Study of the decay B$^{0}_{s} \to D^{(*)}_{s} D^{(*)}_{s}$

arXiv:hep-ex/0702049v1 28 Feb 2007

Measurement of the branching fraction Br(B

s

→

D

(∗)

s

D

(∗)

s

)

V.M. Abazov,35 _{B. Abbott,}75 _{M. Abolins,}65 _{B.S. Acharya,}28 _{M. Adams,}51 _{T. Adams,}49 _{E. Aguilo,}5 _{S.H. Ahn,}30 M. Ahsan,59 _{G.D. Alexeev,}35 _{G. Alkhazov,}39_{A. Alton,}64,∗ _{G. Alverson,}63 _{G.A. Alves,}2 _{M. Anastasoaie,}34 L.S. Ancu,34 _{T. Andeen,}53 _{S. Anderson,}45_{B. Andrieu,}16 _{M.S. Anzelc,}53 _{Y. Arnoud,}13 _{M. Arov,}52_{A. Askew,}49 B. ˚Asman,40_{A.C.S. Assis Jesus,}3_{O. Atramentov,}49 _{C. Autermann,}20 _{C. Avila,}7_{C. Ay,}23 _{F. Badaud,}12_{A. Baden,}61

L. Bagby,52 _{B. Baldin,}50 _{D.V. Bandurin,}59 _{P. Banerjee,}28 _{S. Banerjee,}28 _{E. Barberis,}63_{A.-F. Barfuss,}14 P. Bargassa,80_{P. Baringer,}58 _{J. Barreto,}2 _{J.F. Bartlett,}50 _{U. Bassler,}16 _{D. Bauer,}43 _{S. Beale,}5 _{A. Bean,}58 M. Begalli,3_{M. Begel,}71 _{C. Belanger-Champagne,}40_{L. Bellantoni,}50 _{A. Bellavance,}67 _{J.A. Benitez,}65 _{S.B. Beri,}26

G. Bernardi,16 _{R. Bernhard,}22_{L. Berntzon,}14 _{I. Bertram,}42_{M. Besan¸con,}17 _{R. Beuselinck,}43 _{V.A. Bezzubov,}38 P.C. Bhat,50V. Bhatnagar,26 M. Binder,24C. Biscarat,19G. Blazey,52F. Blekman,43 S. Blessing,49D. Bloch,18

K. Bloom,67 _{A. Boehnlein,}50 _{D. Boline,}62 _{T.A. Bolton,}59 _{G. Borissov,}42 _{K. Bos,}33 _{T. Bose,}77 _{A. Brandt,}78 R. Brock,65_{G. Brooijmans,}70 _{A. Bross,}50_{D. Brown,}78 _{N.J. Buchanan,}49 _{D. Buchholz,}53 _{M. Buehler,}81 V. Buescher,21_{S. Burdin,}50 _{S. Burke,}45 _{T.H. Burnett,}82_{E. Busato,}16_{C.P. Buszello,}43 _{J.M. Butler,}62 _{P. Calfayan,}24

S. Calvet,14 _{J. Cammin,}71 _{S. Caron,}33 _{W. Carvalho,}3 _{B.C.K. Casey,}77_{N.M. Cason,}55 _{H. Castilla-Valdez,}32 S. Chakrabarti,17_{D. Chakraborty,}52 _{K. Chan,}5 _{K.M. Chan,}71 _{A. Chandra,}48 _{F. Charles,}18 _{E. Cheu,}45 F. Chevallier,13 _{D.K. Cho,}62 _{S. Choi,}31_{B. Choudhary,}27 _{L. Christofek,}77_{T. Christoudias,}43 _{S. Cihangir,}50 D. Claes,67 _{B. Cl´ement,}18 _{C. Cl´ement,}40_{Y. Coadou,}5_{M. Cooke,}80_{W.E. Cooper,}50 _{M. Corcoran,}80_{F. Couderc,}17

M.-C. Cousinou,14_{S. Cr´ep´e-Renaudin,}13_{D. Cutts,}77 _{M. ´Cwiok,}29 _{H. da Motta,}2 _{A. Das,}62 _{G. Davies,}43 K. De,78 _{P. de Jong,}33 _{S.J. de Jong,}34 _{E. De La Cruz-Burelo,}64_{C. De Oliveira Martins,}3 _{J.D. Degenhardt,}64 F. D´eliot,17 _{M. Demarteau,}50 _{R. Demina,}71 _{D. Denisov,}50 _{S.P. Denisov,}38_{S. Desai,}50_{H.T. Diehl,}50 _{M. Diesburg,}50

A. Dominguez,67 _{H. Dong,}72 _{L.V. Dudko,}37 _{L. Duflot,}15 _{S.R. Dugad,}28 _{D. Duggan,}49 _{A. Duperrin,}14 _{J. Dyer,}65 A. Dyshkant,52 _{M. Eads,}67 _{D. Edmunds,}65 _{J. Ellison,}48_{V.D. Elvira,}50 _{Y. Enari,}77 _{S. Eno,}61 _{P. Ermolov,}37 H. Evans,54 _{A. Evdokimov,}36 _{V.N. Evdokimov,}38_{A.V. Ferapontov,}59 _{T. Ferbel,}71 _{F. Fiedler,}24 _{F. Filthaut,}34 W. Fisher,50 H.E. Fisk,50 M. Ford,44M. Fortner,52 H. Fox,22 S. Fu,50 S. Fuess,50 T. Gadfort,82 C.F. Galea,34 E. Gallas,50 _{E. Galyaev,}55 _{C. Garcia,}71 _{A. Garcia-Bellido,}82_{V. Gavrilov,}36 _{P. Gay,}12 _{W. Geist,}18 _{D. Gel´e,}18 C.E. Gerber,51 _{Y. Gershtein,}49 _{D. Gillberg,}5_{G. Ginther,}71_{N. Gollub,}40 _{B. G´omez,}7_{A. Goussiou,}55 _{P.D. Grannis,}72

H. Greenlee,50 _{Z.D. Greenwood,}60 _{E.M. Gregores,}4 _{G. Grenier,}19 _{Ph. Gris,}12 _{J.-F. Grivaz,}15 _{A. Grohsjean,}24 S. Gr¨unendahl,50 _{M.W. Gr¨unewald,}29_{F. Guo,}72_{J. Guo,}72 _{G. Gutierrez,}50 _{P. Gutierrez,}75_{A. Haas,}70_{N.J. Hadley,}61

P. Haefner,24 S. Hagopian,49 J. Haley,68 I. Hall,75 R.E. Hall,47L. Han,6 K. Hanagaki,50 P. Hansson,40K. Harder,44 A. Harel,71 _{R. Harrington,}63 _{J.M. Hauptman,}57 _{R. Hauser,}65 _{J. Hays,}43 _{T. Hebbeker,}20 _{D. Hedin,}52 J.G. Hegeman,33 _{J.M. Heinmiller,}51 _{A.P. Heinson,}48 _{U. Heintz,}62 _{C. Hensel,}58 _{K. Herner,}72 _{G. Hesketh,}63 M.D. Hildreth,55 _{R. Hirosky,}81 _{J.D. Hobbs,}72_{B. Hoeneisen,}11_{H. Hoeth,}25_{M. Hohlfeld,}15 _{S.J. Hong,}30_{R. Hooper,}77

P. Houben,33 _{Y. Hu,}72_{Z. Hubacek,}9 _{V. Hynek,}8 _{I. Iashvili,}69 _{R. Illingworth,}50 _{A.S. Ito,}50_{S. Jabeen,}62 _{M. Jaffr´e,}15 S. Jain,75 _{K. Jakobs,}22 _{C. Jarvis,}61_{R. Jesik,}43_{K. Johns,}45_{C. Johnson,}70 _{M. Johnson,}50 _{A. Jonckheere,}50

P. Jonsson,43 _{A. Juste,}50 _{D. K¨afer,}20 _{S. Kahn,}73 _{E. Kajfasz,}14 _{A.M. Kalinin,}35 _{J.M. Kalk,}60 _{J.R. Kalk,}65 S. Kappler,20 _{D. Karmanov,}37 _{J. Kasper,}62 _{P. Kasper,}50 _{I. Katsanos,}70 _{D. Kau,}49 _{R. Kaur,}26 _{V. Kaushik,}78 R. Kehoe,79_{S. Kermiche,}14 _{N. Khalatyan,}38 _{A. Khanov,}76 _{A. Kharchilava,}69_{Y.M. Kharzheev,}35 _{D. Khatidze,}70 H. Kim,31 _{T.J. Kim,}30 _{M.H. Kirby,}34 _{B. Klima,}50 _{J.M. Kohli,}26 _{J.-P. Konrath,}22_{M. Kopal,}75_{V.M. Korablev,}38 J. Kotcher,73_{B. Kothari,}70_{A. Koubarovsky,}37_{A.V. Kozelov,}38_{D. Krop,}54_{A. Kryemadhi,}81_{T. Kuhl,}23 _{A. Kumar,}69

S. Kunori,61 _{A. Kupco,}10 _{T. Kurˇca,}19_{J. Kvita,}8 _{D. Lam,}55 _{S. Lammers,}70 _{G. Landsberg,}77 _{J. Lazoflores,}49 P. Lebrun,19_{W.M. Lee,}50_{A. Leflat,}37 _{F. Lehner,}41 _{V. Lesne,}12 _{J. Leveque,}45_{P. Lewis,}43_{J. Li,}78_{L. Li,}48 _{Q.Z. Li,}50

S.M. Lietti,4 _{J.G.R. Lima,}52_{D. Lincoln,}50 _{J. Linnemann,}65 _{V.V. Lipaev,}38 _{R. Lipton,}50 _{Z. Liu,}5 _{L. Lobo,}43 A. Lobodenko,39 M. Lokajicek,10A. Lounis,18 P. Love,42H.J. Lubatti,82 M. Lynker,55A.L. Lyon,50A.K.A. Maciel,2

R.J. Madaras,46 _{P. M¨attig,}25_{C. Magass,}20 _{A. Magerkurth,}64 _{N. Makovec,}15 _{P.K. Mal,}55 _{H.B. Malbouisson,}3 S. Malik,67 _{V.L. Malyshev,}35_{H.S. Mao,}50 _{Y. Maravin,}59 _{B. Martin,}13 _{R. McCarthy,}72 _{A. Melnitchouk,}66

A. Mendes,14 _{L. Mendoza,}7 _{P.G. Mercadante,}4_{M. Merkin,}37 _{K.W. Merritt,}50 _{A. Meyer,}20 _{J. Meyer,}21 M. Michaut,17_{H. Miettinen,}80_{T. Millet,}19_{J. Mitrevski,}70_{J. Molina,}3_{R.K. Mommsen,}44 _{N.K. Mondal,}28_{J. Monk,}44

R.W. Moore,5 _{T. Moulik,}58 _{G.S. Muanza,}19 _{M. Mulders,}50_{M. Mulhearn,}70 _{O. Mundal,}21 _{L. Mundim,}3 _{E. Nagy,}14 M. Naimuddin,50 _{M. Narain,}77 _{N.A. Naumann,}34 _{H.A. Neal,}64 _{J.P. Negret,}7 _{P. Neustroev,}39 _{H. Nilsen,}22

C. Noeding,22 _{A. Nomerotski,}50 _{S.F. Novaes,}4 _{T. Nunnemann,}24 _{V. O’Dell,}50 _{D.C. O’Neil,}5 _{G. Obrant,}39 C. Ochando,15_{V. Oguri,}3 _{N. Oliveira,}3_{D. Onoprienko,}59_{N. Oshima,}50_{J. Osta,}55 _{R. Otec,}9_{G.J. Otero y Garz´on,}51

M. Owen,44_{P. Padley,}80_{M. Pangilinan,}77 _{N. Parashar,}56_{S.-J. Park,}71 _{S.K. Park,}30 _{J. Parsons,}70_{R. Partridge,}77 N. Parua,72 _{A. Patwa,}73_{G. Pawloski,}80 _{P.M. Perea,}48_{K. Peters,}44_{Y. Peters,}25 _{P. P´etroff,}15 _{M. Petteni,}43 R. Piegaia,1_{J. Piper,}65_{M.-A. Pleier,}21_{P.L.M. Podesta-Lerma,}32,§_{V.M. Podstavkov,}50_{Y. Pogorelov,}55_{M.-E. Pol,}2

A. Pompoˇs,75_{B.G. Pope,}65_{A.V. Popov,}38_{C. Potter,}5_{W.L. Prado da Silva,}3 _{H.B. Prosper,}49 _{S. Protopopescu,}73 J. Qian,64 _{A. Quadt,}21 _{B. Quinn,}66 _{M.S. Rangel,}2_{K.J. Rani,}28 _{K. Ranjan,}27 _{P.N. Ratoff,}42 _{P. Renkel,}79

S. Reucroft,63 _{M. Rijssenbeek,}72 _{I. Ripp-Baudot,}18 _{F. Rizatdinova,}76 _{S. Robinson,}43 _{R.F. Rodrigues,}3 C. Royon,17_{P. Rubinov,}50 _{R. Ruchti,}55 _{G. Sajot,}13 _{A. S´anchez-Hern´andez,}32 _{M.P. Sanders,}16 _{A. Santoro,}3 G. Savage,50 _{L. Sawyer,}60 _{T. Scanlon,}43 _{D. Schaile,}24 _{R.D. Schamberger,}72 _{Y. Scheglov,}39_{H. Schellman,}53 P. Schieferdecker,24_{C. Schmitt,}25 _{C. Schwanenberger,}44_{A. Schwartzman,}68 _{R. Schwienhorst,}65 _{J. Sekaric,}49

S. Sengupta,49 H. Severini,75 E. Shabalina,51 M. Shamim,59 V. Shary,17 A.A. Shchukin,38 R.K. Shivpuri,27 D. Shpakov,50 _{V. Siccardi,}18 _{R.A. Sidwell,}59 _{V. Simak,}9 _{V. Sirotenko,}50 _{P. Skubic,}75 _{P. Slattery,}71_{D. Smirnov,}55

R.P. Smith,50 _{G.R. Snow,}67 _{J. Snow,}74 _{S. Snyder,}73 _{S. S¨oldner-Rembold,}44 _{L. Sonnenschein,}16_{A. Sopczak,}42 M. Sosebee,78 _{K. Soustruznik,}8_{M. Souza,}2_{B. Spurlock,}78_{J. Stark,}13_{J. Steele,}60_{V. Stolin,}36 _{D.A. Stoyanova,}38

J. Strandberg,64 _{S. Strandberg,}40_{M.A. Strang,}69 _{M. Strauss,}75 _{R. Str¨ohmer,}24 _{D. Strom,}53 _{M. Strovink,}46 L. Stutte,50 _{S. Sumowidagdo,}49 _{P. Svoisky,}55 _{A. Sznajder,}3 _{M. Talby,}14 _{P. Tamburello,}45 _{A. Tanasijczuk,}1 W. Taylor,5_{P. Telford,}44 _{J. Temple,}45_{B. Tiller,}24 _{F. Tissandier,}12_{M. Titov,}22 _{V.V. Tokmenin,}35 _{M. Tomoto,}50

T. Toole,61 _{I. Torchiani,}22 _{T. Trefzger,}23_{S. Trincaz-Duvoid,}16 _{D. Tsybychev,}72 _{B. Tuchming,}17 _{C. Tully,}68 P.M. Tuts,70 _{R. Unalan,}65_{L. Uvarov,}39_{S. Uvarov,}39 _{S. Uzunyan,}52_{B. Vachon,}5 _{P.J. van den Berg,}33_{B. van Eijk,}35

R. Van Kooten,54 _{W.M. van Leeuwen,}33 _{N. Varelas,}51 _{E.W. Varnes,}45 _{A. Vartapetian,}78 _{I.A. Vasilyev,}38 M. Vaupel,25_{P. Verdier,}19 _{L.S. Vertogradov,}35_{M. Verzocchi,}50_{F. Villeneuve-Seguier,}43 _{P. Vint,}43 _{J.-R. Vlimant,}16

E. Von Toerne,59 _{M. Voutilainen,}67,‡_{M. Vreeswijk,}33 _{H.D. Wahl,}49 _{J. Walder,}42_{L. Wang,}61 _{M.H.L.S Wang,}50 J. Warchol,55 _{G. Watts,}82 _{M. Wayne,}55 _{G. Weber,}23 _{M. Weber,}50 _{H. Weerts,}65 _{A. Wenger,}22,# _{N. Wermes,}21

M. Wetstein,61 _{A. White,}78 _{D. Wicke,}25 _{G.W. Wilson,}58 _{S.J. Wimpenny,}48 _{M. Wobisch,}50 _{D.R. Wood,}63 T.R. Wyatt,44 _{Y. Xie,}77 _{S. Yacoob,}53 _{R. Yamada,}50 _{M. Yan,}61 _{T. Yasuda,}50_{Y.A. Yatsunenko,}35 _{K. Yip,}73 H.D. Yoo,77 _{S.W. Youn,}53_{C. Yu,}13 _{J. Yu,}78 _{A. Yurkewicz,}72 _{A. Zatserklyaniy,}52_{C. Zeitnitz,}25 _{D. Zhang,}50 T. Zhao,82 _{B. Zhou,}64 _{J. Zhu,}72 _{M. Zielinski,}71 _{D. Zieminska,}54 _{A. Zieminski,}54 _{V. Zutshi,}52 _{and E.G. Zverev}37

(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_{University of Science and Technology of China, Hefei, People’s Republic of China} 7_{Universidad de los Andes, Bogot´a, Colombia}

8_{Center for Particle Physics, Charles University, Prague, Czech Republic} 9_{Czech Technical University, Prague, Czech Republic}

10_{Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic} 11_{Universidad San Francisco de Quito, Quito, Ecuador}

12_{Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universit´e Blaise Pascal, Clermont-Ferrand, France} 13_{Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France}

14_{CPPM, IN2P3-CNRS, Universit´e de la M´editerran´ee, Marseille, France}

15_{Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS et Universit´e Paris-Sud, Orsay, France} 16_{LPNHE, IN2P3-CNRS, Universit´es Paris VI and VII, Paris, France}

17_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France}

18_{IPHC, IN2P3-CNRS, Universit´e Louis Pasteur, Strasbourg, France, and Universit´e de Haute Alsace, Mulhouse, France} 19_{IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France}

20_{III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany} 21_{Physikalisches Institut, Universit¨at Bonn, Bonn, Germany} 22_{Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany}

23_{Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany} 24_{Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany} 25_{Fachbereich Physik, University of Wuppertal, Wuppertal, Germany}

26_{Panjab University, Chandigarh, India} 27_{Delhi University, Delhi, India}

28_{Tata Institute of Fundamental Research, Mumbai, India} 29_{University College Dublin, Dublin, Ireland} 30_{Korea Detector Laboratory, Korea University, Seoul, Korea}

31_{SungKyunKwan University, Suwon, Korea} 32_{CINVESTAV, Mexico City, Mexico}

33_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 34_{Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands}

35_{Joint Institute for Nuclear Research, Dubna, Russia} 36_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

37_{Moscow State University, Moscow, Russia} 38_{Institute for High Energy Physics, Protvino, Russia} 39_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia}

40_{Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and}

Uppsala University, Uppsala, Sweden

41_{Physik Institut der Universit¨at Z¨urich, Z¨urich, Switzerland} 42_{Lancaster University, Lancaster, United Kingdom}

43_{Imperial College, London, United Kingdom} 44_{University of Manchester, Manchester, United Kingdom}

45_{University of Arizona, Tucson, Arizona 85721, USA}

46_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 47_{California State University, Fresno, California 93740, USA}

48_{University of California, Riverside, California 92521, USA} 49_{Florida State University, Tallahassee, Florida 32306, USA} 50_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA}

51_{University of Illinois at Chicago, Chicago, Illinois 60607, USA} 52_{Northern Illinois University, DeKalb, Illinois 60115, USA}

53_{Northwestern University, Evanston, Illinois 60208, USA} 54_{Indiana University, Bloomington, Indiana 47405, USA} 55_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

56_{Purdue University Calumet, Hammond, Indiana 46323, USA} 57_{Iowa State University, Ames, Iowa 50011, USA} 58_{University of Kansas, Lawrence, Kansas 66045, USA} 59_{Kansas State University, Manhattan, Kansas 66506, USA} 60_{Louisiana Tech University, Ruston, Louisiana 71272, USA} 61_{University of Maryland, College Park, Maryland 20742, USA}

62_{Boston University, Boston, Massachusetts 02215, USA} 63_{Northeastern University, Boston, Massachusetts 02115, USA}

64_{University of Michigan, Ann Arbor, Michigan 48109, USA} 65_{Michigan State University, East Lansing, Michigan 48824, USA}

66_{University of Mississippi, University, Mississippi 38677, USA} 67_{University of Nebraska, Lincoln, Nebraska 68588, USA} 68_{Princeton University, Princeton, New Jersey 08544, USA} 69_{State University of New York, Buffalo, New York 14260, USA}

70_{Columbia University, New York, New York 10027, USA} 71_{University of Rochester, Rochester, New York 14627, USA} 72_{State University of New York, Stony Brook, New York 11794, USA}

73_{Brookhaven National Laboratory, Upton, New York 11973, USA} 74_{Langston University, Langston, Oklahoma 73050, USA} 75_{University of Oklahoma, Norman, Oklahoma 73019, USA} 76_{Oklahoma State University, Stillwater, Oklahoma 74078, USA}

77_{Brown University, Providence, Rhode Island 02912, USA} 78_{University of Texas, Arlington, Texas 76019, USA} 79_{Southern Methodist University, Dallas, Texas 75275, USA}

80_{Rice University, Houston, Texas 77005, USA} 81_{University of Virginia, Charlottesville, Virginia 22901, USA}

82_{University of Washington, Seattle, Washington 98195, USA}

(Dated: February 28, 2007) We report a measurement of the branching fraction Br(B0

s → D(∗)s D(∗)s ) using a data sample

corresponding to 1.3 fb−1 _{of integrated luminosity collected by the D0 experiment in 2002–2006}

during Run II of the Fermilab Tevatron Collider. One D(∗)s meson was partially reconstructed

in the decay Ds → φµν, and the other D(∗)s meson was identified using the decay Ds → φπ

Br(Bs0→D(∗)s D(∗)s ) = 0.039+0.019_−0.017(stat)+0.016_−0.015(syst). This was subsequently used to estimate the width difference ∆ΓCP s in the Bs0– ¯Bs0 system: ∆Γ CP s /Γs= 0.079+0.038_−0.035(stat)+0.031 −0.030(syst).

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

In the standard model (SM), mixing in the B0 s sys-tem is expected to produce a large decay width dif-ference ∆Γs = ΓL − ΓH between the light and heavy mass eigenstates with a small CP-violating phase φs [1]. New phenomena could produce a significant CP-violating phase leading to a reduction in the observed value of ∆Γs compared with the SM prediction of ∆Γs/Γs = 0.127 ± 0.024 [2]. ∆ΓCP

s = ∆ΓCP−evens − ∆ΓCP−odds (∆Γs = ∆ΓCPs | cos φs |) can be estimated from the branching fraction Br(B0

s→ D (∗)

s D(∗)s ) [1, 3]. This decay is predominantly CP-even and is related to ∆ΓCP

s [1, 3]: 2Br(B0

s → D

(∗)

s D(∗)s ) ≈ ∆ΓCPs /Γs
[1 + O (∆Γs/Γs)]. Only one measurement of Br(B0

s → D (∗)

s D(∗)s ) has pre-viously been published, by the ALEPH [4] experiment at the CERN LEP collider from the study of correlated production of φφ in Z0_decays.

In this Letter we present a measurement of Br(Bs0 → Ds(∗)Ds(∗)) using a sample of semileptonic Bs0 decays col-lected by the D0 experiment at Fermilab in p¯p collisions at√s = 1.96 TeV. The data correspond to an integrated luminosity of approximately 1.3 fb−1_{. We present an} analysis of the decay chain B0

s→ D (∗)

s D(∗)s where one Ds+ decays to φ1π+, the other D−s decays to D−s → φ2µ−ν, and where each φ meson decays to φ → K+_K−_{. Charge} conjugate states are implied throughout. No attempt was made to reconstruct the photon or π0 _{from the} de-cay D∗

s→ Dsγ/π0and thus the state D(∗)s D(∗)s contains contributions from DsDs, D∗sDs and Ds∗D∗s. To reduce systematic effects, Br(B0 s → D (∗) s D(∗)s ) was normalized to the decay B0 s → D (∗) s µν.

The D0 detector is described in detail elsewhere [5]. The detector components relevant to this analysis are the central tracking and muon systems. The D0 central-tracking system consists of a silicon microstrip tracker (SMT) closest to the beampipe surrounded by a cen-tral scintillating-fiber tracker (CFT) with an outer ra-dius of 52 cm. Both tracking systems are located within a 2 T superconducting solenoidal magnet and are op-timized for tracking and vertexing for pseudorapidities |η| < 3 (SMT) and |η| < 2.5 (CFT), where η = −ln[tan(θ/2)], and θ is the polar angle with respect to the beam axis. The muon system is located outside of the liquid-argon/uranium calorimetry system and has pseu-dorapidity coverage |η| < 2. It consists of a layer of track-ing detectors and trigger scintillation counters in front of a 1.8 T iron toroid, followed by two similar layers out-side of the toroid. The trigger system identifies events of interest in a high-luminosity environment based on muon identification, charged tracking, and vertexing. No

explicit trigger requirement was applied, however most events satisfied inclusive single-muon triggers.

The measurement began with reconstruction of the de-cay chain Ds→ φ1π, φ1→ K+K−, with tracks originat-ing from the same p¯p collision point (primary vertex) as a muon. All charged tracks used in the analysis were required to have at least two hits in both the SMT and CFT. Muons were required to have transverse momen-tum pT > 2 GeV/c, total momentum p > 3 GeV/c, and to have measurements in at least two layers of the muon system. Two oppositely charged particles with pT > 0.8 GeV/c were selected from the remaining particles in the event and were assigned the mass of a kaon. An invariant mass of 1.01 < M (K+_K−_{) < 1.03 GeV/c}2 _{was required,} to be consistent with the mass of a φ meson. Each pair of kaons satisfying these criteria was combined with a third particle with pT > 1.0 GeV/c, which was assigned the mass of a pion. The three tracks were required to form a Dsvertex using the algorithm described in Ref. [6]. The cosine of the angle between the Ds momentum and the direction from the primary vertex to the Dsvertex was required to be greater than 0.9. The Ds vertex was re-quired to have a displacement from the primary vertex in the plane perpendicular to the beam with at least 4σ significance. The helicity angle χ is defined as the angle between the momenta of the Ds and a K meson in the (K+_K−_{) center of mass system. The decay of D}

s→ φπ follows a cos2_{χ distribution, while for background cos χ} is expected to be flat. Therefore, to enhance the signal, the criterion | cos χ| > 0.35 was applied. The muon and pion were required to have opposite charge. The events passing these selections, referred to as the preselection sample, were used to produce the samples of (µφ2Ds) and the normalizing sample (µDs) defined below.

To construct a (µDs) candidate from the preselec-tion sample, the Ds candidate and the muon were re-quired to originate from a common B0

s vertex. The mass of the (µDs) system was required to be less than 5.2 GeV/c2_{. The number of tracks near the B}0

s meson tends to be small, thus to reduce the background from combinatorics, an isolation criterion was applied. The isolation is defined as the sum of the momenta of the tracks used to reconstruct the signal divided by the total momentum of tracks contained within a cone of radius ∆R =p∆η2_{+ ∆φ}2 _{= 0.5 centered on the direction of} the B0

s candidate. We required the isolation to exceed 0.6. To suppress background, the visible proper decay length, defined as M (B0

s) · (~LT · ~pT)/p2T, was required to exceed 150 µm. Here ~LT is the displacement from the primary vertex to the B0

] 2 [GeV/c π φ m 1.8 2 2.2 ) 2 Events/(12 MeV/c 0 2 4 6 3 10 × -1 DØ, L=1.3 fb a) ] 2 [GeV/c KK m 0.98 1 1.02 1.04 1.06 ) 2 Events/(1.5 MeV/c 0 1 2 3 4 3 10 × b) DØ, L=1.3 fb-1

FIG. 1: (a) The (K+_K−_{π) invariant mass spectrum in the}

mass window 1.01 < M (K+_K−_{) < 1.03 GeV/c}2_{. (b) Mass}

spectrum of the (K+K−_{) system in the mass window 1.92 <}

M (K+_K−_{π) < 2.00 GeV/c}2_.

plane, and M (B0

s) is the mass of the Bs0meson [7]. These data are referred to as the (µDs) sample; the result-ing mass spectrum of the (K+_K−_{π) system is shown in} Fig. 1(a), where the Dsand D+mass peaks are described by single Gaussians with a second-order polynomial to parameterize the background. The signals of Ds→ φ1π and D+_{→ φ}

1π+are clearly seen. Figure 1(b) shows the mass spectrum of the (K+_K−_{) system, where a double} Gaussian describes the φ mass peak, and a second-order polynomial is used to parameterize the background.

To construct a (µφ2Ds) candidate from the prese-lection sample, a second φ2 meson from Ds → φ2µν was required. The selection criteria to reconstruct the second φ2 meson were identical to those of the first φ1 meson, with the exception that a wider mass range 0.99 < M (K+_K−_{) < 1.07 GeV/c}2 _{was used to estimate} the background distribution under the φ2 meson. This φ2 meson and muon were required to form a Ds vertex. To suppress background, the mass of the (µφ2) system was required to be 1.2 < M (µφ2) < 1.85 GeV/c2. The Ds(φ1π) and Ds(φ2µ) mesons were required to form a B0

s vertex. The mass of the (µφ2Ds) system, i.e., the combined Ds → φ2µν and Ds → φ1π candidates, was required to be 4.3 < M (µφ2Ds) < 5.2 GeV/c2. An isola-tion value exceeding 0.6 and visible proper decay length greater than 150 µm were required for the B0

s meson. To reduce the effect of systematic uncertain-ties, we calculated the ratio R = Br(B0

s → Ds(∗)Ds(∗)) · Br(Ds → φµν)/Br(Bs0 → µνD (∗) s ). We extracted Br(B0 s → D (∗)

s Ds(∗)) from R using the known values [7] for Br(Ds → φµν), Br(Bs0 → D

(∗)

s µν), and Br(Ds → φπ). R can be expressed in terms of experi-mental observables: R = Nµφ2Ds− Nbkg NµDs f (B 0 s → D (∗) s µν) × 1 2Br(φ → K+_K−₎ ε(B0 s → D (∗) s µν) ε(B0 s → D (∗) s Ds(∗)) , (1)

where NµDs is the number of (µDs) events, Nµφ₂Ds

is the number of (µφ2Ds) events, Nbkg is the number of background events in the (µφ2Ds) sample that are not produced by B0

s → D (∗)

s D(∗)s decays, and f (Bs0 → D(∗)s µν) is the fraction of events in (µDs) coming from Bs0 → D

(∗)

s µνX. The ratio of efficiencies ε(Bs0 → D(∗)s D(∗)s )/ε(Bs0 → D

(∗)

s µν) to reconstruct the two pro-cesses was determined from simulation. All propro-cesses involving b hadrons were simulated with EvtGen [8] interfaced to pythia [9], followed by full modeling of the detector response with geant [10] and event re-construction as in data. The number of (µDs) events was estimated from a binned fit to the (K+_K−_{π) mass} distribution shown in Fig. 1(a) from the 145,000 can-didates passing the selection criteria. The resulting fit is superimposed in Fig. 1(a) as a solid line and gives NµDs= 17670 ± 230 (stat) events.

The number of (µφ2Ds) events was extracted using a unbinned log-likelihood fit to the two-dimensional dis-tribution of the invariant masses MD of the (φ1π) sys-tem and Mφ2 of the two additional kaons from the (φ2µ)

system. All candidates from the (µφ2Ds) sample with 1.7 < MD< 2.3 GeV/c2and 0.99 < Mφ2 < 1.07 GeV/c

2 were included in the fit. In the fit, the masses and widths for both Ds and φ signals were fixed to the values ex-tracted from a fit to the (µDs) data sample. Extracted from the fit were the numbers of: Nµφ2Dsevents from

cor-related (joint) signal production of (φ1π) and φ2, events with a reconstructed (φ1π) in the mass peak of Ds(φ1π) without joint production of φ2 from (φ2µ) (i.e., uncorre-lated), events with a reconstructed φ2from (φ2µ) without joint production of (φ1π) in the mass peak of the Ds(φ1π) (i.e., also uncorrelated), and combinatorial background.

The results of the fit are displayed in Fig. 2. Fig-ure 2(a) displays the invariant mass distribution of (φ1π) candidates from the invariant mass signal window of Ds(φ2µ), and Fig. 2(b) displays the φ2 meson from Ds(φ2µ) in the invariant mass signal decay window of Ds(φ1π) candidates. The fit gives Nµφ2Ds = 13.4

+6.6 −6.0 events from the 340 candidates included in the fit.

As a consistency check, a similar sample was produced, but requiring the same charge for the muon and pion. From the fit, the number of (µ+_φ

2D+_s) signal events is found to be zero with an upper limit of 2.6 events (68% CL).

To extract the number of B0 s → D

(∗)

s µν and B0s → D(∗)s D(∗)s events, the composition of the selected sam-ples must be determined. The decays B0

s → D (∗) s µνX and B0 s → D (∗)

s τ (→ µν)νX were considered as sig-nal. The branching fractions for B → DsD(∗)X and B0

s → D (∗)

s Ds(∗) are taken from the Ref. [7]. There is no experimental information for the Br(B0

] 2 [GeV/c π φ m 1.8 2 2.2

)

Events/(30 MeV/c

)

Events/(4.5 MeV/c

FIG. 2: Invariant mass distributions of (a) Ds(φ1π) events

in the signal window of the invariant mass (K+_K−_{) from}

Ds(φ2µ), and (b) (K+K−) events from Ds(φ2µ) in the

in-variant mass window of the Ds(φ1π) signal region. The solid

curve is the projected result of the unbinned log-likelihood fit, the dotted curve shows the polynomial background contribu-tion, and the dashed line shows the uncorrelated production of (a) Ds(φ1π) and (b) φ2 mesons.

therefore we used the value 15.4% provided by Ref. [8] with an assigned uncertainty of 100%.

In addition, the (µDs) sample includes the processes c¯c → DsµνX, b¯b → DsµνX, and events with a misiden-tified muon, etc. which we refer to as the “peaking back-ground.” The estimated contribution of these processes in the (µDs) signal is (2 ± 1)%. In total, we estimate that the fraction of events in the (µDs) signal coming from B0 s→ D (∗) s µνX is f (Bs0→ D (∗) s µν) = 0.82 ± 0.05. We considered the number of events Nµφ2Ds from the

(µφ2Ds) sample to contain contributions from 1) the main signal B0

s → D

(∗)

s D(∗)s , and the following back-ground processes 2) B → D(∗)s D(∗)s KX, 3) Bs0 → Ds(∗)Ds(∗)X, 4) Bs0 → D (∗) s φµν, 5) peaking background, and 6) B0 s → D (∗)

s µν combined with a φ meson from fragmentation. There is no experimental information for most of the processes, therefore their contributions were estimated by counting events in different regions of the (µφ2Ds) phase space and comparing the obtained num-bers with the expected mass distribution for each back-ground process.

The mass of the (µφ2Ds) system for the second and third processes is much less than that for the main decay B0

s → D

(∗)

s D(∗)s because of the additional par-ticles, and the requirement M (µφ2Ds) > 4.3 GeV/c2 strongly suppresses them. The contribution of B0

s → Ds(∗)Ds(∗)X is much less than B → D(∗)s D(∗)s KX because of higher production rates of B+ _{and B}0 _{compared to} B0

s. Compared to the B → D (∗)

s D(∗)s KX process, the final state in the decay B0

s → D

(∗)

s Ds(∗)X includes at

least two pions due to isospin considerations. At least two gluons are required to produce this state (similar to ψ(2S) → J/ψππ); it is therefore additionally sup-pressed and its contribution was neglected. Simulation shows that for the B → D(∗)s D(∗)s KX decay, the fraction of events with M (µφ2Ds) > 4.3 GeV/c2 is 0.05. Re-quiring M (µφ2Ds) < 4.3 GeV/c2 and keeping all other selections, we observe 2.8+11.2_−2.8 events in data. Assum-ing that all these events are due to B → D(∗)s D(∗)s KX, we estimate their contribution to the signal (µφ2Ds) as 0.14+0.56−0.14 events.

The fourth process produces a high mass for both the (µφ2) and (µφ2Ds) systems and requiring M (µφ2) < 1.85 GeV/c2 _{strongly suppresses it. Simulation shows that} for this process, the fraction of events with M (µφ2) < 1.85 GeV/c2 _{is 0.14. Requiring M (µφ}

2) > 1.85 GeV/c2 and keeping all other selections, we observe 13±11 events. Assuming that all these events are due to the fourth background process, we estimate its contribution to the (µφ2Ds) signal as 1.88 ± 1.51 events.

The contribution of the peaking background is strongly suppressed by the event selection with an upper limit of 0.4 events. We therefore included it as an additional uncertainty in the number of background events.

The fitting procedure accounts for the possible back-ground contribution of the decay B0

s → D

(∗) s µν to-gether with the uncorrelated production of a φ meson from fragmentation. In addition, an attempt was made to reconstruct (µφ2Ds) events in the Bs0 → D

(∗) s µν simulation containing approximately 9200 reconstructed (µDs) events, and no such events were found. There-fore the contribution of this process was neglected. In total, we estimate the number of background events as Nbkg= 2.0 ± 1.6.

In determination of efficiencies, the final states in the (µDs) and (µφ2Ds) samples differ only by the two kaons from the additional φ2 meson. With the excep-tion of the isolaexcep-tion criterion, all other applied selec-tions are the same, so many detector-related system-atic uncertainties cancel. The muon pT spectrum in B0

s → D (∗)

s µν decay differs between data and simula-tion due to trigger effects and the uncertainties in B meson production in simulation. To correct for this dif-ference, weighting functions were applied to all Monte Carlo events. They were obtained from the ratio of simulated and data events for pT distributions of the B0

s meson and muon. With this correction, the ratio of efficiencies is ε(B0 s→ D (∗) s D(∗)s )/ε(Bs0→ D (∗) s µν) = 0.055±0.001 (stat). The systematic uncertainty in this value is discussed below. The difference in efficiency is mainly due to the softer momentum spectrum of the muon from the Ds→ φµν decay in the (µφ2Ds(∗)) sam-ple, compared to the muon from the B0

s → D (∗)

s µν decay in the (µD(∗)s ) sample.

Using all these inputs and taking the value Br(φ → K+_K−

) = 0.492 ± 0.006 [7], we obtain R = 0.015 ± 0.007 (stat). The statistical uncertainty shown includes only the uncertainty in Nµφ2Ds. All other uncertainties

are included in the systematics.

The experimental extraction of both Br(B0 s→ D

(∗) s µν) and Br(Ds → φµν) depend on Br(Ds → φπ). Factoriz-ing the dependence on Br(Ds→ φπ), we obtain Br(Bs0→ µνD(∗)s )Br(Ds → φπ) = (2.84 ± 0.49) × 10−3, Br(Ds → φµν) = (0.55 ± 0.04) · Br(Ds → φπ). Using these numbers, we finally obtain Br(B0

s → D

(∗)

s Ds(∗)) = 0.039+0.019−0.018(stat).

The systematic uncertainties in the measured value of Br(B0

s → D (∗) s D

(∗)

s ) were estimated as follows. All exter-nal branching fractions [7] were varied within one stan-dard deviation. A 100% uncertainty in the number of background events Nbkg in the (µφ2Ds) sample was as-sumed. The ratio of efficiencies can be affected by the uncertainties of reconstruction of two additional charged particles from the φ meson decay. The efficiency to re-construct a charged pion from the decay D∗+ _{→ D}0_π+ was measured in Ref. [11], and the obtained value was in a good agreement with the MC estimate. This compari-son is valid within the uncertainty of branching fractions of different B meson semileptonic decays, which is about 7%. Therefore we conservatively assigned a 14% system-atic uncertainty (7% for each charged particle, 100% cor-related) to the ratio of efficiencies and propagated it to the final result. For the ratio of efficiencies, a 15% uncer-tainty was assigned for the reweighting procedure, which reflects the difference in efficiency between weighted and unweighted estimates. The dependence of the number of (µφ2Ds) events on the fitting procedure was estimated by adding a possible signal contribution from D+_events which decreased the correlated signal by 3%, which we assigned as a systematic uncertainty.

Using these numbers, we obtain Br(B0 s → D (∗) s Ds(∗)) = 0.039+0.019 −0.017(stat) ± 0.014(syst) · [0.044/Br(Ds→ φπ)]2. Using Br(Ds→ φπ) = 0.044 ± 0.006 [7], we find Br(B0 s→ D(∗)s D(∗)s ) = 0.039 +0.019 −0.017(stat) +0.016 −0.015(syst). (2) The result is consistent with, and more precise than the ALEPH measurement Br(B0

s → D

(∗)

s D(∗)s ) = 0.077 ± 0.034+0.038_−0.026[4], where the value has been recalculated us-ing the current value of Br(Ds → φπ) [7]. We calculate ∆ΓCP

s [1] assuming that the decay Bs0 → D (∗) s D(∗)s is mainly CP-even and gives the primary contribution to the width difference between the CP-even and CP-odd B0 s states [3]: ∆ΓCP s Γs = 0.079+0.038−0.035(stat) +0.031 −0.030(syst). (3) Assuming CP-violation in B0

s mixing is small [2], this estimate is in good agreement with the SM prediction ∆Γs/Γs = 0.127 ± 0.024 [2] and with the direct mea-surement of this parameter by the D0 experiment in B0

s → J/ψφ decays [12]. The agreement with the CDF measurement of ∆Γs/Γs, which was also performed in B0

s → J/ψφ [13], is not as good, although still within two standard deviations.

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.

[*] Visitor from Augustana College, Sioux Falls, SD, USA. [§] Visitor from ICN-UNAM, Mexico City, Mexico.

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

[#] Visitor from Universit¨at Z¨urich, Z¨urich, Switzerland. [1] I. Dunietz et al., Phys. Rev. D 63, 114015 (2001). [2] A. Lenz and U. Nierste, arXiv:hep-ph/0612167. [3] R. Aleksan et al., Phys. Lett. B 316, 567 (1993). [4] R. Barate et al. (ALEPH Collaboration), Phys. Lett. B

486_{, 286 (2000).}

[5] V.M. Abazov et al. (D0 Collaboration), Nucl. Instrum. and Methods A 565, 463 (2006).

[6] J. Abdallah et al., (DELPHI Collaboration), Eur. Phys. J. C 32, 185 (2004).

[7] W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

[8] D.J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001). [9] T. Sj¨ostrand et al., Comp. Phys. Commun. 135, 238

(2001).

[10] R. Brun and F. Carminati, CERN Program Library Long Writeup W5013 (1993).

[11] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 94_{, 182001 (2005).}

[12] V.M. Abazov et al. (D0 Collaboration), arXiv:hep-ex/0701012.

[13] D. Acosta et al. (CDF Collaboration), Phys. Rev. Lett. 94, 101803 (2005).