended maximum likelihood fit with the like-lihood function: L = _{N !}1 exp −X i Ni ! N Y j=1 " X i NiPi( ~xj; ~αi) # , (2) where N is the total number of events entering the fit. The probabilities Pi are products of Probability

Den-sity Functions (PDF) for each of the independent vari-ables ~x = {mmiss, mB, L2/L0, mKK, cos θH}. In the case

of B+

→ φh+ _{the variable θ}

c is also used in the fit.

The ~αi are the parameters of the PDFs for ~x. The

con-tinuum parameters are allowed to vary, except for the mmiss end-point. All other parameters αi are fixed to

their values derived from data control samples. These are varied within their uncertainties to evaluate the sys-tematic error. By minimizing the quantity − ln L in two separate fits, we determine the yields for φπ+ _{and φπ}0_.

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6 There are three B backgrounds to B+

→ φπ+ _decay

(B+

→ (K+_K−₎

S−waveh+ and B+ → φK+), while only

B0

→ (K+_K−₎

S−waveπ0 contributes to the B0 → φπ0

mode. All the yields in Eq. 2 are allowed to fluctuate to negative values in the fits.

The distributions of L2/L0and cos θHare described by

a parametric step function [14] and a second-order poly-nomial respectively. We use a Gaussian for the mmiss

distribution for φπ+ _{signal and S-wave components, a}

Gaussian with exponential tails for the mB distribution

for φπ+ _{signal and S-wave components, and for both}

mmiss and mB for φπ0 signal and S-wave components.

For the continuum mmissdistribution we use the function

x√1 − x2_exp_{−ξ(1 − x}2₎_{, with x ≡ 2m}

miss/√s and ξ a

floating parameter. The mKK invariant mass

distribu-tion is described by a relativistic Breit-Wigner funcdistribu-tion for signal, a relativistic Breit-Wigner plus exponential for the continuum background and a Flatt´e [15, 16] function for the S-wave background. The Flatt´e function takes into account the coupling of the scalar resonances to the π+_π− _{and K}+_K− _{channels [17].}

The Cherenkov angle θc PDFs are obtained from a

large data sample of D∗+ _{→ D}0_π+ _(D0

→ K−_π+₎

decays where K∓_/π± _{tracks are identified through the}

charge correlation with the π± _{from the D}∗± _{decay. The}

PDFs are constructed separately for K+_{, K}−_{, π}+ _and

π− _{tracks as a function of momentum and polar angle}

using the expected values of θc, and its uncertainty.

Using a large number of simulated experiments, we find that the usual maximum likelihood fitting technique does not provide an unbiased estimate of the true values of signal and S-wave yields (NS and NS−wave) because of

the non-Gaussian shape of the likelihood function when the yield is very small. Therefore we use a Bayesian sta-tistical approach to obtain a modified likelihood function L(NS):

L(NS) = N0

Z ∞

0

dNS−waveL(NS, NS−wave), (3)

where the normalization N0 is such that

R∞

0 dNSL(NS) = 1. The two dimensional

likeli-hood L(NS, NS−wave) is given at each point on the

NS-NS−wave plane by the function defined in Eq. 2,

maximized with respect to all of the other fit variables. When seeking the central value for the branching fraction we take the median of L, with the lower limit replaced by −∞ and NS unrestricted. This is because we find

from simulations that in the case of very low yields, the median provides a less biased estimator of the true value of NS than the maximum of L. We correct the central

value of the branching fractions for the residual biases. When calculating upper limits, we impose the a priori constraints NS > 0 and NS−wave> 0.

Fig. 2 shows the mmissand mB distributions for data,

with the PDF corresponding to the maximum likelihood

fit overlaid. We do not observe evidence for either B+

→ φπ+ _{or B}0

→ φπ0_decays.

TABLE I: Signal yield (evaluated as the median of the like-lihood), detection efficiency ε (the uncertainty includes both statistical and systematic effects), measured branching frac-tion B with statistical error, after the correcfrac-tion for the fit bias has been applied, for the two decay modes considered and upper limit at 90% probability.

B+ → φπ+ B0 → φπ0 Yield −1.5 ± 5.9 4.0 ± 3.5 ε(%) 37.1 ± 0.1 29.5 ± 0.8 B(10−6₎ _{−0.04 ± 0.17} _{0.12 ± 0.13} UL(B)(10−7₎ _2.4 _2.8

The signal yields, extracted from the median of the likelihood L(NS) (Eq. 3), are reported in Table I. In

the case of B+

→ φh+_{, we also measure the N}

φK+ yield, which is found to be compatible with the expectation from published branching fractions [5].

The branching fraction B is calculated from the ob-served number of signal events as

B = NS

ε · NB ¯B· B(φ → K+K−)

(4) where NB ¯B is the number of B ¯B pairs produced and

ε is the reconstruction efficiency for the B candidates. In Eq. 4 we assume equal branching fractions for Υ (4S) decays to charged and neutral B-meson pairs [18].

The systematic uncertainties are summarized in Ta-ble II. The uncertainty arising from the lack of knowledge of continuum background PDFs is part of the statistical error since the background parameters are free to vary in the fit. The uncertainty on the signal PDFs repre-sents the dominant error. We estimate it by using sim-ulated and high-statistics data control samples of B+

→ π+_D0 _(D0

→ K+_π−_{) and B}0

→ π+_D− _(D− _{→ K}_Sπ0 −₎

events. In order to estimate the systematic uncertainty on mB for B0 → φπ0 we use a data control sample of

TABLE II: Summary of systematic uncertainties contributing to the total error for the upper limit on the branching fraction. They are given in units of 10−8_.

B+ → φπ+ B0 → φπ0 PDF Uncertainty +1.9 −2.8 +3.6 −4.2 PID Efficiency 0.1 0.1 Tracking Efficiency 0.1 0.2 π0 Efficiency - 0.1 L2/L0 Cut 0.1 0.3 B ¯B Pair Counting 0.1 0.2 Interference Effects 0.3 0.6 B(φ → K+ K−_{), B(π}0 → γγ) 0.1 0.1 Total +2.8 −3.6 +3.7 −4.3

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) 2 (GeV/c miss m 5.12 5.16 5.2 5.24 5.28 2 Events/13 MeV/c ) 2 (GeV/c miss m 2 Events/13 MeV/c 0 5 10 15 20 25 BABAR ) 2 (GeV/c miss m 2 Events/10 MeV/c 0 5 10 15 20 25 ) 2 (GeV/c miss m 5.12 5.16 5.2 5.24 5.28 2 Events/10 MeV/c BABAR ) 2 (GeV/c miss m 2 Events/10 MeV/c ) 2 (GeV/c miss m 5.12 5.16 5.2 5.24 5.28 2 Events/10 MeV/c 0 20 40 60 80 100 120 140 BABAR ) 2 (GeV/c B m 2 Events/20 MeV/c 0 4 8 12 16 20 24 ) 2 (GeV/c B m 5.15 5.2 5.25 5.3 5.35 5.4 2 Events/20 MeV/c BABAR ) 2 (GeV/c B m 2 Events/14 MeV/c ) 2 (GeV/c B m 5.15 5.2 5.25 5.3 5.35 5.4 2 Events/14 MeV/c 0 4 8 12 16 20 BABAR ) 2 (GeV/c B m 2 Events/14 MeV/c 0 20 40 60 80 ) 2 (GeV/c B m 5.15 5.2 5.25 5.3 5.35 5.4 2 Events/14 MeV/c BABAR

FIG. 2: Distribution of mmiss(top) and mB (bottom) for reconstructed B0→ φπ0 (left), B+→ φπ+ (middle) and B+→ φh+

(h = {π, K}) (right), after applying a requirement on the ratio of signal likelihood to signal-plus-background likelihood to enhance the signal. The curves are projections from the likelihood fit for total yield (solid line), for the continuum background (fine dashed line) and for continuum plus S-wave component (dashed line). For B+

→ φh+

decay we do not apply any particle identification criteria and assign the pion mass to the primary track. For this reason, the mB distribution for B+ → φK+

events is shifted with respect to the nominal B+_{mass (positive bump in bottom middle and bottom right plot), while it peaks}

at the nominal value for B+

→ φπ+

events (negative bump in bottom middle plot).

B+

→ h+_π0 _{events. The control channels have event}

topologies similar to those of B+

→ φh+_{and B}0

→ φπ0_.

We use them to determine the signal PDF parameters and take the difference in yields found by varying these parameters within one standard deviation as the system-atic error. The second most important error comes from the uncertainty on the efficiency ε. The track detection efficiency uncertainty is estimated to be 0.8% per track from a study of a variety of control samples, such as τ → 3-track decays. We assign 0.5% uncertainty on the kaon identification efficiency. The uncertainty on the re-construction efficiency for the π0 _{is 3%, as measured in a}

large sample of τ− _{→ ρ}−_ν

τ, ρ− → π−π0 decays coming

from e+_e−_{→ τ}+_τ−_{. We assign a 1.8% uncertainty on the}

L2/L0cut efficiency, estimated by the difference between

Monte Carlo and data control samples, 1.1% on the total number of Υ (4S) → B ¯B decays in the sample and 1.2% on the knowledge of B(π0

→ γγ) and B(φ → K+_K−_).

We estimate the systematic error introduced by the ap-proximation of ignoring interference effects between the φ and the K+_K−_{S-wave components by varying the}

rel-ative strong phases and taking the largest observed vari-ation as the error. In this study we include the f0(980)

resonance and a non-resonant component, whose contri-bution is taken from a B+ _{→ K}+_K−_K+ _{Dalitz plot}

measurement by the Belle Collaboration[19]. The result-ing uncertainty is 4.4% for both modes.

Under the assumption that NB ¯B and ε are distributed

as Gaussians, we obtain a likelihood function, LB, for

the branching fraction, B, based on Eq. 4, by convolving the likelihood (L in Eq. 3) with the distributions of NB ¯B

and ε. We also include the additional uncertainty coming from the systematic error on the signal yield. The result-ing likelihood is shown in Fig. 3 for each of the two decay modes. In the plots, the upper boundary of the dark re-gion represents the 90% probability Bayesian upper limit BUL, defined as: Z BUL 0 LB(B)dB = 9 10 Z +∞ 0 LB(B)dB (5) We determine B(B+ → φπ+ ) < 2.4 × 10−7 _{and B(B}0 → φπ0 ) < 2.8 × 10−7_.

We compute the central values for the branching frac-tions by correcting the fitted signal yields for the fit bias, estimated using a large number of simulated ex-periments, and including a systematic uncertainty equiv-alent to half the fit bias. This error corresponds to a shift of −0.8 and −0.4 events in the signal yield, and −1.9 × 10−8 _{and −1.2 × 10}−8 _{in the branching fraction}

for B+ _{→ φπ}+ _{and B}0 _{→ φπ}0_{, respectively. Without}

taking into account the a priori knowledge of NS > 0

and NS−wave > 0, and integrating the likelihood in

Eq. 3 around the median, we obtain as 68%-probability regions B(B+

→ φπ+

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8 ] -6 )[10 + π φ BF ( 0 0.2 0.4 0.6 0.8 1 Probability density 0 2 4 6 ] -6 )[10 + π φ BF (φπ+)[10-6] BF (

B

A

B

AR ] -6 )[10 0 π φ BF ( 0 0.2 0.4 0.6 0.8 1 Probability density 0 2 4 ] -6 )[10 0 π φ BF (φπ0)[10-6] BF (

B

A

B

AR

FIG. 3: Likelihood distribution, LB(B), for B(B+ → φπ+)

(left) and B(B0

→ φπ0

) (right) in arbitrary units. The upper boundary of the dark region represents the 90% probability upper limit.

B(B0 _{→ φπ}0_{) = (0.12 ± 0.13) × 10}−6_{. The results are}

summarized in Table I.

In summary we have searched for B+ _{→ φπ}+ _and

B0

→ φπ0 _{decays in a sample of 232 million BB}

me-son pairs. We find no evidence of signal and therefore we place upper limits B(B+

→ φπ+

) < 2.4 × 10−7 _and

B(B0

→ φπ0

) < 2.8 × 10−7 _{at 90% probability. These}

limits are more stringent than earlier results [5, 6, 7] and they supersede our previous publications [5, 6]. They are consistent with existing SM predictions [1].

We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BA_BAR_{. The collaborating}

institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Indi-viduals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

∗ _Also _at _Laboratoire _de _Physique _{Corpusculaire,}

Clermont-Ferrand, France

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

Perugia, Italy

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

[1] S. Bar-Shalom, G. Eilam and Y. D. Yang, Phys. Rev. D 67, 014007 (2003).

[2] Throughout this paper, charge conjugate reactions are included implicitly and φ refers to the φ(1020).

[3] See for example A. J. Buras and L. Silvestrini, Nucl. Phys. B 569 3 (2000).

[4] Y. Grossman et al., Phys. Rev. D 68, 015004 (2003). [5] BABARCollaboration, B. Aubert et al., Phys. Rev. D 69

011102 (2004).

[6] BABARCollaboration, B. Aubert et al., Phys. Rev. D 70 032006 (2004).

[7] CLEO Collaboration, T. Bergfeld et al., Phys. Rev. Lett. 81, 272 (1998).

[8] BABAR _{Collaboration, B. Aubert et al., Nucl. Instr.} Methods Phys. Res., Sect. A 479, 1 (2002).

[9] PEP-II Conceptual Design Report, SLAC-R-418 (1993). [10] D. J. Lange, Nucl. Instr. Methods Phys. Res., Sect.

A 462, 152 (2001).

[11] GEANT Collaboration, S. Agostinelli et al., Nucl. Instr. Methods Phys. Res., Sect. A 506, 250 (2003).

[12] Particle Data Group, S. Eidelman et al. Phys. Lett. B 592, 1 (2004).

[13] BABARCollaboration, B. Aubert et al. Phys. Rev. D 71, 091102 (2005)

[14] BABARCollaboration, B. Aubert et al., Phys. Rev. Lett. 91, 241801 (2003).

[15] S. Flatt´e, Phys. Lett. B 63, 224 (1976).

[16] V. Baru, J. Haidenbauer, C. Hanhart, A. Kudryavtsev and U. G. Meissner, Eur. Phys. J. A 23, 523 (2005). [17] X. Shen, Int. J. Mod. Phys. A 20 1706 (2005).

[18] BABARCollaboration, B. Aubert et al., Phys. Rev. D 69, 071101 (2004).

[19] Belle Collaboration, A. Garmash et al., Phys. Rev. D 71, 092003 (2005).