Branching Fraction Limits for $B^0$ Decays to $\eta^' \eta, \eta^' \pi^0$ and $\eta \pi^0$

arXiv:hep-ex/0603013v2 8 Mar 2006

SLAC-PUB-11735

Branching Fraction Limits for B

Decays to η

_{η, η}

_π

and ηπ

B. Aubert,1 _{R. Barate,}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. S. Best,}6 _{D. N. Brown,}6_{J. Button-Shafer,}6 R. N. Cahn,6 E. Charles,6 C. T. Day,6M. S. Gill,6 A. V. Gritsan,6, ∗Y. Groysman,6 R. G. Jacobsen,6J. 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 _{M. Fritsch,}8 _{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 A. Buzykaev,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 _{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 D. del Re,16 _{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 _{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,18P. Spradlin,18D. C. Williams,18 M. G. Wilson,18 J. Albert,19 E. Chen,19 G. P. Dubois-Felsmann,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_{E. A. Antillon,}21 _{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,22D. D. Altenburg,23 E. Feltresi,23 A. Hauke,23H. Jasper,23B. Spaan,23 T. Brandt,24 V. Klose,24 _{H. M. Lacker,}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 _{Y. Xie,}26_{M. Andreotti,}27 D. Bettoni,27 _{C. Bozzi,}27 _{R. Calabrese,}27 _{G. Cibinetto,}27 _{E. Luppi,}27 _{M. Negrini,}27 _{L. Piemontese,}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 _{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 _{W. F. Mader,}33 _{U. Mallik,}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 _{G. Schott,}35

N. Arnaud,36 _{M. Davier,}36 _{G. Grosdidier,}36_{A. H¨ocker,}36 _{F. Le Diberder,}36 _{V. Lepeltier,}36 _{A. M. Lutz,}36 A. Oyanguren,36_{T. C. Petersen,}36 _{S. Pruvot,}36 _{S. Rodier,}36 _{P. Roudeau,}36_{M. H. Schune,}36 _{A. Stocchi,}36 W. F. Wang,36 G. Wormser,36 C. H. Cheng,37D. J. Lange,37D. M. Wright,37C. A. Chavez,38 I. J. Forster,38 J. R. Fry,38 _{E. Gabathuler,}38 _{R. Gamet,}38_{K. A. George,}38 _{D. E. Hutchcroft,}38 _{D. J. Payne,}38 _{K. C. Schofield,}38

C. Touramanis,38 _{A. J. Bevan,}39 _{F. Di Lodovico,}39 _{W. Menges,}39 _{R. Sacco,}39 _{C. L. Brown,}40_{G. Cowan,}40 H. U. Flaecher,40 _{D. A. Hopkins,}40_{P. S. Jackson,}40_{T. R. McMahon,}40_{S. Ricciardi,}40_{F. Salvatore,}40_{D. N. Brown,}41

C. L. Davis,41 _{J. Allison,}42 _{N. R. Barlow,}42 _{R. J. Barlow,}42 _{Y. M. Chia,}42 _{C. L. Edgar,}42_{M. P. Kelly,}42 G. D. Lafferty,42 _{M. T. Naisbit,}42 _{J. C. Williams,}42 _{J. I. Yi,}42 _{C. Chen,}43 _{W. D. Hulsbergen,}43 _{A. Jawahery,}43

D. Kovalskyi,43 _{C. K. Lae,}43_{D. A. Roberts,}43 _{G. Simi,}43 _{G. Blaylock,}44_{C. Dallapiccola,}44 _{S. S. Hertzbach,}44 X. Li,44_{T. B. Moore,}44_{S. Saremi,}44 _{H. Staengle,}44_{S. Y. Willocq,}44 _{R. Cowan,}45_{K. Koeneke,}45 _{G. Sciolla,}45 S. J. Sekula,45 _{M. Spitznagel,}45 _{F. Taylor,}45_{R. K. Yamamoto,}45_{H. Kim,}46 _{P. M. Patel,}46 _{C. T. Potter,}46 S. H. Robertson,46 _{A. Lazzaro,}47_{V. Lombardo,}47_{F. Palombo,}47 _{J. M. Bauer,}48 _{L. Cremaldi,}48 _{V. Eschenburg,}48

R. Godang,48 _{R. Kroeger,}48 _{J. Reidy,}48 _{D. A. Sanders,}48_{D. J. Summers,}48_{H. W. Zhao,}48 _{S. Brunet,}49_{D. Cˆot´e,}49 M. Simard,49 _{P. Taras,}49_{F. B. Viaud,}49 _{H. Nicholson,}50_{N. Cavallo,}51, § _{G. De Nardo,}51 _{F. Fabozzi,}51, §_{C. Gatto,}51

L. Lista,51 _{D. Monorchio,}51_{D. Piccolo,}51 _{C. Sciacca,}51_{M. Baak,}52 _{H. Bulten,}52 _{G. Raven,}52 _{H. L. Snoek,}52 C. P. Jessop,53 _{J. M. LoSecco,}53 _{T. Allmendinger,}54_{G. Benelli,}54 _{K. K. Gan,}54 _{K. Honscheid,}54 _{D. Hufnagel,}54

P. D. Jackson,54 _{H. Kagan,}54 _{R. Kass,}54_{T. Pulliam,}54 _{A. M. Rahimi,}54 _{R. Ter-Antonyan,}54 _{Q. K. Wong,}54 N. L. Blount,55 _{J. Brau,}55 _{R. Frey,}55 _{O. Igonkina,}55_{M. Lu,}55 _{R. Rahmat,}55 _{N. B. Sinev,}55 _{D. Strom,}55 J. Strube,55 _{E. Torrence,}55_{F. Galeazzi,}56_{A. Gaz,}56_{M. Margoni,}56 _{M. Morandin,}56_{A. Pompili,}56 _{M. Posocco,}56 M. Rotondo,56 _{F. Simonetto,}56 _{R. Stroili,}56 _{C. Voci,}56_{M. Benayoun,}57_{J. Chauveau,}57_{P. David,}57_{L. Del Buono,}57

Ch. de la Vaissi`ere,57<sub>O. Hamon,</sub>57 <sub>B. L. Hartfiel,</sub>57<sub>M. J. J. John,</sub>57 <sub>Ph. Leruste,</sub>57 <sub>J. Malcl`es,</sub>57 _{J. Ocariz,}57 L. Roos,57 _{G. Therin,}57 _{P. K. Behera,}58 _{L. Gladney,}58 _{J. Panetta,}58_{M. Biasini,}59 _{R. Covarelli,}59 _{M. Pioppi,}59 C. Angelini,60 _{G. Batignani,}60 _{S. Bettarini,}60 _{F. Bucci,}60_{G. Calderini,}60 _{M. Carpinelli,}60 _{R. Cenci,}60 _{F. Forti,}60 M. A. Giorgi,60A. Lusiani,60 G. Marchiori,60M. A. Mazur,60M. Morganti,60 N. Neri,60 E. Paoloni,60M. Rama,60

G. Rizzo,60 _{J. Walsh,}60 _{M. Haire,}61_{D. Judd,}61 _{D. E. Wagoner,}61 _{J. Biesiada,}62 _{N. Danielson,}62 _{P. Elmer,}62 Y. P. Lau,62 _{C. Lu,}62 _{J. Olsen,}62_{A. J. S. Smith,}62 _{A. V. Telnov,}62_{F. Bellini,}63_{G. Cavoto,}63_{A. D’Orazio,}63_{E. Di}

Marco,63_{R. Faccini,}63_{F. Ferrarotto,}63_{F. Ferroni,}63 _{M. Gaspero,}63_{L. Li Gioi,}63 _{M. A. Mazzoni,}63 _{S. Morganti,}63 G. Piredda,63 _{F. Polci,}63 _{F. Safai Tehrani,}63_{C. Voena,}63 _{H. Schr¨oder,}64 _{R. Waldi,}64_{T. Adye,}65 _{N. De Groot,}65 B. Franek,65 _{E. O. Olaiya,}65_{F. F. Wilson,}65 _{S. Emery,}66_{A. Gaidot,}66 _{S. F. Ganzhur,}66_{G. Hamel de Monchenault,}66

W. Kozanecki,66 _{M. Legendre,}66 _{B. Mayer,}66_{G. Vasseur,}66 _{Ch. Y`eche,}66_{M. Zito,}66 _{W. Park,}67_{M. V. Purohit,}67 A. W. Weidemann,67 _{J. R. Wilson,}67 _{M. T. Allen,}68 _{D. Aston,}68 _{R. Bartoldus,}68 _{P. Bechtle,}68_{N. Berger,}68 A. M. Boyarski,68 _{R. Claus,}68_{J. P. Coleman,}68_{M. R. Convery,}68_{M. Cristinziani,}68 _{J. C. Dingfelder,}68 _{D. Dong,}68

J. Dorfan,68 _{D. Dujmic,}68 _{W. Dunwoodie,}68_{R. C. Field,}68_{T. Glanzman,}68 _{S. J. Gowdy,}68 _{V. Halyo,}68 _{C. Hast,}68 T. Hryn’ova,68_{W. R. Innes,}68 _{M. H. Kelsey,}68_{P. Kim,}68 _{M. L. Kocian,}68_{D. W. G. S. Leith,}68 _{J. Libby,}68_{S. Luitz,}68

V. Luth,68 _{H. L. Lynch,}68 _{D. B. MacFarlane,}68 _{H. Marsiske,}68_{R. Messner,}68 _{D. R. Muller,}68 _{C. P. O’Grady,}68 V. E. Ozcan,68 _{A. Perazzo,}68_{M. Perl,}68 _{B. N. Ratcliff,}68 _{A. Roodman,}68 _{A. A. Salnikov,}68 _{R. H. Schindler,}68 J. Schwiening,68_{A. Snyder,}68 _{J. Stelzer,}68_{D. Su,}68_{M. K. Sullivan,}68 _{K. Suzuki,}68_{S. K. Swain,}68_{J. M. Thompson,}68

J. Va’vra,68 _{N. van Bakel,}68 _{M. Weaver,}68 _{A. J. R. Weinstein,}68 _{W. J. Wisniewski,}68 _{M. Wittgen,}68 D. H. Wright,68 _{A. K. Yarritu,}68 _{K. Yi,}68 _{C. C. Young,}68 _{P. R. Burchat,}69 _{A. J. Edwards,}69 _{S. A. Majewski,}69

B. A. Petersen,69 _{C. Roat,}69 _{L. Wilden,}69 _{S. Ahmed,}70 _{M. S. Alam,}70 _{R. Bula,}70 _{J. A. Ernst,}70 _{V. Jain,}70 B. Pan,70 _{M. A. Saeed,}70 _{F. R. Wappler,}70 _{S. B. Zain,}70 _{W. Bugg,}71 _{M. Krishnamurthy,}71 _{S. M. Spanier,}71 R. Eckmann,72_{J. L. Ritchie,}72_{A. Satpathy,}72_{R. F. Schwitters,}72 _{J. M. Izen,}73 _{I. Kitayama,}73_{X. C. Lou,}73_{S. Ye,}73

F. Bianchi,74_{M. Bona,}74_{F. Gallo,}74 _{D. Gamba,}74 _{M. Bomben,}75 _{L. Bosisio,}75 _{C. Cartaro,}75_{F. Cossutti,}75 G. Della Ricca,75 _{S. Dittongo,}75_{S. Grancagnolo,}75_{L. Lanceri,}75_{L. Vitale,}75 _{V. Azzolini,}76_{F. Martinez-Vidal,}76

R. S. Panvini,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 M. T. Graham,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, Fac. Fisica Dept. ECM,}

Avda Diagonal 647, 6a planta, 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}

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</sub> 28<sub>Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy</sub> 29<sub>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_{Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany} 36_{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 37_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA}

38_{University of Liverpool, Liverpool L69 7ZE, United Kingdom} 39_{Queen Mary, University of London, E1 4NS, United Kingdom}

40_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom} 41_{University of Louisville, Louisville, Kentucky 40292, USA}

42_{University of Manchester, Manchester M13 9PL, United Kingdom} 43_{University of Maryland, College Park, Maryland 20742, USA} 44_{University of Massachusetts, Amherst, Massachusetts 01003, USA}

45_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA} 46_{McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8}

47_{Universit`a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy} 48_{University of Mississippi, University, Mississippi 38677, USA}

49_{Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7} 50_{Mount Holyoke College, South Hadley, Massachusetts 01075, USA}

51_{Universit`a di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy}

52_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands} 53_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

54_{Ohio State University, Columbus, Ohio 43210, USA} 55_{University of Oregon, Eugene, Oregon 97403, USA}

56_{Universit`a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy}

57_{Universit´es Paris VI et VII, Laboratoire de Physique Nucl´eaire et de Hautes Energies, F-75252 Paris, France} 58_{University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA}

59_{Universit`a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy}

60_{Universit`a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy} 61_{Prairie View A&M University, Prairie View, Texas 77446, USA}

62_{Princeton University, Princeton, New Jersey 08544, USA}

63_{Universit`a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy} 64_{Universit¨at Rostock, D-18051 Rostock, Germany}

65_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom} 66_{DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France}

67_{University of South Carolina, Columbia, South Carolina 29208, USA} 68_{Stanford Linear Accelerator Center, Stanford, California 94309, USA}

69_{Stanford University, Stanford, California 94305-4060, USA} 70_{State University of New York, Albany, New York 12222, USA}

71_{University of Tennessee, Knoxville, Tennessee 37996, USA} 72_{University of Texas at Austin, Austin, Texas 78712, USA} 73_{University of Texas at Dallas, Richardson, Texas 75083, USA}

74_{Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy</sub> 75<sub>Universit`a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy}

76_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain} 77_{Vanderbilt University, Nashville, Tennessee 37235, USA} 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: January 28, 2018)

We describe searches for decays to two-body charmless final states η′_{η, η}′_π0_{and ηπ}0_{of B}0 _mesons produced in e+_e− _{annihilation. The data, collected with the BABAR detector at the Stanford} Linear Accelerator Center, represent 232 million produced BB pairs. The results for branching fractions are, in units of 10−6 _{(upper limits at 90% C.L.): B(B}0 _→η′_{η) = 0.2}+0.7

−0.5±0.4 (< 1.7), B(B0 _→ηπ0_{) = 0.6}+0.5

−0.4±0.1 (< 1.3), and B(B

0 _→η′_π0_{) = 0.8}+0.8

−0.6±0.1 (< 2.1). The first error quoted is statistical and the second systematic.

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

We present the results of searches for neutral B me-son decays to η′_{η, ηπ}0 _{and η}′_π0_{, with a data sample} expanded by about a factor of 2.6 over the one used for our previous measurements [1, 2]. In the Standard Model (SM) the processes that contribute to these de-cays are described by color-suppressed tree and one-loop gluonic, electroweak or flavor-singlet penguin amplitudes. For B0 _{→ η}′_π0 _{and B}0_{→ ηπ}0 _{the color-suppressed tree} diagram is also suppressed by approximate cancellation between the amplitudes for the π0 _{and for the isoscalar} meson to contain the spectator quark, resulting from the mesons’ isospin couplings to the quarks. Estimates of the branching fractions for these modes have been obtained from calculations based on QCD factorization [3, 4], per-turbative QCD (for B0 _{→ η}(′)_π0_{) [5], soft collinear} ef-fective theory [6], and flavor-SU(3) symmetry [7, 8]. The expectations lie in the approximate ranges 0.2–1.0 ×10−6 for B0→ η(′)π0, and 0.3–2 × 10−6 for B0→ η′_η.

These decays are also of interest in constraining the ex-pected value of the time-dependent CP -violation asym-metry parameter Sfin the decay with f = η′KS0[7, 9, 10]. The leading-order SM calculation gives the equality Sη′K0

S = SJ/ψK 0

S, where the latter has been precisely measured [11], and equals sin2β in the SM. The CP asym-metry in the charmless modes is sensitive to contributions from new physics, but also to contamination from sub-leading SM amplitudes. The most stringent constraint on such contamination in Sη′K0

S comes from the mea-sured branching fractions of the three decay modes stud-ied in this paper [7, 9, 10]. Recently it has also been suggested [12, 13] that B0_{→ η}′_π0 _{and B}0_{→ ηπ}0_{can be} used to constrain the contribution from isospin-breaking effects on the value of sin2α in B → π+_π− _decays.

The results presented here are based on data col-lected with the BA_BAR_{detector [14] at the PEP-II}

asym-metric e+_e− _{collider [15] located at the Stanford} Lin-ear Accelerator Center. An integrated luminosity of 211 fb−1, corresponding to 232 × 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

TABLE I: Selection requirements on the invariant masses of resonances and the laboratory energies of photons from their decay.

State Invariant mass (MeV) E(γ) (MeV) π0 _{120 < m(γγ) < 150 > 50} ηγγ 490 < m(γγ) < 600 > 100 η3π 520 < m(π+π−π0) < 570 > 30 η′ ηππ 910 < m(π+π−η) < 1000 > 100 η′ ργ 910 < m(π+π−γ) < 1000 > 200 ρ0 _{510 < m(π}+_π−_{) < 1000 —}

and a 40-layer drift chamber, both operating in the 1.5 T magnetic field of a superconducting solenoid. Photons and electrons are identified with a CsI(Tl) electromag-netic calorimeter (EMC). Further charged particle iden-tification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally re-flecting ring imaging Cherenkov detector (DIRC) cover-ing the central region.

We establish the event selection criteria with the aid of a detailed Monte Carlo (MC) simulation of the B produc-tion and decay sequences, and of the detector response [16]. These criteria are designed to retain signal events with high efficiency. Applied to the data, they result in a sample much larger than the expected signal, but with well characterized backgrounds. We extract the sig-nal yields from this sample with a maximum likelihood (ML) fit.

The B-daughter candidates are reconstructed through their decays π0_{→ γγ, η → γγ (η}

γγ), η → π+π−π0(η3π), η′ _{→ η}

γγπ+π− (η′ηππ), and additionally for η′η modes, η′ _{→ ρ}0_{γ (η}′

ργ), where ρ0→ π+π−. Table I lists the re-quirements on the invariant mass of these particles’ final states. Secondary charged pions in η′ _{and η candidates} are rejected if classified as protons, kaons, or electrons by their DIRC, dE/dx, and EMC PID signatures.

We reconstruct the B-meson candidate by combining the four-momenta of a pair of daughter mesons, with a vertex constraint if the ultimate final state includes at least two charged particles. Since the natural widths of the η, η′_{, and π}0 _{are much smaller than the resolution,}

we also constrain their masses to nominal values [17] in the fit of the B candidate. From the kinematics of Υ (4S) decay we determine the energy-substituted mass mES= q

1

4s − p2Band energy difference ∆E = EB−1₂√s, where (EB, pB) is the B-meson 4-momentum vector, and all values are expressed in the Υ (4S) frame. The resolution in mES is 3.0 MeV and in ∆E is 24–50 MeV, depending on the decay mode. We require 5.25 GeV < mES < 5.29 GeV and |∆E| < 0.3 GeV (< 0.2 GeV for η′_η).

Backgrounds arise primarily from random combina-tions of particles in continuum e+_e− _{→ qq events (q =} u, d, s, c). We reduce these with requirements on the an-gle θT between the thrust axis of the B candidate in the Υ (4S) frame and that of the rest of the charged tracks and neutral calorimeter clusters in the event. The distribution is sharply peaked near | cos θT| = 1 for qq jet pairs, and nearly uniform for B-meson decays. The requirement, which optimizes the expected signal yield relative to its background-dominated statistical error, is | cos θT| < 0.7–0.9 depending on the mode.

In the ML fit we discriminate further against qq back-ground with a Fisher discriminant F that combines sev-eral variables which characterize the energy flow in the event [1]. It provides about one standard deviation of separation between B decay events and combinatorial background (see Fig. 1d).

We also impose restrictions on decay angles to exclude the most asymmetric decays where soft-particle back-grounds concentrate and the acceptance changes rapidly. We define the decay angle θk

dec for a meson k as the an-gle between the momenta of a daughter particle and the meson’s parent, measured in the meson’s rest frame. We require for the η′

ργ decays | cos θdecρ | < 0.9 and for η(′)π0 | cos θπ0

dec| < 0.95. For B0 → ηργ′ ηγγ the requirement is | cos θdecη | < 0.86 to suppress the background B → K∗γ.

The average number of candidates found per selected event is in the range 1.06 to 1.23, depending on the final state. We choose the candidate with the smallest value of a χ2 _{constructed from the deviations from expected} values of one or more of the daughter resonance masses. From the simulation we find that this algorithm selects the correct-combination candidate in about two thirds of the events containing multiple candidates, and that it induces negligible bias.

We obtain yields for each channel from a maximum likelihood fit with the input observables ∆E, mES, F, and m1,(2), the daughter invariant mass spectrum of the η and/or η′ _{candidate. The selected sample sizes are} given in the second column of Table II. Besides any sig-nal events they contain qq (dominant) and BB with b → c combinatorial background, and a fraction that we estimate from the simulation to be less than 0.2% of feed-across from other charmless BB modes. The latter events have ultimate final states different from the sig-nal, but with similar kinematics so that broad peaks near

those of the signal appear in some observables, requiring a separate component in the probability density function (PDF). The likelihood function is

L = exp (−X j Yj) N Y i X j Yj× (1) Pj(mESi)Pj(∆Ei)Pj(Fi)Pj(mi1)Pj(mi2) , where N is the number of events in the sample, and for each component j, Yj is the yield of events and Pj(xi) the PDF for observable x in event i. For the modes B0 _{→ η}′

ηππη we found no need for the BB background component. The factored form of the PDF indicated in Eq. 1 is a good approximation, particularly for the combi-natorial qq component, since correlations among observ-ables measured in the data (dominantly this component) are small. Distortions of the fit results caused by this approximation are measured in simulation and included in the bias corrections and systematic errors discussed below.

We determine the PDFs for the signal and BB back-ground components from fits to MC data. We calibrate the resolutions in ∆E and mESwith large control samples of B decays to charmed final states of similar topology (e.g. B → D(Kππ)π). For the combinatorial background the PDFs are determined in the fits to the data. However the functional forms are first deduced from fits of that component alone to sidebands in (mES, ∆E), so that we can validate the fit before applying it to data containing the signal.

We use the following functional forms for the PDFs: sum of two Gaussians for Psig(mES), P_sig,BB(∆E), and the sharper structures in PBB(mES) and Pj(mk); lin-ear or quadratic dependences for combinatorial compo-nents of PBB,qq(mk) and for Pqq(∆E); and a conjunc-tion of two Gaussian segments below and above the peak with different widths, plus a broad Gaussian, for Pj(F). The qq background in mESis described by the function x√1 − x2_{exp−ξ(1 − x}2_{), with x ≡ 2m}

ES/√s and pa-rameter ξ. These are discussed in more detail in [1], and some of them are illustrated in Fig. 1.

We allow the parameters most important for the de-termination of the combinatorial background PDFs to vary in the fit, along with the yields for all components. Specifically, the free background parameters are most or all of the following, depending on the decay mode: ξ for mES, linear and quadratic coefficients for ∆E, area and slope of the combinatorial component for mk, and the mean, width, and width difference parameters for F. Results for the yields are presented in the third column of Table II for each sample.

We test and calibrate the fitting procedure by apply-ing it to ensembles of simulated qq experiments drawn from the PDF into which we have embedded the expected number of signal and BB background events randomly

TABLE II: Number of events N in the sample, fitted signal yield YS in events (ev.), measured bias, detection efficiency ǫ, daughter branching fraction product (Q B_{i), and measured branching fraction B with statistical error for each decay chain, and} for the combined measurements the significance S (with systematic uncertainties included), branching fraction with statistical and systematic error, and in parentheses the 90% C.L. upper limits. The number of produced BB pairs is (231.8 ± 2.6) × 106_.

Mode N (ev.) YS (ev.) Bias (ev.) ǫ (%)Q Bi (%) S (σ) B(10−6) η′ ηππη3π 539 2.0+3.1−2.0 1.9 ± 1.0 13.8 3.95 0.1 +2.4 −1.6 η′ ηππηγγ 1448 2.1+3.5−2.2 0.7 ± 0.4 22.3 6.89 0.4 +1.0 −0.6 η′ ργη3π 8268 −8.6+8.7−7.0 0.0 ± 0.4 14.9 6.67 −3.8 +3.8 −3.0 η′ ργηγγ 16861 1.5+10.5−8.5 0.0 ± 0.5 21.8 11.63 0.2 +1.8 −1.4 η′_{η 0.4 0.2}+0.7 −0.5± 0.4 (<1.7) η3ππ0 2334 10.3+8.6−6.7 1.2 ± 0.7 16.3 22.6 1.1 +1.0 −0.8 ηγγπ0 5493 6.5+11.5−9.6 1.2 ± 0.8 20.7 39.4 0.3 +0.6 −0.5 ηπ0 1_.3 0_.6+0.5 −0.4± 0.1 (<1.3) η′_π0 _{3663 7.9}+6.9 −5.2 1.2 ± 0.6 17.5 17.5 1.4 0.8 +0.8 −0.6± 0.1 (<2.1)

extracted from the fully simulated MC samples. We find biases of 0–2 events, somewhat dependent on the signal size. The bias values obtained for simulations that repro-duce the yields found in the data are given in the fourth column of Table II.

In Fig. 1 we show, as representative of the sev-eral fits, the projections of the PDF and data for the B0 _{→ η}′

ηπππ0 sample. The goodness-of-fit is further demonstrated by the distribution of the likelihood ratio Lsig/[Lsig+P Lbkg] for data and for simulation gener-ated from the PDF model, shown for the same decay mode in Fig. 2. We see good agreement between the model and the data. By construction the background is concentrated near zero, while any signal would appear in a peak near one.

We determine the reconstruction efficiencies, given in Table II, as the ratio of reconstructed and accepted events in simulation to the number generated. We com-pute the branching fraction for each channel by subtract-ing the fit bias from the measured yield, and dividsubtract-ing the result by the efficiency and the number of produced BB pairs [1]. We assume equal decay rates of the Υ (4S) to B+_B− _{and B}0_B0_{. Table II gives the numbers pertinent} to these computations. The statistical error on the signal yield or branching fraction is taken as the change in the central value when the quantity −2 ln L increases by one unit from its minimum value.

We combine results where we have multi-ple decay channels by adding the functions −2 ln {[L(B)/L(B0)] ⊗ G(B; 0, σ′)}, where B0 is the central value from the fit, σ′ _{is the systematic} uncer-tainty, and ⊗G denotes convolution with a Gaussian function. We give the resulting final branching fractions for each mode in Table II with the significance, taken as the square root of the difference between the value of −2 ln L (with additive systematic uncertainties included) for zero signal and the value at its minimum. The 90% C.L. upper limits are taken to be the branching fraction

E [GeV] ∆ -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Events / 40 MeV 0 50 100 150 200 250 300 350 400 E [GeV] ∆ -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Events / 40 MeV 0 50 100 150 200 250 300 350 400 (a) [GeV] ES m 5.25 5.26 5.27 5.28 5.29 Events / 2 MeV 0 50 100 150 200 250 300 [GeV] ES m 5.25 5.26 5.27 5.28 5.29 Events / 2 MeV 0 50 100 150 200 250 300 (b) [GeV] ’ η m 0.92 0.94 0.96 0.98 1 Events / 2.5 MeV 0 20 40 60 80 100 120 140 160 180 200 [GeV] ’ η m 0.92 0.94 0.96 0.98 1 Events / 2.5 MeV 0 20 40 60 80 100 120 140 160 180 200 (c) Fisher discriminant -3 -2 -1 0 1 2 3 4 Events / bin 0 100 200 300 400 500 600 Fisher discriminant -3 -2 -1 0 1 2 3 4 Events / bin 0 100 200 300 400 500 600 (d)

FIG. 1: Plots of the B0_→η′

ηπππ0data distribution projected on each of the fit variables: (a) ∆E, (b) mES, (c) η′mass, and (d) F. The solid line represents the result of the fit, and the dashed line the background contribution. (The absence of signal here nearly hides the dashed curve.) The dotted line il-lustrates the expected shape for signal, normalized arbitrarily to the data.

below which lies 90% of the total of the likelihood integral in the positive branching fraction region.

The systematic uncertainties on the branching frac-tions arising from lack of knowledge of the PDFs have been included in part in the statistical error since most background parameters are free in the fit. For the signal, the uncertainties in PDF parameters are estimated from the consistency of fits to MC and data in control modes. Varying the signal-PDF parameters within these errors, we estimate yield uncertainties of 0–2 events, depend-ing on the mode. The uncertainty from fit bias (Table

Likelihood ratio

Events / bin

Likelihood ratio

Events / bin

FIG. 2: The likelihood ratio Lsig/[Lsig+P Lbkg] for B0 → η′

ηπππ

0_{. The open circles represent an arbitrarily large} sim-ulated signal component, the solid points represent the data, the solid histograms are from toy samples of background (shaded) and background plus signal (white, barely visible in the rightmost bins, given the small signal yield).

II) includes its statistical uncertainty from the simulated experiments, and half of the correction itself, added in quadrature. Similarly we estimate the uncertainty from modeling the BB backgrounds by taking half of the con-tribution of that component to the fitted signal yield, 0.2–1.2 events. These additive systematic errors are dom-inant for these modes with little or no signal yield.

Uncertainties in our knowledge of the efficiency, found from auxiliary studies, include 0.8% × Ntand 1.5% × Nγ, where Ntand Nγ are the number of tracks and photons, respectively, in the B candidate. The uncertainty in the total number of BB pairs in the data sample is 1.1%. Published data [17] provide the uncertainties in the B-daughter product branching fractions (0.7–3.9%). The uncertainties in the efficiency from the event selection are about 1% .

After combining the measurements we obtain the cen-tral values and 90% C.L. upper limits for the branching fractions: B(B0_{→ η}′_{η) = (0.2}+0.7 −0.5± 0.4) × 10−6 (< 1.7 × 10−6), B(B0→ ηπ0) = (0.6+0.5−0.4± 0.1) × 10−6 (< 1.3 × 10−6), and B(B0_{→ η}′_π0_{) = (0.8}+0.8 −0.6± 0.1) × 10−6 (< 2.1 × 10−6). We find no evidence for these decays, and our upper lim-its represent two to three-fold improvement over the pre-vious measurements [1, 2, 18]. The range of sensitivity of these measurements is comparable to the range of the theoretical estimates.

These results can be used to constrain the expected

value of the CP asymmetry Sfin relation to sin2β for the decay B0_{→ η}′_K0_{[7, 9, 10]. Using the method proposed} by Gronau et al. [10], we estimate that our results will provide approximately 20% improvement of the predic-tion for the contribupredic-tion of the color suppressed tree am-plitude in B0_{→ η}′_K0_{decays. This translates into a 20%} reduction of this theoretical uncertainty in Sη′K0

S. We find a similar improvement in the corresponding uncer-tainty of sin2α measured with B → π+_π−_{decays [12, 13].} 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 CONACyT (Mex-ico), Marie Curie EIF (European Union), the A. P. Sloan Foundation, the Research Corporation, and the Alexan-der von Humboldt Foundation.

∗ _{Also with the Johns Hopkins University, Baltimore,} Maryland 21218 , USA

† _{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} ¶ _Deceased

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