Measurement of the lifetime difference in the B$_s^0$ system

arXiv:hep-ex/0507084v1 19 Jul 2005

Measurement of the Lifetime Difference in the B

s

System

V.M. Abazov,35_{B. Abbott,}72 _{M. Abolins,}63_{B.S. Acharya,}29_{M. Adams,}50 _{T. Adams,}48 _{M. Agelou,}18 _{J.-L. Agram,}19 S.H. Ahn,31 _{M. Ahsan,}57 _{G.D. Alexeev,}35 _{G. Alkhazov,}39 _{A. Alton,}62_{G. Alverson,}61_{G.A. Alves,}2 _{M. Anastasoaie,}34 T. Andeen,52 _{S. Anderson,}44 _{B. Andrieu,}17 _{Y. Arnoud,}14 _{M. Arov,}51 _{A. Askew,}48 _{B. ˚Asman,}40 _{A.C.S. Assis Jesus,}3

O. Atramentov,55 _{C. Autermann,}21 _{C. Avila,}8 _{F. Badaud,}13_{A. Baden,}59_{L. Bagby,}51 _{B. Baldin,}49 _{P.W. Balm,}33 P. Banerjee,29 _{S. Banerjee,}29 _{E. Barberis,}61_{P. Bargassa,}76_{P. Baringer,}56_{C. Barnes,}42 _{J. Barreto,}2_{J.F. Bartlett,}49

U. Bassler,17 _{D. Bauer,}53 _{A. Bean,}56 _{S. Beauceron,}17 _{M. Begalli,}3 _{M. Begel,}68 _{A. Bellavance,}65 _{S.B. Beri,}27 G. Bernardi,17 _{R. Bernhard,}49,∗_{I. Bertram,}41_{M. Besan¸con,}18 _{R. Beuselinck,}42 _{V.A. Bezzubov,}38_{P.C. Bhat,}49 V. Bhatnagar,27_{M. Binder,}25 _{C. Biscarat,}41_{K.M. Black,}60_{I. Blackler,}42 _{G. Blazey,}51_{F. Blekman,}42 _{S. Blessing,}48

D. Bloch,19 _{U. Blumenschein,}23 _{A. Boehnlein,}49 _{O. Boeriu,}54 _{T.A. Bolton,}57_{F. Borcherding,}49 _{G. Borissov,}41 K. Bos,33 _{T. Bose,}67 _{A. Brandt,}74 _{R. Brock,}63_{G. Brooijmans,}67 _{A. Bross,}49_{N.J. Buchanan,}48 _{D. Buchholz,}52 M. Buehler,50_{V. Buescher,}23_{S. Burdin,}49 _{S. Burke,}44_{T.H. Burnett,}78 _{E. Busato,}17_{C.P. Buszello,}42 _{J.M. Butler,}60

J. Cammin,68 _{S. Caron,}33_{W. Carvalho,}3_{B.C.K. Casey,}73_{N.M. Cason,}54 _{H. Castilla-Valdez,}32 _{S. Chakrabarti,}29 D. Chakraborty,51 K.M. Chan,68 A. Chandra,29 D. Chapin,73 F. Charles,19 E. Cheu,44D.K. Cho,60 S. Choi,47

B. Choudhary,28_{T. Christiansen,}25 _{L. Christofek,}56 _{D. Claes,}65 _{B. Cl´ement,}19 _{C. Cl´ement,}40 _{Y. Coadou,}5 M. Cooke,76_{W.E. Cooper,}49 _{D. Coppage,}56 _{M. Corcoran,}76 _{A. Cothenet,}15 _{M.-C. Cousinou,}15 _{B. Cox,}43 S. Cr´ep´e-Renaudin,14_{D. Cutts,}73 _{H. da Motta,}2_{M. Das,}58_{B. Davies,}41_{G. Davies,}42 _{G.A. Davis,}52 _{K. De,}74 P. de Jong,33_{S.J. de Jong,}34 _{E. De La Cruz-Burelo,}62 _{C. De Oliveira Martins,}3_{S. Dean,}43 _{J.D. Degenhardt,}62 F. D´eliot,18 _{M. Demarteau,}49 _{R. Demina,}68 _{P. Demine,}18 _{D. Denisov,}49 _{S.P. Denisov,}38 _{S. Desai,}69 _{H.T. Diehl,}49

M. Diesburg,49 _{M. Doidge,}41 _{H. Dong,}69 _{S. Doulas,}61 _{L.V. Dudko,}37 _{L. Duflot,}16 _{S.R. Dugad,}29_{A. Duperrin,}15 J. Dyer,63_{A. Dyshkant,}51_{M. Eads,}51_{D. Edmunds,}63 _{T. Edwards,}43_{J. Ellison,}47_{J. Elmsheuser,}25 _{V.D. Elvira,}49 S. Eno,59 _{P. Ermolov,}37 _{O.V. Eroshin,}38 _{J. Estrada,}49 _{H. Evans,}67 _{A. Evdokimov,}36_{V.N. Evdokimov,}38_{J. Fast,}49 S.N. Fatakia,60_{L. Feligioni,}60 _{A.V. Ferapontov,}38_{T. Ferbel,}68 _{F. Fiedler,}25 _{F. Filthaut,}34_{W. Fisher,}49_{H.E. Fisk,}49

I. Fleck,23 _{M. Fortner,}51 _{H. Fox,}23 _{S. Fu,}49 _{S. Fuess,}49 _{T. Gadfort,}78_{C.F. Galea,}34 _{E. Gallas,}49_{E. Galyaev,}54 C. Garcia,68 _{A. Garcia-Bellido,}78_{J. Gardner,}56 _{V. Gavrilov,}36_{A. Gay,}19 _{P. Gay,}13 _{D. Gel´e,}19 _{R. Gelhaus,}47 K. Genser,49 _{C.E. Gerber,}50 _{Y. Gershtein,}48_{D. Gillberg,}5 _{G. Ginther,}68 _{T. Golling,}22 _{N. Gollub,}40 _{B. G´omez,}8

K. Gounder,49 _{A. Goussiou,}54 _{P.D. Grannis,}69 _{S. Greder,}3 _{H. Greenlee,}49 _{Z.D. Greenwood,}58_{E.M. Gregores,}4 Ph. Gris,13 J.-F. Grivaz,16L. Groer,67 S. Gr¨unendahl,49 M.W. Gr¨unewald,30 S.N. Gurzhiev,38G. Gutierrez,49 P. Gutierrez,72 _{A. Haas,}67_{N.J. Hadley,}59 _{S. Hagopian,}48 _{I. Hall,}72_{R.E. Hall,}46 _{C. Han,}62_{L. Han,}7 _{K. Hanagaki,}49

K. Harder,57_{A. Harel,}26 _{R. Harrington,}61_{J.M. Hauptman,}55 _{R. Hauser,}63 _{J. Hays,}52_{T. Hebbeker,}21 _{D. Hedin,}51 J.M. Heinmiller,50 _{A.P. Heinson,}47 _{U. Heintz,}60 _{C. Hensel,}56 _{G. Hesketh,}61_{M.D. Hildreth,}54 _{R. Hirosky,}77 J.D. Hobbs,69 _{B. Hoeneisen,}12 _{M. Hohlfeld,}24 _{S.J. Hong,}31 _{R. Hooper,}73 _{P. Houben,}33 _{Y. Hu,}69 _{J. Huang,}53 V. Hynek,9 _{I. Iashvili,}47 _{R. Illingworth,}49_{A.S. Ito,}49 _{S. Jabeen,}56 _{M. Jaffr´e,}16_{S. Jain,}72_{V. Jain,}70_{K. Jakobs,}23 A. Jenkins,42_{R. Jesik,}42_{K. Johns,}44_{M. Johnson,}49_{A. Jonckheere,}49_{P. Jonsson,}42_{A. Juste,}49_{D. K¨afer,}21_{S. Kahn,}70

E. Kajfasz,15 _{A.M. Kalinin,}35 _{J. Kalk,}63 _{D. Karmanov,}37 _{J. Kasper,}60_{I. Katsanos,}67_{D. Kau,}48 _{R. Kaur,}27 R. Kehoe,75 _{S. Kermiche,}15 _{S. Kesisoglou,}73_{A. Khanov,}68 _{A. Kharchilava,}54_{Y.M. Kharzheev,}35_{H. Kim,}74 T.J. Kim,31 _{B. Klima,}49 _{J.M. Kohli,}27_{J.-P. Konrath,}23_{M. Kopal,}72 _{V.M. Korablev,}38_{J. Kotcher,}70_{B. Kothari,}67 A. Koubarovsky,37_{A.V. Kozelov,}38 _{J. Kozminski,}63 _{A. Kryemadhi,}77_{S. Krzywdzinski,}49 _{Y. Kulik,}49_{A. Kumar,}28

S. Kunori,59 _{A. Kupco,}11 _{T. Kurˇca,}20 _{J. Kvita,}9 _{S. Lager,}40 _{N. Lahrichi,}18_{G. Landsberg,}73_{J. Lazoflores,}48 A.-C. Le Bihan,19 _{P. Lebrun,}20 _{W.M. Lee,}48 _{A. Leflat,}37 _{F. Lehner,}49,∗ _{C. Leonidopoulos,}67 _{J. Leveque,}44

P. Lewis,42 _{J. Li,}74 _{Q.Z. Li,}49 _{J.G.R. Lima,}51 _{D. Lincoln,}49 _{S.L. Linn,}48 _{J. Linnemann,}63 _{V.V. Lipaev,}38 R. Lipton,49 L. Lobo,42A. Lobodenko,39M. Lokajicek,11A. Lounis,19P. Love,41H.J. Lubatti,78 L. Lueking,49

M. Lynker,54 _{A.L. Lyon,}49 _{A.K.A. Maciel,}51 _{R.J. Madaras,}45 _{P. M¨attig,}26 _{C. Magass,}21 _{A. Magerkurth,}62 A.-M. Magnan,14 _{N. Makovec,}16_{P.K. Mal,}29 _{H.B. Malbouisson,}3 _{S. Malik,}65_{V.L. Malyshev,}35 _{H.S. Mao,}6 Y. Maravin,49_{M. Martens,}49 _{S.E.K. Mattingly,}73 _{A.A. Mayorov,}38_{R. McCarthy,}69 _{R. McCroskey,}44_{D. Meder,}24 A. Melnitchouk,64 _{A. Mendes,}15 _{D. Mendoza,}8_{M. Merkin,}37_{K.W. Merritt,}49_{A. Meyer,}21_{J. Meyer,}22_{M. Michaut,}18

H. Miettinen,76 J. Mitrevski,67 J. Molina,3 N.K. Mondal,29 R.W. Moore,5 T. Moulik,56 G.S. Muanza,20 M. Mulders,49_{L. Mundim,}3 _{Y.D. Mutaf,}69_{E. Nagy,}15 _{M. Naimuddin,}28_{M. Narain,}60_{N.A. Naumann,}34 _{H.A. Neal,}62

E. Nurse,43 _{V. O’Dell,}49 _{D.C. O’Neil,}5 _{V. Oguri,}3 _{N. Oliveira,}3 _{N. Oshima,}49 _{G.J. Otero y Garz´on,}50_{P. Padley,}76 N. Parashar,58_{S.K. Park,}31_{J. Parsons,}67 _{R. Partridge,}73_{N. Parua,}69 _{A. Patwa,}70 _{G. Pawloski,}76 _{P.M. Perea,}47 E. Perez,18 _{P. P´etroff,}16 _{M. Petteni,}42 _{R. Piegaia,}1_{M.-A. Pleier,}68_{P.L.M. Podesta-Lerma,}32_{V.M. Podstavkov,}49 Y. Pogorelov,54_{M.-E. Pol,}2_{A. Pompoˇs,}72_{B.G. Pope,}63_{W.L. Prado da Silva,}3_{H.B. Prosper,}48_{S. Protopopescu,}70

J. Qian,62 _{A. Quadt,}22 _{B. Quinn,}64 _{K.J. Rani,}29 _{K. Ranjan,}28 _{P.A. Rapidis,}49 _{P.N. Ratoff,}41 _{S. Reucroft,}61 M. Rijssenbeek,69_{I. Ripp-Baudot,}19_{F. Rizatdinova,}57 _{S. Robinson,}42 _{R.F. Rodrigues,}3_{C. Royon,}18 _{P. Rubinov,}49

R. Ruchti,54 _{V.I. Rud,}37 _{G. Sajot,}14 _{A. S´anchez-Hern´andez,}32_{M.P. Sanders,}59 _{A. Santoro,}3 _{G. Savage,}49 L. Sawyer,58 _{T. Scanlon,}42_{D. Schaile,}25_{R.D. Schamberger,}69 _{Y. Scheglov,}39 _{H. Schellman,}52_{P. Schieferdecker,}25

C. Schmitt,26 _{C. Schwanenberger,}22_{A. Schwartzman,}66 _{R. Schwienhorst,}63 _{S. Sengupta,}48 _{H. Severini,}72 E. Shabalina,50 _{M. Shamim,}57 _{V. Shary,}18 _{A.A. Shchukin,}38_{W.D. Shephard,}54 _{R.K. Shivpuri,}28 _{D. Shpakov,}61 R.A. Sidwell,57 _{V. Simak,}10_{V. Sirotenko,}49_{P. Skubic,}72 _{P. Slattery,}68 _{R.P. Smith,}49 _{K. Smolek,}10 _{G.R. Snow,}65

J. Snow,71 S. Snyder,70 S. S¨oldner-Rembold,43 X. Song,51 L. Sonnenschein,17 A. Sopczak,41 M. Sosebee,74 K. Soustruznik,9_{M. Souza,}2 _{B. Spurlock,}74_{N.R. Stanton,}57 _{J. Stark,}14_{J. Steele,}58 _{K. Stevenson,}53 _{V. Stolin,}36

A. Stone,50 _{D.A. Stoyanova,}38_{J. Strandberg,}40 _{M.A. Strang,}74 _{M. Strauss,}72 _{R. Str¨ohmer,}25_{D. Strom,}52 M. Strovink,45 _{L. Stutte,}49 _{S. Sumowidagdo,}48 _{A. Sznajder,}3 _{M. Talby,}15 _{P. Tamburello,}44 _{W. Taylor,}5 P. Telford,43 _{J. Temple,}44 _{M. Titov,}23 _{M. Tomoto,}49 _{T. Toole,}59 _{J. Torborg,}58 _{S. Towers,}69 _{T. Trefzger,}24 S. Trincaz-Duvoid,17 _{D. Tsybychev,}69 _{B. Tuchming,}18 _{C. Tully,}66 _{A.S. Turcot,}43 _{P.M. Tuts,}67 _{L. Uvarov,}39 S. Uvarov,39_{S. Uzunyan,}51 _{B. Vachon,}5_{P.J. van den Berg,}33 _{R. Van Kooten,}53_{W.M. van Leeuwen,}33 _{N. Varelas,}50

E.W. Varnes,44 _{A. Vartapetian,}74 _{I.A. Vasilyev,}38_{M. Vaupel,}26 _{P. Verdier,}20 _{L.S. Vertogradov,}35_{M. Verzocchi,}49 F. Villeneuve-Seguier,42 _{J.-R. Vlimant,}17 _{E. Von Toerne,}57 _{M. Vreeswijk,}33 _{T. Vu Anh,}16 _{H.D. Wahl,}48_{L. Wang,}59

J. Warchol,54 _{G. Watts,}78 _{M. Wayne,}54 _{M. Weber,}49 _{H. Weerts,}63_{N. Wermes,}22 _{M. Wetstein,}59 _{A. White,}74 V. White,49 _{D. Wicke,}49_{D.A. Wijngaarden,}34_{G.W. Wilson,}56_{S.J. Wimpenny,}47 _{J. Wittlin,}60 _{M. Wobisch,}49 J. Womersley,49_{D.R. Wood,}61 _{T.R. Wyatt,}43 _{Y. Xie,}73 _{Q. Xu,}62 _{N. Xuan,}54 _{S. Yacoob,}52 _{R. Yamada,}49 _{M. Yan,}59

T. Yasuda,49 _{Y.A. Yatsunenko,}35 _{Y. Yen,}26 _{K. Yip,}70 _{H.D. Yoo,}73 _{S.W. Youn,}52 _{J. Yu,}74 _{A. Yurkewicz,}69 A. Zabi,16 _{A. Zatserklyaniy,}51 _{M. Zdrazil,}69 _{C. Zeitnitz,}24 _{D. Zhang,}49 _{X. Zhang,}72 _{T. Zhao,}78 _{Z. Zhao,}62 B. Zhou,62_{J. Zhu,}69_{M. Zielinski,}68 _{D. Zieminska,}53 _{A. Zieminski,}53 _{R. Zitoun,}69 _{V. Zutshi,}51 _{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_{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}

27_{Panjab University, Chandigarh, India} 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_{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_{Lancaster University, Lancaster, United Kingdom} 42_{Imperial College, London, United Kingdom} 43_{University of Manchester, Manchester, United Kingdom}

44_{University of Arizona, Tucson, Arizona 85721, USA}

45_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 46_{California State University, Fresno, California 93740, USA}

47_{University of California, Riverside, California 92521, USA} 48_{Florida State University, Tallahassee, Florida 32306, USA} 49_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA}

50_{University of Illinois at Chicago, Chicago, Illinois 60607, USA} 51_{Northern Illinois University, DeKalb, Illinois 60115, USA}

52_{Northwestern University, Evanston, Illinois 60208, USA} 53_{Indiana University, Bloomington, Indiana 47405, USA} 54_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

55_{Iowa State University, Ames, Iowa 50011, USA} 56_{University of Kansas, Lawrence, Kansas 66045, USA} 57_{Kansas State University, Manhattan, Kansas 66506, USA} 58_{Louisiana Tech University, Ruston, Louisiana 71272, USA} 59_{University of Maryland, College Park, Maryland 20742, USA}

60_{Boston University, Boston, Massachusetts 02215, USA} 61_{Northeastern University, Boston, Massachusetts 02115, USA}

62_{University of Michigan, Ann Arbor, Michigan 48109, USA} 63_{Michigan State University, East Lansing, Michigan 48824, USA}

64_{University of Mississippi, University, Mississippi 38677, USA} 65_{University of Nebraska, Lincoln, Nebraska 68588, USA} 66_{Princeton University, Princeton, New Jersey 08544, USA}

67_{Columbia University, New York, New York 10027, USA} 68_{University of Rochester, Rochester, New York 14627, USA} 69_{State University of New York, Stony Brook, New York 11794, USA}

70_{Brookhaven National Laboratory, Upton, New York 11973, USA} 71_{Langston University, Langston, Oklahoma 73050, USA} 72_{University of Oklahoma, Norman, Oklahoma 73019, USA}

73_{Brown University, Providence, Rhode Island 02912, USA} 74_{University of Texas, Arlington, Texas 76019, USA} 75_{Southern Methodist University, Dallas, Texas 75275, USA}

76_{Rice University, Houston, Texas 77005, USA} 77_{University of Virginia, Charlottesville, Virginia 22901, USA}

78_{University of Washington, Seattle, Washington 98195, USA}

(Dated: July 19, 2005)

We present a study of the decay Bs0→ J/ψ φ. We obtain the CP-odd fraction in the final state at time zero, R⊥= 0.16 ± 0.10 (stat) ± 0.02 (syst), the average lifetime of the (Bs0, B

0

s) system, τ (B0

s) = 1.39+0.13−0.16 (stat)+0.01−0.02 (syst) ps, and the relative width difference between the heavy and light mass eigenstates, ∆Γ/Γ ≡ (ΓL− ΓH)/Γ = 0.24+0.28−0.38 (stat)+0.03−0.04 (syst). With the additional constraint from the world average of the B0

s lifetime measurements using semileptonic decays, we find τ (B0

s) = 1.39 ± 0.06 ps and ∆Γ/Γ = 0.25+0.14−0.15. For the ratio of the Bs0 and B0 lifetimes we obtain τ(B

0 s)

τ(B0₎ = 0.91 ± 0.09 (stat) ± 0.003 (syst).

PACS numbers: 13.25.Hw, 11.30.Er

Within the framework of the standard model (SM), the B0

mass and decay width differences between the heavy and light eigenstates, ∆M ≡ MH− MLand ∆Γ ≡ ΓL− ΓH, are sizeable. The mixing phase δφ is small and to a good approximation the two mass eigenstates correspond to CP eigenstates. New phenomena may alter δφ, leading to a reduction of the observed ∆Γ/Γ compared to the SM prediction [1].

The decay B0

s → J/ψ φ, proceeding through the quark process b → c¯cs, gives rise to both CP-even and CP-odd final states. It is possible to separate the two CP com-ponents of the decay B0

s → J/ψ φ, and thus to measure the lifetime difference, through a simultaneous study of the time evolution and angular distributions of the decay products of the J/ψ and φ mesons. Angular distribu-tion of B0

s → J/ψ(→ µ+µ−) φ(→ K+K−) involve three angles. Current statistics are such that the use of all three angles characterizing the final state is not yet ben-eficial. We use a variable particularly sensitive to sepa-rating the CP states, the cosine of the transversity polar angle (called ”tranversity”), as defined below.

The analysis of data collected with the DØ detector [2] at the Fermilab Tevatron collider presented in this Letter is an extension of a recently published study [3] done un-der the single B0

s lifetime hypothesis. We perform an un-binned maximum likelihood fit to the data, including the B0

s candidate mass, lifetime, and transversity, in the de-cay sequence Bs0→ J/ψ φ, J/ψ → µ+µ−, φ → K+K−. We extract three parameters characterizing the B0

s sys-tem and its decay: τ (B0

s) = 1/Γ, where Γ ≡ (ΓH+ΓL)/2; ∆Γ/Γ; and R⊥, the relative rate of the decay to the CP-odd states at time zero. The average lifetimes of B0

s and B0_{, as defined above, are expected to be equal to within} 1% [4], and their ratio is determined by measuring the lifetime of B0_{in the similar decay topology of J/ψK}∗_.

The data were collected between June 2002 and Au-gust 2004. The sample is selected by requiring two recon-structed muons with a transverse momentum pT > 1.5 GeV. Each muon is required to be detected as a track segment in at least one layer of the muon system and to be matched to a central track. One muon is required to have segments both inside and outside the toroid. We require the events to satisfy a muon trigger that does not include any cuts on the impact parameter. The sample corresponds to an integrated luminosity of approximately 450 pb−1_.

To select the B0

s candidate sample, we apply the fol-lowing kinematic and quality cuts. Minimum values of momenta in the transverse plane for B0

s, φ, and K mesons are set at 6.0 GeV, 1.5 GeV, and 0.7 GeV, respectively. J/ψ candidates are accepted if the invariant mass is in the range 2.90 – 3.25 GeV. Successful candidates are con-strained to the average reconstructed J/ψ mass of 3.072 GeV. Decay products of the φ candidates are required to satisfy a fit to a common vertex and to have an invari-ant mass in the range 1.01 – 1.03 GeV. We require the (J/ψ, φ) pair to be consistent with coming from a

com-Mass (GeV)

5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Candidates per 20.0 MeV

0 50 100 150 200 250 300 350 400 450 Data Total Fit Prompt Bkg. Non-prompt Bkg.

φ

ψ

J/

→

B

D

FIG. 1: The invariant mass distribution of the (J/ψ, φ) sys-tem for B0

s candidates. The curves are projections of the maximum likelihood fit (see text).

mon vertex, and to have an invariant mass in the range 5.0 – 5.8 GeV. In case of multiple φ meson candidates, we select the one with the highest transverse momentum. Monte Carlo (MC) studies show that the pT spectrum of the φ mesons coming from B0

s decay is harder than the spectrum of a pair of random tracks from the underlying event. We define the signed decay length of a B0

s meson LB

xyas the vector pointing from the primary vertex to the decay vertex projected on the B0

s transverse momentum. To reconstruct the primary vertex, we select tracks with pT > 0.3 GeV that are not used as decay products of the Bscandidate and apply a constraint to the average beam spot position. The proper decay length, ct, is defined by the relation ct = LB

xy· MB0

s/pT where MB 0

s is the world average mass of the B0

s meson [5]. The distribution of the proper decay length uncertainty σ(ct) of B0

s mesons peaks around 25 µm. We accept events with σ(ct) < 60 µm. There are 9699 events satisfying the above cuts.

The resulting invariant mass distribution of the (J/ψ, φ) system is shown in Fig. 1. The curves are pro-jections of the maximum likelihood fit, described below. The fit assigns 513±33 events to B0

s decay.

Using the same data sample and analogous kinematic and quality cuts, we select a sample of 1913 events of the decay sequence B0_{→ J/ψK}∗_{, J/ψ → µ}+_µ−_, K∗ _{→ K}±_π∓_{, and update the B}0 _{lifetime measurement} reported in Ref. [3] with larger statistics.

We perform a simultaneous unbinned maximum like-lihood fit to the proper decay length, transversity, and mass. The likelihood function L is given by:

L = N Y i=1

[fsigFsigi + (1 − fsig)Fbcki ], (1)

where N is the total number of events, Fi

sig (Fbcki ) is the product of the mass, proper decay length, and the

transversity probability density functions for the signal (background), and fsigis the fraction of signal in the sam-ple. Background is divided into two categories, based on their origin and lifetime characteristics. “Prompt” back-ground is due to directly produced J/ψ mesons accompa-nied by random tracks arising from hadronization. This background is distinguished from “non-prompt” back-ground, where the J/ψ meson is a product of a B-hadron decay while the tracks forming the φ candidate emanate from a multibody decay of the same B hadron or from the underlying event. We allow for independent parame-ters for the two background components in mass, lifetime, and transversity. There are nineteen free parameters in the fit.

For the signal mass distribution, we use a sum of two Gaussian functions with a fixed ratio of widths and nor-malizations, obtained in a fit to the signal-dominated

subset satisfying ct/σ(ct) > 5. We allow for two free parameters, the common mean value and the width of the narrow component. The lifetime distribution of the signal is parametrized by an exponential convoluted with a Gaussian function with the width taken from the event-by-event estimate of σ(ct). To allow for the possibility of the lifetime uncertainty to be systematically underes-timated, we introduce a free scale factor.

The transversity distribution of the signal is deter-mined in the following way. The time-dependent three-angle distribution for the decay of untagged B0

s mesons, i.e., summed over B0

s and B 0

s, expressed in terms of the linear polarization amplitudes |Ax(t)| and their relative phases δi is [6]:

d3_Γ(t)

d cos θ dϕ d cos ψ ∝ 2|A0(0)|

2_e−ΓLt_cos2

ψ(1 − sin2θ cos2ϕ) + sin2ψ{|Ak(0)|2e−ΓLt(1 − sin2θ sin2ϕ)

+|A⊥(0)|2e−ΓHtsin2θ} + 1 √

2sin 2ψ|A0(0)||Ak(0)| cos(δ2− δ1)e −ΓLt

sin2θ sin 2ϕ

+  ₁

√

2|A0(0)||A⊥(0)| cos δ2sin 2ψ sin 2θ cos ϕ − |Ak(0)||A⊥(0)| cos δ1sin

2_{ψ sin 2θ sin ϕ} 1 2 e

−ΓHt

− e−ΓLt
δφ . (2)

In the coordinate system of the J/ψ rest frame (where the φ meson moves in the x direction, the z axis is perpendic-ular to the decay plane of φ → K+_K−_{, and p}

y(K+) ≥ 0), the transversity polar and azimuthal angles (θ, ϕ) de-scribe the direction of the µ+_{, and ψ is the angle between} ~

p(K+_{) and −~p(J/ψ) in the φ rest frame.}

We model the acceptance in the three angles by poly-nomials, with parameters determined using Monte Carlo simulations. We have used the SVV HELAMP model in the EvtGen generator [7], interfaced to the Pythia program [8]. Reconstructed events were reweighted to match the kinematic distributions with the data.

To obtain the one-angle (transversity) distribution, we integrate the three-angle distribution over the angles ψ and ϕ. The resulting distribution depends on one free parameter, R⊥ = |A⊥(0)|2. There is a small correction term due to the nonuniformity of the acceptance in the angle ϕ, which is proportional to |A0(0)|2− |Ak(0)|2. We use the CDF Collaboration measurement [9] of this dif-ference, 0.355±0.066.

The lifetime shape of the background is described as a sum of a prompt component, simulated as a Gaus-sian function centered at zero, and a non-prompt

com-ponent, simulated as a superposition of one exponen-tial for the negative ct region and two exponenexponen-tials for the positive ct region, with free slopes and normaliza-tion. The mass distributions of the backgrounds are parametrized by first-order polynomials. The transver-sity distributions of backgrounds are parametrized as (1 + a2cos2θ + a4cos4θ).

Results of the fit are presented in Figs. 1 – 4. The proper decay length distribution, and the transversity distribution, both with the fit results overlaid are shown in Figs. 2 and 3. Figure 4 shows the one standard devia-tion ( one-σ) contour for cτ (B0

s) versus ∆Γ/Γ. It provides the best display of the uncertainty range for these cor-related parameters. Our best fit returns R⊥= 0.16±0.10 and ∆Γ/Γ = 0.24+0.28−0.38at τ (B0s) = 1.39

+0.13 −0.16ps.

We do a series of alternative fits, at discrete values of τ (B0

s). The results for ∆Γ/Γ, its one standard de-viation range, and the corresponding value of the like-lihood, are listed in Table I. We verify the procedure by performing fits on a sample of approximately 50,000 MC events passed through the full chain of detector sim-ulation, event reconstruction, and maximum likelihood fitting. We see no bias in the event reconstruction or

ct (cm) -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 m µ Candidates per 50.0 10-2 10-1 1 10 102 103 Data Total Fit Total Signal CP-even CP-odd Background ) < 5.42 GeV s0 5.26 < M(B

_D

FIG. 2: The proper decay length ct of the B0

s candidates in the signal mass region. The curves show the signal contribu-tion, dashed (red); the background, lower solid line (green); and total, upper solid line (black) in the signal mass region.

Transversity -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Events per 0.2 0 20 40 60 80 100 (ct) > 5 σ ct/ Data Total Fit Total Signal CP-even CP-odd Bkg.

D

FIG. 3: The distribution of the cosine of the transversity angle in the signal mass region, for “non-prompt” events, with the results of the maximum likelihood fit overlaid.

in the fitting procedure. The fits reproduce the inputs (cτ = 439 µm, ∆Γ/Γ = 0, and a range of R⊥ between 0 and 1) correctly within the statistical precision of 2 µm for cτ , 0.01 for R⊥, and 0.025 for ∆Γ/Γ. We test the sensitivity of the results to the parametrization of the signal and background mass distributions by varying the parameters of the two-Gaussian function. To test the sensitivity of the results to the background model, we add a quadratic term in the background mass distribu-tion. We find a non-negligible effect from the extra term in the non-prompt background on cτ and ∆Γ/Γ. We have also tested the sensitivity of the results to the assump-tion that the lifetime and the transversity distribuassump-tions of background are independent of mass. The effect of the uncertainty of the detector alignment on the lifetime measurement was estimated in Ref. [3]. The effects of systematic uncertainties are listed in Table II.

(cm) τ c (ps) τ 0.037 0.0397 0.0425 0.0452 0.048

Γ

/

Γ

∆

D

FIG. 4: The DØ default one-σ (stat.) contour (δ ln(L) = 0.5) compared to a one-σ band for the world average (WA) mea-surement based on flavor-specific decays, τf s= 1.442 ± 0.066 ps. A simultaneous fit to our data and the WA gives a one-σ range τ (Bs0) = 1.39 ± 0.06 ps and ∆Γ/Γ = 0.25+0.14−0.15. The SM theoretical prediction is shown as the horizontal band.

TABLE I: Fit results for ∆Γ/Γ at fixed values of τ (B0 s). For each assumed value of τ (Bs0), the likelihood as function of ∆Γ/Γ is symmetric and parabolic.

τ (Bs0) (ps) ∆Γ/Γ ∆ ln(L) 1.23 −0.13 ± 0.15 0.51 1.27 −0.03 ± 0.17 0.32 1.31 0.07 ± 0.19 0.17 1.35 0.16 ± 0.21 0.04 1.39 0.24 ± 0.20 0.0 1.43 0.31 ± 0.19 0.06 1.47 0.37 ± 0.18 0.20 1.51 0.43 ± 0.18 0.42 1.55 0.48 ± 0.18 0.69

We also conduct a test with an ensemble of 1000 pseudo-experiments with similar statistical sensitivity, chosen from the distribution described by Eq. 1, with the same parameters as obtained in this analysis. Both the spread of uncertainties and of the central values of the fit parameters are in good agreement with the results reported here. Our results are consistent with the CDF Collaboration results [9], also shown in Fig. 4.

B0

s lifetime measurements from semileptonic (flavor-specific) data provide an independent constraint on the average lifetime and lifetime difference in the B0

s sys-tem. The world average [5] B0

s lifetime is τf s = 1/Γf s= 1.442 ± 0.066 ps. This result is based on single-exponential fits in the flavor-specific decay channels, which determine the following relation [10] (shown in Fig. 4) of Γ and ∆Γ/Γ: Γf s = Γ − (∆Γ)2/2Γ + O(∆Γ)3/Γ

2 . Applying the above constraint to our measurement, we obtain τ (B0

s) = 1.39 ± 0.06 ps and ∆Γ/Γ = 0.25 +0.14 −0.15. This result is consistent with the SM expectation [11] of

TABLE II: Sources of systematic uncertainty. The numbers reflect the variation of the fitted central values associated with the one-σ variation of the corresponding external input pa-rameters. The second item includes contributions from the variation of the acceptance as a function of ϕ and ψ, as well as from a one-σ variation of the quantity |A0(0)|2− |Ak(0)|2.

Source cτ (B0 s), µm ∆Γ/Γ R⊥ Acceptance vs. cos θ ±0.6 ±0.001 ±0.005 Integration over ϕ, ψ ±0.2 ±0.001 ±0.02 Procedure test ±2.0 ±0.025 ±0.01 Momentum scale −3.0 – –

Signal mass model ±1.0 +0.009,−0.017 ±0.007 Background mass −3.5 +0.02 −0.002

Detector alignment ±2.0 – –

Background model ±0.5 ±0.016 ±0.005 Total −5.6,+3.1 −0.04, +0.03 ±0.02

0.12 ± 0.05.

All the results presented above are obtained under a tacit assumption that the CP-violating phase is negli-gible, as predicted by the SM (δφ = φCKM = −0.03). Future improvements on the measurement of ∆Γ/Γ may exclude models predicting large deviations of δφ from the SM value.

In summary, we have measured the CP-odd fraction for the decay B0

s → J/ψ φ, and the correlated parameters of the average lifetime of the (B0

s, B 0

s) system τ (Bs0) = 1/Γ, and the relative width difference ∆Γ/Γ, or, equivalently, the mean lifetimes of the light and heavy B0

s eigenstates, respectively. We obtain R⊥= 0.16 ± 0.10 (stat) ± 0.02 (syst), ∆Γ/Γ = 0.24+0.28−0.38(stat) +0.03 −0.04 (syst), τ (B0 s) = 1.39 +0.13 −0.16(stat) +0.01 −0.02(syst) ps, τL= 1.24+0.14−0.11(stat)+0.01−0.02 (syst) ps, τH= 1.58+0.39−0.42(stat)+0.01−0.02(syst) ps.

We have updated the measurement of the mean life-time of the B0 _{meson with doubled statistics. With the} systematic uncertainty estimated in Ref. [3], the updated measurement is

τ (B0_{) = 1.530 ± 0.043 (stat) ± 0.023 (syst) ps.} For the ratio of the average B0

s lifetime to the B0

life-time, we obtain τ(B0

s)

τ(B0₎ = 0.91 ± 0.09 (stat) ± 0.003 (syst).

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 (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 (Ger-many); SFI (Ireland); Research Corporation, Alexander von Humboldt Foundation, and the Marie Curie Pro-gram.

[*] Visitor from University of Zurich, Zurich, Switzerland. [1] I. Dunietz, R. Fleischer, and U. Nierste, Phys. Rev. D

63, 114015 (2001).

[2] DØ Collaboration, V. Abazov et al., “The Upgraded DØ Detector”, submitted to Nucl. Instrum. Methods Phys. Res. A.

[3] DØ Collaboration, V. M. Abazov et al., Phys. Rev. Lett. 94_{, 042001 (2005).}

[4] I. I. Bigi and N. G. Uraltsev, Phys. Lett. B280, 271 (1992).

[5] S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592_{, 1 (2004) and 2005 partial update for edition 2006;} http://pdg.lbl.gov 2005.

[6] A. S. Dighe, I. Dunietz, and R. Fleischer, Eur. Phys. J. C 6, 647 (1999).

[7] A. Ryd and D. Lange,

http://www.slac.stanford.edu/ lange/EvtGen 2000. [8] T. Sj¨ostrand et al., Comp. Phys. Comm. 135, 238 (2001). [9] CDF Collaboration, D. Acosta et al., Phys. Rev. Lett.,

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