Search for the rare decay $B^0_s \rightarrow \phi \mu^+ \mu^-$ with the D0 detector

arXiv:hep-ex/0604015v1 6 Apr 2006

Search for the Rare Decay B

s

→ φ µ

+

_µ

with the DØ Detector

V.M. Abazov,36_{B. Abbott,}76 _{M. Abolins,}66_{B.S. Acharya,}29_{M. Adams,}52 _{T. Adams,}50 _{M. Agelou,}18 _{J.-L. Agram,}19 S.H. Ahn,31 _{M. Ahsan,}60 _{G.D. Alexeev,}36 _{G. Alkhazov,}40 _{A. Alton,}65_{G. Alverson,}64_{G.A. Alves,}2 _{M. Anastasoaie,}35

T. Andeen,54 _{S. Anderson,}46 _{B. Andrieu,}17 _{M.S. Anzelc,}54 _{Y. Arnoud,}14 _{M. Arov,}53 _{A. Askew,}50 _{B. ˚Asman,}41 A.C.S. Assis Jesus,3 _{O. Atramentov,}58_{C. Autermann,}21 _{C. Avila,}8 _{C. Ay,}24 _{F. Badaud,}13 _{A. Baden,}62_{L. Bagby,}53 B. Baldin,51 _{D.V. Bandurin,}36_{P. Banerjee,}29_{S. Banerjee,}29_{E. Barberis,}64_{P. Bargassa,}81_{P. Baringer,}59_{C. Barnes,}44 J. Barreto,2_{J.F. Bartlett,}51_{U. Bassler,}17_{D. Bauer,}44_{A. Bean,}59 _{M. Begalli,}3 _{M. Begel,}72_{C. Belanger-Champagne,}5

A. Bellavance,68_{J.A. Benitez,}66 _{S.B. Beri,}27 _{G. Bernardi,}17 _{R. Bernhard,}42 _{L. Berntzon,}15 _{I. Bertram,}43 M. Besan¸con,18 _{R. Beuselinck,}44_{V.A. Bezzubov,}39 _{P.C. Bhat,}51 _{V. Bhatnagar,}27 _{M. Binder,}25 _{C. Biscarat,}43 K.M. Black,63_{I. Blackler,}44_{G. Blazey,}53_{F. Blekman,}44_{S. Blessing,}50_{D. Bloch,}19 _{K. Bloom,}68 _{U. Blumenschein,}23

A. Boehnlein,51 _{O. Boeriu,}56 _{T.A. Bolton,}60 _{F. Borcherding,}51_{G. Borissov,}43 _{K. Bos,}34 _{T. Bose,}78_{A. Brandt,}79 R. Brock,66_{G. Brooijmans,}71 _{A. Bross,}51_{D. Brown,}79 _{N.J. Buchanan,}50 _{D. Buchholz,}54 _{M. Buehler,}82 V. Buescher,23_{S. Burdin,}51_{S. Burke,}46 _{T.H. Burnett,}83 _{E. Busato,}17 _{C.P. Buszello,}44 _{J.M. Butler,}63 _{S. Calvet,}15

J. Cammin,72 S. Caron,34W. Carvalho,3B.C.K. Casey,78N.M. Cason,56 H. Castilla-Valdez,33 S. Chakrabarti,29 D. Chakraborty,53_{K.M. Chan,}72_{A. Chandra,}49_{D. Chapin,}78 _{F. Charles,}19_{E. Cheu,}46 _{F. Chevallier,}14 _{D.K. Cho,}63

S. Choi,32 _{B. Choudhary,}28 _{L. Christofek,}59 _{D. Claes,}68 _{B. Cl´ement,}19_{C. Cl´ement,}41 _{Y. Coadou,}5_{M. Cooke,}81 W.E. Cooper,51 _{D. Coppage,}59 _{M. Corcoran,}81_{M.-C. Cousinou,}15_{B. Cox,}45_{S. Cr´ep´e-Renaudin,}14 _{D. Cutts,}78 M. ´Cwiok,30_{H. da Motta,}2 _{A. Das,}63_{M. Das,}61 _{B. Davies,}43 _{G. Davies,}44 _{G.A. Davis,}54 _{K. De,}79 _{P. de Jong,}34 S.J. de Jong,35 _{E. De La Cruz-Burelo,}65_{C. De Oliveira Martins,}3 _{J.D. Degenhardt,}65_{F. D´eliot,}18 _{M. Demarteau,}51

R. Demina,72 _{P. Demine,}18 _{D. Denisov,}51 _{S.P. Denisov,}39 _{S. Desai,}73 _{H.T. Diehl,}51 _{M. Diesburg,}51 _{M. Doidge,}43 A. Dominguez,68 _{H. Dong,}73 _{L.V. Dudko,}38_{L. Duflot,}16 _{S.R. Dugad,}29 _{A. Duperrin,}15_{J. Dyer,}66 _{A. Dyshkant,}53

M. Eads,68_{D. Edmunds,}66_{T. Edwards,}45 _{J. Ellison,}49 _{J. Elmsheuser,}25_{V.D. Elvira,}51 _{S. Eno,}62 _{P. Ermolov,}38 J. Estrada,51 _{H. Evans,}55 _{A. Evdokimov,}37_{V.N. Evdokimov,}39_{S.N. Fatakia,}63 _{L. Feligioni,}63_{A.V. Ferapontov,}60

T. Ferbel,72 _{F. Fiedler,}25_{F. Filthaut,}35 _{W. Fisher,}51 _{H.E. Fisk,}51 _{I. Fleck,}23 _{M. Ford,}45 _{M. Fortner,}53 _{H. Fox,}23 S. Fu,51_{S. Fuess,}51_{T. Gadfort,}83 _{C.F. Galea,}35 _{E. Gallas,}51 _{E. Galyaev,}56 _{C. Garcia,}72 _{A. Garcia-Bellido,}83

J. Gardner,59_{V. Gavrilov,}37 _{A. Gay,}19 _{P. Gay,}13 _{D. Gel´e,}19_{R. Gelhaus,}49 _{C.E. Gerber,}52 _{Y. Gershtein,}50 D. Gillberg,5 _{G. Ginther,}72 _{N. Gollub,}41 _{B. G´omez,}8 _{K. Gounder,}51 _{A. Goussiou,}56 _{P.D. Grannis,}73 H. Greenlee,51Z.D. Greenwood,61 E.M. Gregores,4 G. Grenier,20 Ph. Gris,13J.-F. Grivaz,16 S. Gr¨unendahl,51 M.W. Gr¨unewald,30 _{F. Guo,}73_{J. Guo,}73 _{G. Gutierrez,}51_{P. Gutierrez,}76 _{A. Haas,}71_{N.J. Hadley,}62 _{P. Haefner,}25

S. Hagopian,50 _{J. Haley,}69 _{I. Hall,}76 _{R.E. Hall,}48 _{L. Han,}7 _{K. Hanagaki,}51 _{K. Harder,}60 _{A. Harel,}72 R. Harrington,64 _{J.M. Hauptman,}58 _{R. Hauser,}66 _{J. Hays,}54_{T. Hebbeker,}21 _{D. Hedin,}53 _{J.G. Hegeman,}34 J.M. Heinmiller,52 _{A.P. Heinson,}49 _{U. Heintz,}63 _{C. Hensel,}59 _{G. Hesketh,}64_{M.D. Hildreth,}56 _{R. Hirosky,}82 J.D. Hobbs,73_{B. Hoeneisen,}12 _{M. Hohlfeld,}16 _{S.J. Hong,}31_{R. Hooper,}78 _{P. Houben,}34 _{Y. Hu,}73 _{V. Hynek,}9 I. Iashvili,70_{R. Illingworth,}51 _{A.S. Ito,}51 _{S. Jabeen,}63 _{M. Jaffr´e,}16 _{S. Jain,}76 _{K. Jakobs,}23 _{C. Jarvis,}62_{A. Jenkins,}44

R. Jesik,44_{K. Johns,}46 _{C. Johnson,}71 _{M. Johnson,}51 _{A. Jonckheere,}51 _{P. Jonsson,}44 _{A. Juste,}51 _{D. K¨afer,}21 S. Kahn,74_{E. Kajfasz,}15 _{A.M. Kalinin,}36_{J.M. Kalk,}61_{J.R. Kalk,}66_{S. Kappler,}21_{D. Karmanov,}38_{J. Kasper,}63 I. Katsanos,71_{D. Kau,}50 _{R. Kaur,}27_{R. Kehoe,}80 _{S. Kermiche,}15 _{S. Kesisoglou,}78_{A. Khanov,}77 _{A. Kharchilava,}70 Y.M. Kharzheev,36 _{D. Khatidze,}71_{H. Kim,}79 _{T.J. Kim,}31_{M.H. Kirby,}35 _{B. Klima,}51 _{J.M. Kohli,}27_{J.-P. Konrath,}23

M. Kopal,76 _{V.M. Korablev,}39 _{J. Kotcher,}74 _{B. Kothari,}71_{A. Koubarovsky,}38_{A.V. Kozelov,}39 _{J. Kozminski,}66 A. Kryemadhi,82 _{S. Krzywdzinski,}51 _{T. Kuhl,}24 _{A. Kumar,}70 _{S. Kunori,}62_{A. Kupco,}11 _{T. Kurˇca,}20,∗_{J. Kvita,}9 S. Lager,41_{S. Lammers,}71 _{G. Landsberg,}78_{J. Lazoflores,}50_{A.-C. Le Bihan,}19 _{P. Lebrun,}20_{W.M. Lee,}53_{A. Leflat,}38

F. Lehner,42 C. Leonidopoulos,71 V. Lesne,13 J. Leveque,46 P. Lewis,44J. Li,79 Q.Z. Li,51 J.G.R. Lima,53 D. Lincoln,51 _{J. Linnemann,}66_{V.V. Lipaev,}39 _{R. Lipton,}51_{Z. Liu,}5 _{L. Lobo,}44_{A. Lobodenko,}40_{M. Lokajicek,}11 A. Lounis,19 _{P. Love,}43_{H.J. Lubatti,}83 _{M. Lynker,}56_{A.L. Lyon,}51 _{A.K.A. Maciel,}2 _{R.J. Madaras,}47_{P. M¨attig,}26 C. Magass,21_{A. Magerkurth,}65_{A.-M. Magnan,}14_{N. Makovec,}16 _{P.K. Mal,}56 _{H.B. Malbouisson,}3 _{S. Malik,}68 V.L. Malyshev,36_{H.S. Mao,}6 _{Y. Maravin,}60 _{M. Martens,}51_{S.E.K. Mattingly,}78_{R. McCarthy,}73_{R. McCroskey,}46 D. Meder,24 A. Melnitchouk,67 A. Mendes,15 L. Mendoza,8 M. Merkin,38K.W. Merritt,51A. Meyer,21 J. Meyer,22

M. Michaut,18 _{H. Miettinen,}81 _{T. Millet,}20 _{J. Mitrevski,}71 _{J. Molina,}3 _{N.K. Mondal,}29 _{J. Monk,}45 _{R.W. Moore,}5 T. Moulik,59 _{G.S. Muanza,}16 _{M. Mulders,}51 _{M. Mulhearn,}71 _{L. Mundim,}3 _{Y.D. Mutaf,}73 _{E. Nagy,}15

M. Naimuddin,28 _{M. Narain,}63_{N.A. Naumann,}35 _{H.A. Neal,}65 _{J.P. Negret,}8 _{S. Nelson,}50 _{P. Neustroev,}40 C. Noeding,23 _{A. Nomerotski,}51 _{S.F. Novaes,}4 _{T. Nunnemann,}25 _{V. O’Dell,}51 _{D.C. O’Neil,}5 _{G. Obrant,}40 V. Oguri,3 _{N. Oliveira,}3_{N. Oshima,}51 _{R. Otec,}10 _{G.J. Otero y Garz´on,}52_{M. Owen,}45 _{P. Padley,}81 _{N. Parashar,}57

S.-J. Park,72 _{S.K. Park,}31_{J. Parsons,}71_{R. Partridge,}78 _{N. Parua,}73_{A. Patwa,}74_{G. Pawloski,}81 _{P.M. Perea,}49 E. Perez,18_{K. Peters,}45 _{P. P´etroff,}16 _{M. Petteni,}44 _{R. Piegaia,}1_{M.-A. Pleier,}22 _{P.L.M. Podesta-Lerma,}33 V.M. Podstavkov,51_{Y. Pogorelov,}56_{M.-E. Pol,}2_{A. Pompoˇs,}76 _{B.G. Pope,}66 _{A.V. Popov,}39_{W.L. Prado da Silva,}3 H.B. Prosper,50_{S. Protopopescu,}74 _{J. Qian,}65 _{A. Quadt,}22 _{B. Quinn,}67 _{K.J. Rani,}29_{K. Ranjan,}28_{P.A. Rapidis,}51 P.N. Ratoff,43 _{P. Renkel,}80_{S. Reucroft,}64 _{M. Rijssenbeek,}73 _{I. Ripp-Baudot,}19_{F. Rizatdinova,}77 _{S. Robinson,}44

R.F. Rodrigues,3 _{C. Royon,}18 _{P. Rubinov,}51 _{R. Ruchti,}56 _{V.I. Rud,}38 _{G. Sajot,}14 _{A. S´anchez-Hern´andez,}33 M.P. Sanders,62 _{A. Santoro,}3 _{G. Savage,}51_{L. Sawyer,}61 _{T. Scanlon,}44 _{D. Schaile,}25 _{R.D. Schamberger,}73 Y. Scheglov,40 _{H. Schellman,}54 _{P. Schieferdecker,}25 _{C. Schmitt,}26 _{C. Schwanenberger,}45 _{A. Schwartzman,}69 R. Schwienhorst,66S. Sengupta,50 H. Severini,76 E. Shabalina,52M. Shamim,60V. Shary,18 A.A. Shchukin,39

W.D. Shephard,56 _{R.K. Shivpuri,}28 _{D. Shpakov,}64 _{V. Siccardi,}19 _{R.A. Sidwell,}60 _{V. Simak,}10 _{V. Sirotenko,}51 P. Skubic,76 _{P. Slattery,}72 _{R.P. Smith,}51 _{G.R. Snow,}68 _{J. Snow,}75 _{S. Snyder,}74_{S. S¨oldner-Rembold,}45 _{X. Song,}53 L. Sonnenschein,17 _{A. Sopczak,}43_{M. Sosebee,}79_{K. Soustruznik,}9 _{M. Souza,}2 _{B. Spurlock,}79_{J. Stark,}14_{J. Steele,}61

K. Stevenson,55 _{V. Stolin,}37 _{A. Stone,}52 _{D.A. Stoyanova,}39 _{J. Strandberg,}41 _{M.A. Strang,}70 _{M. Strauss,}76 R. Str¨ohmer,25 _{D. Strom,}54 _{M. Strovink,}47 _{L. Stutte,}51 _{S. Sumowidagdo,}50 _{A. Sznajder,}3 _{M. Talby,}15 P. Tamburello,46 _{W. Taylor,}5 _{P. Telford,}45 _{J. Temple,}46 _{B. Tiller,}25 _{M. Titov,}23 _{V.V. Tokmenin,}36_{M. Tomoto,}51

T. Toole,62_{I. Torchiani,}23 _{S. Towers,}43 _{T. Trefzger,}24_{S. Trincaz-Duvoid,}17 _{D. Tsybychev,}73_{B. Tuchming,}18 C. Tully,69 _{A.S. Turcot,}45_{P.M. Tuts,}71 _{R. Unalan,}66 _{L. Uvarov,}40_{S. Uvarov,}40 _{S. Uzunyan,}53 _{B. Vachon,}5 P.J. van den Berg,34 _{R. Van Kooten,}55 _{W.M. van Leeuwen,}34_{N. Varelas,}52_{E.W. Varnes,}46 _{A. Vartapetian,}79 I.A. Vasilyev,39 _{M. Vaupel,}26 _{P. Verdier,}20_{L.S. Vertogradov,}36_{M. Verzocchi,}51 _{F. Villeneuve-Seguier,}44 _{P. Vint,}44

J.-R. Vlimant,17 _{E. Von Toerne,}60 _{M. Voutilainen,}68,† _{M. Vreeswijk,}34 _{H.D. Wahl,}50 _{L. Wang,}62_{J. Warchol,}56 G. Watts,83 _{M. Wayne,}56 _{M. Weber,}51 _{H. Weerts,}66 _{N. Wermes,}22 _{M. Wetstein,}62 _{A. White,}79 _{D. Wicke,}26

G.W. Wilson,59 _{S.J. Wimpenny,}49 _{M. Wobisch,}51 _{J. Womersley,}51 _{D.R. Wood,}64 _{T.R. Wyatt,}45 _{Y. Xie,}78 N. Xuan,56 _{S. Yacoob,}54 _{R. Yamada,}51 _{M. Yan,}62 _{T. Yasuda,}51 _{Y.A. Yatsunenko,}36_{K. Yip,}74 _{H.D. Yoo,}78

S.W. Youn,54 _{C. Yu,}14 _{J. Yu,}79 _{A. Yurkewicz,}73 _{A. Zatserklyaniy,}53_{C. Zeitnitz,}26 _{D. Zhang,}51 _{T. Zhao,}83 Z. Zhao,65 _{B. Zhou,}65 _{J. Zhu,}73_{M. Zielinski,}72 _{D. Zieminska,}55 _{A. Zieminski,}55 _{V. Zutshi,}53 _{and E.G. Zverev}38

(DØ Collaboration)

1_{Universidad de Buenos Aires, Buenos Aires, Argentina} 2_{LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil}

3_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil} 4_{Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil}

5_{University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada,}

York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada

6_{Institute of High Energy Physics, Beijing, People’s Republic of China} 7_{University of Science and Technology of China, Hefei, People’s Republic of China}

8_{Universidad de los Andes, Bogot´a, Colombia}

9_{Center for Particle Physics, Charles University, Prague, Czech Republic} 10_{Czech Technical University, Prague, Czech Republic}

11_{Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic} 12_{Universidad San Francisco de Quito, Quito, Ecuador}

13_{Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universit´e Blaise Pascal, Clermont-Ferrand, France} 14_{Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France}

15_{CPPM, IN2P3-CNRS, Universit´e de la M´editerran´ee, Marseille, France} 16_{IN2P3-CNRS, Laboratoire de l’Acc´el´erateur Lin´eaire, Orsay, France} 17_{LPNHE, IN2P3-CNRS, Universit´es Paris VI and VII, Paris, France} 18_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France}

19_{IReS, IN2P3-CNRS, Universit´e Louis Pasteur, Strasbourg, France, and Universit´e de Haute Alsace, Mulhouse, France} 20_{Institut de Physique Nucl´eaire de Lyon, IN2P3-CNRS, Universit´e Claude Bernard, Villeurbanne, France}

21_{III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany} 22_{Physikalisches Institut, Universit¨at Bonn, Bonn, Germany} 23_{Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany}

24_{Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany} 25_{Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany} 26_{Fachbereich Physik, University of Wuppertal, Wuppertal, Germany}

28_{Delhi University, Delhi, India}

29_{Tata Institute of Fundamental Research, Mumbai, India} 30_{University College Dublin, Dublin, Ireland} 31_{Korea Detector Laboratory, Korea University, Seoul, Korea}

32_{SungKyunKwan University, Suwon, Korea} 33_{CINVESTAV, Mexico City, Mexico}

34_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 35_{Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands}

36_{Joint Institute for Nuclear Research, Dubna, Russia} 37_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

38_{Moscow State University, Moscow, Russia} 39_{Institute for High Energy Physics, Protvino, Russia} 40_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia}

41_{Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and}

Uppsala University, Uppsala, Sweden

42_{Physik Institut der Universit¨at Z¨urich, Z¨urich, Switzerland} 43_{Lancaster University, Lancaster, United Kingdom}

44_{Imperial College, London, United Kingdom} 45_{University of Manchester, Manchester, United Kingdom}

46_{University of Arizona, Tucson, Arizona 85721, USA}

47_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 48_{California State University, Fresno, California 93740, USA}

49_{University of California, Riverside, California 92521, USA} 50_{Florida State University, Tallahassee, Florida 32306, USA} 51_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA}

52_{University of Illinois at Chicago, Chicago, Illinois 60607, USA} 53_{Northern Illinois University, DeKalb, Illinois 60115, USA}

54_{Northwestern University, Evanston, Illinois 60208, USA} 55_{Indiana University, Bloomington, Indiana 47405, USA} 56_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

57_{Purdue University Calumet, Hammond, Indiana 46323, USA} 58_{Iowa State University, Ames, Iowa 50011, USA} 59_{University of Kansas, Lawrence, Kansas 66045, USA} 60_{Kansas State University, Manhattan, Kansas 66506, USA} 61_{Louisiana Tech University, Ruston, Louisiana 71272, USA} 62_{University of Maryland, College Park, Maryland 20742, USA}

63_{Boston University, Boston, Massachusetts 02215, USA} 64_{Northeastern University, Boston, Massachusetts 02115, USA}

65_{University of Michigan, Ann Arbor, Michigan 48109, USA} 66_{Michigan State University, East Lansing, Michigan 48824, USA}

67_{University of Mississippi, University, Mississippi 38677, USA} 68_{University of Nebraska, Lincoln, Nebraska 68588, USA} 69_{Princeton University, Princeton, New Jersey 08544, USA} 70_{State University of New York, Buffalo, New York 14260, USA}

71_{Columbia University, New York, New York 10027, USA} 72_{University of Rochester, Rochester, New York 14627, USA} 73_{State University of New York, Stony Brook, New York 11794, USA}

74_{Brookhaven National Laboratory, Upton, New York 11973, USA} 75_{Langston University, Langston, Oklahoma 73050, USA} 76_{University of Oklahoma, Norman, Oklahoma 73019, USA} 77_{Oklahoma State University, Stillwater, Oklahoma 74078, USA}

78_{Brown University, Providence, Rhode Island 02912, USA} 79_{University of Texas, Arlington, Texas 76019, USA} 80_{Southern Methodist University, Dallas, Texas 75275, USA}

81_{Rice University, Houston, Texas 77005, USA} 82_{University of Virginia, Charlottesville, Virginia 22901, USA}

83_{University of Washington, Seattle, Washington 98195, USA}

(Dated: January 31, 2018)

We present a search for the flavor-changing neutral current decay B0

s → φ µ+µ −

using about 0.45 fb−1 of data collected in p¯p collisions at√s=1.96 TeV with the DØ detector at the Fermilab Tevatron Collider. We find an upper limit on the branching ratio of this decay normalized to

B0 s → J/ψ φ of B(B0 s→φ µ +_µ−₎ B(B0 s→J/ψ φ) < 4.4 × 10

−3 _{at the 95% C.L. Using the central value of the world}

average branching fraction of B0

s → J/ψ φ, the limit corresponds to B(B0s→ φ µ+µ −

) < 4.1 × 10−6

at the 95% C.L., the most stringent upper bound to date.

PACS numbers: 13.20.He, 12.15.Mm, 14.40.Nd

The investigation of rare flavor changing neutral cur-rent (FCNC) B meson decays has received special atten-tion in the past since this opens up the possibility of pre-cision tests of the flavor structure of the standard model (SM). In the SM, FCNC decays are absent at tree level but proceed at higher order through electroweak pen-guin and box diagrams. FCNC decays are sensitive to new physics, since decay amplitudes involving new par-ticles interfere with SM amplitudes. Although inclusive FCNC decays like B → Xsℓ+ℓ− or B → Xsγ are the-oretically easier to calculate, exclusive decays with one hadron in the final state are experimentally easier to study. For instance, the exclusive decays B0

d → K∗ℓ+ℓ− and B± _{→ K}±_ℓ+_ℓ− _{have been already measured at} B-factories [1, 2] and were found to be consistent with the SM within the present experimental uncertainties. Re-lated to the same quark-level transition of b → s ℓ+_ℓ− _is the corresponding exclusive FCNC decay B0

s → φ µ+µ− in the B0

s meson system. An observation of this decay or experimental upper limit on its rate will yield additional important information on the flavor dynamics of FCNC decays.

Within the SM, the decay rate for the B0

s → φ µ+µ− decay, neglecting the interference effects with the much stronger B0

s → J/ψ φ and Bs0 → ψ(2S) φ resonance de-cays, is predicted to be of the order of 1.6 × 10−6 _[3] with about 30% uncertainty due to poorly known form factors. The interference effects with the B0

s resonance decay amplitudes are large, with their expected magni-tude depending on the exact modeling of the charmo-nium states [4]. To separate experimentally the FCNC-mediated process B0

s → φ µ+µ−, one has to restrict the invariant mass of the final state lepton pair to be outside the charmonium resonances. Presently, the only existing experimental bound on the B0

s → φ µ+µ− decay is given by CDF from the analysis of Run I data [5]. CDF sets an upper limit at the 95% C.L. of B(B0

s → φ µ+µ−) < 6.7 × 10−5_.

In this Letter, we report on a new experimental limit on the decay B0

s→ φ µ+µ−, that is an order of magnitude more stringent than the existing limit. The φ mesons are reconstructed through their K+_K− _{decay mode and} the invariant mass of the two muons in the final state is required to be outside the charmonium resonances. The events in our search are normalized to resonant decay B0

s → J/ψ φ events. Using the Bs0 → J/ψ φ mode as the normalization channel has the advantage that the efficiencies to detect the φ µ+_µ− _{system in signal and} normalization events are similar, and systematic effects

tend to cancel.

The search uses a data set corresponding to approx-imately 0.45 fb−1of p¯p collisions at √s = 1.96 TeV recorded by the DØ detector operating at the Fermilab Tevatron Collider. The DØ detector is described in de-tail elsewhere [6]. The main elements relevant for this analysis are the central tracking and muon detector sys-tems. The central tracking system consists of a silicon mi-crostrip tracker (SMT) and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet. The muon detector, which is located outside the calorimeter, consists of a layer of tracking detectors and scintillation trigger counters in front of 1.8 T toroidal magnets, followed by two more similar layers after the toroids, allowing for efficient muon detection out to pseu-dorapidity (η) of ±2.0.

Dimuon triggers were used in the data selection for this analysis. A trigger simulation was used to estimate the trigger efficiency for the signal and normalization ples. These efficiencies were also checked with data sam-ples collected with single muon triggers. The event pre-selection starts with a loose pre-selection of B0

s → φ µ+µ− candidates. These candidates are identified by requir-ing exactly two muons fulfillrequir-ing quality cuts on the num-ber of hits in the muon system and the two additional charged particle tracks to form a good vertex. The re-constructed invariant mass of the Bs0 candidate should be within 4.4 < mφ µ+_µ−< 6.2 GeV/c

2_.

We then require the invariant mass of the two muons to be within 0.5 < mµ+_µ− < 4.4 GeV/c

2_{. In this mass} re-gion, the J/ψ(→ µ+_µ−_{) and ψ(2S)(→ µ}+_µ−_{) resonances} are excluded to discriminate against dominant resonant decays by rejecting the mass region 2.72 < mµ+_µ− < 4.06 GeV/c2_{. The J/ψ mass resolution in data is given} by a Gaussian distribution with σ = 75 MeV/c2_{. The} re-jected mass region then covers ±5σ wide windows around the resonance masses.

The χ2_{/d.o.f. of the two-muon vertex is required to} be less than 10. The tracks that are matched to each muon are required to have at least three (four) measure-ments in the SMT (CFT) and the transverse momen-tum of each of the muons (pµ_T) is required to be greater than 2.5 GeV/c with |η| < 2.0 to be well inside the fidu-cial tracking and muon detector acceptances. In order to select well-measured secondary vertices, we define the two-dimensional decay length Lxyin the plane transverse to the beamline, and require its uncertainty δLxy to be less than 0.15 mm. Lxy is calculated as Lxy = ~lvtx·~p

B T pB

T , where pB

B0

s, and ~lvtxrepresents the vector pointing from the pri-mary vertex to the secondary vertex. The uncertainty on the transverse decay length, δLxy, is calculated by taking into account the uncertainties in both the primary and secondary vertex positions. The primary vertex itself is found for each event using a beam-spot constrained fit as described in Ref. [7].

Next, the number of B0

s → φ µ+µ− candidates is fur-ther reduced by requiring pB

T > 5 GeV/c and asking the B0

s candidate vertex to have χ2 < 36 with 5 d.o.f. The two tracks forming the φ candidate are further required to have pT > 0.7 GeV/c and their invariant mass within the range 1.008 < mφ < 1.032 GeV/c2. The successive cuts and the remaining candidates surviving each cut are shown in Table I. We apply the same selection for the

TABLE I: Number of candidate events surviving the cuts in data used in the pre-selection analysis.

Cut Value # candidates

Good B0

s vertex 1555320

Mass region (GeV/c2_{) 0.5 < m}

µ+_µ− <4.4 530892 excl. J/ψ,ψ(2S) Muon quality 276875 χ2/d.o.f. of vertex < 10 127509 Muon pT (GeV/c) > 2.5 73555 Muon |η| < 2.0 72350 Tracking hits CFT> 3, SMT > 2 58012 δLxy (mm) < 0.15 54752 B0s candidate pT (GeV/c) > 5.0 54399 B0 s χ2vertex < 36 53195 Kaon pT (GeV/c) > 0.7 9639 φ mass (GeV/c2_{) 1.008 < m} φ<1.032 2602 resonant B0

s → J/ψ φ candidates except that the invari-ant mass of the muon pair is now required to be within ±250 MeV/c2_{of the J/ψ mass.}

For the final event selection, we require the candidate events to satisfy additional criteria. The long lifetime of the B0

s mesons allows us to reject the random combi-natoric background. For this purpose we use the decay length significance Lxy/δLxyas one of the discriminating variables, since it gives better discriminating power than the transverse decay length alone.

The fragmentation characteristics of the b quark are such that most of its momentum is carried by the B hadron. Thus the number of extra tracks near the B0 s candidate tends to be small. Therefore the second dis-criminant is an isolation variable, I, of the muon and kaon pairs, defined as:

I = |~p(φ µ +_µ−_)| |~p(φ µ+_µ−_{)| +} P track i6=B pi(∆R < 1) . (1) Here, P track i6=B

pi is the scalar sum over all tracks exclud-ing the muon and kaon pairs within a cone of ∆R < 1

around the momentum vector ~p(φ µ+_µ−_{) of the B}0 s can-didate where ∆R =p(∆φ)2_{+ (∆η)}2_{. The final} discrim-inating variable used is the pointing angle α, defined as the angle between the momentum vector ~p(φ µ+_µ−_{) of} the B0

s candidate and the vector ~lvtx between the pri-mary and secondary vertices. This requirement ensures consistency between the direction of the decay vertex and the momentum vector of the B0

s candidate.

We generate signal Monte Carlo (MC) events for the decay B0

s → φ µ+µ− using a decay model which includes the NNLO improved Wilson coefficients [8] for the short-distance part. The form factors obtained from QCD light-cone sum rules are taken from Ref. [9]. These form factors were originally determined for B → K∗ tran-sitions and were compared with experimental measure-ments of the branching fraction B(B0

d → K∗ℓ+ℓ−) in Ref. [8]. Recently, new form factors for the B0

s → φ tran-sition, obtained from the light cone QCD sum rules, were published [10]. The difference between the form factors in Ref. [8] and those in Ref. [10] reaches 20% for mµ+_µ− < 1 GeV/c2_{, while elsewhere it remains well below 10%.}

The analysis is carried out based on signal MC events in the B0

s mass region and on data events in regions out-side the experimental signal window defined as 4.51 < mφ µ+_µ− < 6.13 GeV/c

2_{. A 44 MeV/c}2 _{mass shift in} the mass region of interest is introduced to calibrate the DØ tracker.

In order to avoid biasing the analysis procedure, data candidates in the signal mass region are not examined until completion of the analysis, and events in the side-band regions around the B0

s mass are used instead. The expected mass resolution for B0

s→ φ µ+µ−in the MC is 75 MeV/c2_{. The start (end) of the upper (lower)} side-band was chosen such that it is at least 270 MeV/c2_away from the B0

s mass. The widths of the sidebands used for background estimation are chosen to be 540 MeV/c2 each. The size of the blind signal region is ±225 MeV/c2 which corresponds to a ±3σ region around the B0

s mass. To determine the final limit on the branching fraction, we use a smaller mass region of ±2.5σ.

A random-grid search [11] was used to find simultane-ously the optimal values of the discriminants by maxi-mizing the figure of merit [12] P = ǫsig/(a/2 +√Nback). Here, ǫsig is the reconstruction efficiency of the signal events relative to the preselection (estimated using MC), and Nbackis the expected number of background events interpolated from the sidebands. The constant a is the number of standard deviations corresponding to the con-fidence level at which the signal hypothesis is tested. This constant a was set to 2.0, corresponding to about the 95% C.L. After optimization, we find the following values for the discriminating variables: Lxy/δLxy> 10.3, I > 0.72, and α < 0.1 rad.

The total signal efficiency relative to pre-selection of the three discriminating cuts is (54 ± 3)% where the un-certainty is statistical only. After a linear interpolation of

the sideband population for the whole data sample into the mass window signal region, we obtain an expected number of 1.6±0.4 background events with statistical un-certainty only.

Upon examining the data in the mass region, zero can-didate events are observed in the signal region, consistent with the background events as estimated from sidebands. Figure 1 shows the remaining events populating the lower and upper sidebands. The Poisson probability of observ-ing zero events for an expected background of 1.6 ± 0.4 is p = 0.22. ] 2 ) [GeV/c K + K -µ + µ Invariant mass ( 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 2 Events / 5 MeV/c 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Signal region Sideband 1 Sideband 2 DØ

FIG. 1: The invariant mass distribution after optimized re-quirements on the discriminating variables. The solid line shows the sidebands background interpolation into the signal region.

In the absence of an apparent signal, a limit on the branching fraction B(B0

s → φ µ+µ−) can be computed by normalizing the upper limit on the number of events in the B0

s signal region to the number of reconstructed B0 s → J/ψ φ events: B(Bs0→ φ µ+µ−) B(B0 s→ J/ψ φ) = Nul NB0 s ·_ǫǫJ/ψφ φµ+_µ− · B(J/ψ → µ+µ−), (2)

where Nulis the upper limit on the number of signal de-cays, estimated from the number of observed events and expected background events, and NB0

s is the observed number of B0

s → J/ψ φ events. The measured branching fractions are B(J/ψ → µ+_µ−_{) = (5.88 ± 0.10) × 10}−2 and B(B0

s→ J/ψ φ) = (9.3±3.3)×10−4[13]. The global efficiencies of the signal and normalization channels are ǫφµ+_µ− and ǫJ/ψφ respectively, and include all event se-lection cuts and the acceptance relative to the entire di-muon mass region. They are determined from MC yield-ing an efficiency ratio of (ǫJ/ψφ/ǫφµ+_µ−) = 2.80 ± 0.21, where the uncertainty is due to MC statistics. Applying no cut around the charmonium resonances the efficiency ratio would be (ǫJ/ψφ/ǫ′φµ+_µ−) = 1.06 ± 0.07. In order to avoid large uncertainties associated with the poorly known branching fraction of B0

s → J/ψ φ, we normalize the limit of B0

s → φ µ+µ− relative to B(B0s→ J/ψ φ) as shown by Eq. 2.

The same cuts are applied to the B0

s → J/ψ φ candi-dates. The contamination of muon pairs from the non-resonant φ µ+_µ− _{decay in the resonant normalization}

re-gion J/ψ(→ µ+_µ−_{)φ is negligible. We therefore} con-strain the two muons to have an invariant mass equal to the J/ψ mass [13] when calculating the µ+_µ−_K+_K− invariant mass. The mass spectrum of the reconstructed B0

s → J/ψ φ is shown in Fig. 2. A fit using a Gaussian function for the signal and a second order polynomial for the background yields 73 ± 10 ± 4 B0

s candidates, where the first uncertainty is due to statistics and the second represents the systematic uncertainty which is estimated by varying the fit range as well as the background and signal shape hypotheses.

] 2 ) [GeV/c K + K -µ + µ Invariant mass ( 5 5.2 5.4 5.6 5.8 2 Events / 25 MeV/c 0 10 20 30 DØ _B0_s→ _J/ψφ 4 ± 10 ± = 73 s 0 B N

FIG. 2: The normalization channel B0

s → J/ψ φ. The different sources of relative uncertainty that enter into the limit calculation of B of B0

s → φ µ+µ− are given in Table II. The largest uncertainty, 25%, is due to the background interpolation into the signal region and is based on the statistical uncertainty of the fit integral. The uncertainty on the number of observed B0

s → J/ψ φ events in the normalization channel is 14.8%.

The pT distribution of the Bs0 in data is on aver-age slightly higher than that from MC. Therefore, MC events for the signal and normalization channels have been reweighted accordingly and an additional uncer-tainty of 3.7% is applied. The CP-even signal MC events are generated with a B0

s lifetime of 1.44 ps [14]. To account for a possible efficiency difference related with the shorter lifetime of the CP-even B0

s, the signal MC events are weighted according to the combined world av-erage CP-even lifetime [15]. The efficiency difference is estimated to be 8% which is taken as an additional sys-tematic uncertainty. The statistical uncertainty on the efficiency ratio ǫJ/ψφ/ǫφµ+_µ− is found to be 7.5%. The signal efficiency obtained from MC is based on the in-put for the NNLO Wilson coefficients and form factors of Ref. [8]. We do not include any theoretical uncertainty in our systematics uncertainty estimation.

The statistical and systematic uncertainties can be in-cluded in the limit calculation by integrating over proba-bility functions that parameterize the uncertainties. We use a prescription [16] where we construct a frequentist confidence interval with the Feldman and Cousins [17] or-dering scheme for the MC integration. The background

TABLE II: The relative uncertainties found for the upper limit on B.

Source Relative Uncertainty [%] # of B0s → J/ψφ 14.8 ǫJ/ψφ/ǫφµµ 7.5 MC weighting 3.7 CP-even lifetime 8.0 B(J/ψ → µµ) 1.7 Total 18.9 Background uncertainty 25.0

is modeled as a Gaussian distribution with its mean value equal to the expected number of background events and its standard deviation equal to the background tainty. Including the statistical and systematic uncer-tainties, the Feldman and Cousins (FC) limit is

B(B0 s→φ µ + µ−₎ B(B0 s→J/ψ φ) < 4.4 (3.5) × 10 −3

at the 95% (90%) C.L. respectively. Taking a Bayesian approach [18] with a flat prior and the uncertainties treated as Gaussian distributions in the integration, we find an upper limit of B(B0

s → φ µ+µ−)/B(Bs0 → J/ψ φ) < 7.4 (5.6) × 10−3_{at the 95% (90%) C.L.,} respec-tively.

Since we have fewer events observed than expected, we also quote the sensitivity of our search. Assuming there is only background, we calculate for each possible value of observation a 95% C.L. upper limit weighted by the Pois-son probability of occurrence. Including the statistical and systematical uncertainties, our sensitivity is given by hB(B0

s → φ µ+µ−)i/B(Bs0 → J/ψ φ) = 1.1 (1.2) × 10−2 at the 95% C.L. using the FC (Bayesian) approaches, respectively.

Using only the central value of the world average branching fraction [13] of B(B0

s → J/ψ φ) = (9.3±3.3) × 10−4_{, the FC limit corresponds to B(B}0

s → φ µ+µ−) < 4.1 (3.2) ×10−6_{at the 95% (90%) C.L. respectively. This} is presently the most stringent upper bound and can be compared with the SM calculation of B(B0

s → φ µ+µ−) = 1.6 × 10−6_{of Ref. [3].}

We thank the staffs at Fermilab and collaborating in-stitutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ,

FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); PPARC (United Kingdom); MSMT (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Re-search Council (Sweden); ReRe-search Corporation; Alexan-der von Humboldt Foundation; and the Marie Curie Pro-gram.

[*] On leave from IEP SAS Kosice, Slovakia.

[†] Visitor from Helsinki Institute of Physics, Helsinki, Fin-land.

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