Combined D0 measurements constraining the CP-violating phase and width difference in the $B_s^0$ system

arXiv:hep-ex/0702030v1 20 Feb 2007

Combined D0 Measurements Constraining the CP-violating Phase and Width

Difference in the B

s

System

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 _{C. Barnes,}43 _{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,}50 _{V. Bhatnagar,}26 _{M. Binder,}24 _{C. Biscarat,}19 _{I. Blackler,}43_{G. Blazey,}52 F. Blekman,43 _{S. Blessing,}49 _{D. 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,}22_{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_{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 _{B. Cox,}44_{S. Cr´ep´e-Renaudin,}13_{D. Cutts,}77 _{M. ´Cwiok,}29_{H. da Motta,}2 _{A. Das,}62 _{B. Davies,}42

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 _{M. Doidge,}42 _{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,}44_{M. 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,}47 _{L. Han,}6 K. Hanagaki,50 _{P. Hansson,}40_{K. 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_{A. Jenkins,}43 _{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 _{R. Kehoe,}79 _{S. Kermiche,}14 _{N. Khalatyan,}62 _{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,}10_{A. Lounis,}18_{P. Love,}42_{H.J. Lubatti,}82 _{M. Lynker,}55 _{A.L. Lyon,}50 A.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

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,}62 _{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 _{A. Stone,}51 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 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_{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}

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 20, 2007)

We combine the D0 measurement of the width difference between the light and heavy B0 s mass

eigenstates and of the CP-violating mixing phase determined from the time-dependent angular distributions in the B0

s → J/ψφ decays along with the charge asymmetry in semileptonic decays

flavor-specific B0

s lifetime, we obtain ∆Γs ≡ (ΓL− ΓH) = 0.13 ± 0.09 ps−1 and φs= −0.70+0.47 −0.39.

The data sample corresponds to an integrated luminosity of 1.1 fb−1 _{accumulated with the D0}

detector at the Fermilab Tevatron Collider.

PACS numbers: 13.25.Hw, 11.30.Er

One of the great challenges for elementary particle physics is to trace all possible sources of the violation of CP symmetry. In the standard model (SM) of parti-cle physics, CP symmetry is violated through the CKM mechanism [1]. Although the SM picture of CP viola-tion has so far been confirmed by all laboratory mea-surements, it has an unsolved problem: the level of CP violation in the SM is too small to produce the observed baryon number density in the universe [2]. Sources of CP violation beyond the CKM mechanism must, therefore, exist to account for the deficit. One source of CP viola-tion arises in the mixing of doublets of neutral mesons. CP violation in K0 _{mesons, composed of a down quark} and a strange quark, was discovered 40 years ago [3]. The B0

smesons are similar quark-antiquark bound states, with the down quark replaced by a bottom quark.

In the SM, the light (L) and heavy (H) mass eigen-states of the mixed B0

s system are expected to have size-able mass and decay width differences: ∆Ms≡ MH−ML and ∆Γs ≡ ΓL − ΓH. The two mass eigenstates are expected to be almost pure CP eigenstates. The CP-violating mixing phase is predicted [4] to be φs= (4.2 ± 1.4) × 10−3_{. New phenomena may alter φ}

sleading to a reduction of the observed ∆Γscompared to the SM pre-diction [4] ∆ΓSM

s : ∆Γs= ∆ΓSMs × | cos φs|. While Bs0– ¯

B0

s oscillations have been detected [5] and the mass dif-ference has recently been measured to high precision [6], the CP-violating phase remains unknown. The D0 ex-periment [7] at the Fermilab Tevatron Collider has con-ducted a series of studies [8, 9, 10, 11] of B0

s mesons produced in proton-antiproton (p¯p) interactions. This Letter utilises these results to obtain the best estimate of the CP-violating phase in the B0

s system. In Ref. [8], we studied the decay sequence B0

s → J/ψφ, J/ψ → µ+_µ−_{, φ → K}+_K−_{. From a fit to the} time-dependent angular distribution of the decay products, we obtained the mean lifetime, τs = 1/Γs (where Γs ≡ (ΓH + ΓL)/2), ∆Γs, and the first direct constraint on φs. As discussed in Ref. [8], there is a 4-fold ambiguity in the result for φs: ±φs and ±(π − φs). The sign of sin φs is reversed with the simultaneous reversal of the signs of the cosines of the CP-conserving strong phases δ1and δ2. (We adopted the amplitude definition and sign convention of Ref. [12]). The possible solutions are

|φs| = 0.79 ± 0.56 (stat)+0.01−0.14(syst), ∆Γs = 0.17 ± 0.08 (stat) ± 0.02 (syst) ps−1;

|φs| = 2.35 ± 0.56 (stat)+0.14−0.01(syst),

∆Γs = −0.17 ± 0.08 (stat) ± 0.02 (syst) ps−1;

(1) The first two solutions are consistent with the SM pre-diction [4]. (ps) s τ 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 (1/ps) _s Γ ∆ -0.1 0 0.1 0.2 0.3 0.4 0.5 φ ψ J/ → 0 s B SM Flavour DØ , 1.1 fb-1 Constrained Specific WA Lifetime

FIG. 1: The error ellipse (∆ ln(L) = 0.5) in the plane ∆Γs

versus τsfor the fit to the B0s → J/ψφ data (dashed blue line)

and for the fit with the constraint from the two D0 measure-ments of the charge asymmetry in semileptonic B0

sdecay, and

from the world average flavor-specific lifetime (solid red line). Also shown is a one-σ band representing the world average re-sult [14] for τfsand a one-σ band representing the theoretical

prediction ∆ΓSM

s = 0.088 ± 0.017 ps−1 [4]. [color online]

Flavor-specific decays of B0

s mesons provide indepen-dent constraints on the parameters of the system. An ef-fective mean lifetime, resulting from a single-exponential fit to the decay time distribution, τfs= 1/Γfs, is related to the physics parameters Γsand ∆Γsthrough the equa-tion Γfs = Γs− (∆Γs)2/2Γs + O(∆Γs)3/Γ

2

s [13]. We use the world-average value, τfs= 1/Γfs= 1.440 ± 0.036 ps [14], from a fit including the recent D0 measurement, τfs= 1/Γfs= 1.398 ± 0.044 (stat)+0.028_−0.025(syst) ps [9].

Independently, we obtained another constraint on the parameters of the B0

s system from the measurements of the semileptonic charge asymmetry induced by B0

s mix-ing. In general, the semileptonic charge asymmetry is defined as [15]: Aq_SL= N ( ¯B 0 q → ℓ+X) − N (Bq0→ ℓ−X) N ( ¯B0 q → ℓ+X) + N (Bq0→ ℓ−X) . (2)

It is related to the CP phase φq by [16]:

Aq_SL= ∆Γq ∆Mq

In Ref. [10], we measured the same-sign dimuon charge asymmetry defined as:

Aµµ_SL =N (b¯b → µ

+_µ+_{X) − N (b¯b → µ}−_µ−_X) N (b¯b → µ+_µ+_{X) + N (b¯b → µ}−_µ−_X). (4)

Both B0

dand Bs0contribute to this quantity [17], and the result of Ref. [10] is given as:

Ad SL + fsZs fdZd As SL= = −0.0092 ± 0.0044 (stat) ± 0.0032 (syst); (5) Zq = 1 1 − y2 q − 1 1 + x2 q ; xq = ∆Mq/Γq; yq = ∆Γq/(2Γq); where Ad

SLand AsSLare the charge asymmetries of the B 0 d and B0

s semileptonic decays, and fd and fsare the pro-duction rates of B0

d and B 0

s mesons in the hadronization of the b quark, respectively. In deriving relation (5), it is assumed that there is no direct CP violation in semilep-tonic B decays and that the semilepsemilep-tonic width of all B mesons is the same. Using the world-average values [15] fd= 0.398±0.012, fs= 0.103±0.014, xd= 0.776±0.008, and Zd= 0.376 ± 0.006 we obtain:

fsZs fdZd

= 0.70 ± 0.07 (syst) ± 0.10 (PDG). (6)

The value of Zs was computed using the measured val-ues of ∆Γs [8], τs [8], and ∆Ms [6]: Zs = 1.015+0.018−0.010. We have tested that propagating the Zs dependence on ∆Γs has negligible effect on the final results. The sys-tematic uncertainty arises mainly from a conservative es-timate of a possible variation in the reconstruction effi-ciency of muons from semileptonic decays of different B mesons [18].

The asymmetry Ad

SL has been measured at B facto-ries where only B0

d and B± mesons are produced. The average value of Ad

SL is [14]: AdSL = −0.0047 ± 0.0046. Combining this value and (5,6), and adding statistical and systematic uncertainties in quadrature, we obtain:

AsSL = −0.0064 ± 0.0101. (7)

In Ref. [11], we measured As

SL directly by using all events with at least one muon that were consistent with the sequential decay B0

s → µνDs with Ds → φπ. The result of this measurement is:

As

SL= +0.0245 ± 0.0193 (stat) ± 0.0035 (syst). (8) The measurements (7) and (8) are nearly independent since the fraction of dimuon final states in the sam-ple of semileptonic B0

s decays used in Ref. [11] is only about 10% [19], and the fraction of semileptonic decays B0

s → µνDswith Ds→ φπ in the dimuon sample used in

(radians) s φ -2 -1.5 -1 -0.5 0 0.5 1 (ps)_s τ 1.35 1.4 1.45 1.5 1.55 1.6 1.65 φ ψ J/ → 0 s B -1 D , 1.1 fb Constrained

FIG. 2: The error ellipse (∆ ln(L) = 0.5) in the plane (τs,

φs) for the fit to the Bs0→ J/ψφ data (dashed blue line) and

for the fit with the constraint from the two D0 measurements of the charge asymmetry in semileptonic B0

s decay, and from

the world average flavor-specific lifetime (solid red line).[color online] (radians) s φ -3 -2 -1 0 1 2 3 (1/ps) _s Γ ∆ -0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5 φ ψ J/ → 0 s B -1 DØ , 1.1 fb Constrained Combined semileptonic asymmetry charge band )| s φ |cos( × SM s Γ ∆ = Γ ∆ SM

FIG. 3: The error ellipse (∆ ln(L) = 0.5) in the plane (∆Γs,

φs) for the fit to the Bs0→ J/ψφ data (dashed blue line)

and for the fit with the constraint from the two D0 mea-surements of the charge asymmetry in semileptonic B0

s decay,

and from the world average flavor-specific lifetime (solid red line). The central values for all four solutions of the uncon-strained fit are indicated by blue squares. Also shown is the band representing the relation ∆Γs= ∆Γ

SM

s × | cos φs|, with

∆ΓSM

s = 0.088 ± 0.017 ps−1 [4] (dark shade), and the area

corresponding to Eq. 10 (light shade) . [color online]

Ref. [10] is less than 1%. Also, the systematic uncertain-ties of the two measurements are uncorrelated. The main source of systematic uncertainty in (7) is the correction due to K±_{decays, while in the case of the measurement} (8) it is the fitting procedure.

Their combination gives the best estimate of the charge asymmetry in semileptonic B0

s decays:

AsSL= 0.0001 ± 0.0090. (9) Using relation (3) and the result ∆Ms= 17.8 ± 0.1 ps−1

from the CDF experiment [6], we obtain: ∆Γs· tan φs= AsSL· ∆Ms= 0.02 ± 0.16 ps−1. (10) (radians) s φ -1.65 -1.3 -0.95 -0.6 -0.25 0.1 ) min -2ln(L/L 0 0.5 1 1.5 2 2.5 3 (radians) s φ likelihood scan:

FIG. 4: The likelihood scan versus φs for the constrained fit

(see text).

We have repeated the fit to the B0

s→ J/ψφ data, in-cluding the constraints from Eq. 10, and from the world-average measurement of τfs discussed earlier. To illus-trate the fit results and the impact of the constraints, in Figs. 1 – 3 we present likelihood contours in three planes, ∆Γs versus τs, τs versus φs, and ∆Γs versus φs, respectively. The contours indicate error ellipses, ∆ ln(L) = 0.5, corresponding to the confidence level of 39%. The 4-fold ambiguity remains unresolved. The like-lihood profile as a function of φs for the first solution listed in Eq. 1 is shown in Fig. 4. The extracted value of φsdeviates from zero by 1.2 standard deviations.

In summary, for the solution with φs < 0, cos δ1 > 0 and cos δ2 < 0, we find the decay width difference and the CP-violating phase in the B0

s system to be: ∆Γs = 0.13 ± 0.09 ps−1,

φs = −0.70+0.47−0.39. (11)

The measurement uncertainty is dominated by the lim-ited statistics. The systematic uncertainties include a variation of the background model in the analysis of the decay B0

s → J/ψφ, detector acceptance, and sensitivity to the details of the track and vertex reconstruction. The results are consistent with the SM predictions [4].

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.

[1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys., 49, 652 (1973).

[2] P. Huet and E. Sather, Phys. Rev. D 51, 379 (1995). [3] J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay,

Phys. Rev. Lett. 13, 138 (1964).

[4] A. Lenz, and U. Nierste, hep-ph/0612167.

[5] D0 Collaboration, V.M. Abazov et al., Phys. Rev. Lett. 97_{, 021802 (2006).}

[6] CDF Collaboration, A. Abulencia et al., Phys. Rev. Lett. 97_{, 242003 (2006);}

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

[8] D0 Collaboration, V.M. Abazov et al., submitted to Phys. Rev. Lett., hep-ex/0701012.

[9] D0 Collaboration, V.M. Abazov et al., Phys. Rev. Lett., 97_{, 241801 (2006).}

[10] D0 Collaboration, V.M. Abazov et al., Phys. Rev. D 74, 092001 (2006).

[11] D0 Collaboration, V.M. Abazov et al., submitted to Phys. Rev. Lett., hep-ex/0701007.

[12] A.S. Dighe, I. Dunietz, and R. Fleischer, Phys. Lett. B 433, 147 (1998); K. Anikeev et al., “B physics at the Tevatron: Run II and beyond,” FERMILAB-Pub-01/197, hep-ph/0201071, p. 375.

[13] K. Anikeev et al., “B physics at the Tevatron: Run II and beyond,” FERMILAB-Pub-01/197, hep-ph/0201071, p. 360.

[14] E. Barberio et al. [Heavy Flavor Averaging Group (HFAG)], “Averages of b-hadron properties as of fall 2006,” in preparation.

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

[16] M. Beneke, G. Buchalla, A. Lenz and U. Nierste, Phys. Lett. B 576, 173 (2003).

[17] Y. Grossman, Y. Nir, and G. Raz, “Constraining the Phase of Bs – BsMixing”, hep-ph/0605028v2.

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

[19] D0 Collaboration, V.M. Abazov et al., Phys. Rev. D 74, 112002 (2006).