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Measurement of the Lifetime Difference in the B

0

s

System

V. M. Abazov,35B. Abbott,72M. Abolins,63B. S. Acharya,29M. Adams,50T. Adams,48M. Agelou,18J.-L. Agram,19 S. H. Ahn,31M. Ahsan,57G. D. Alexeev,35G. Alkhazov,39A. Alton,62G. Alverson,61G. A. Alves,2M. Anastasoaie,34

T. Andeen,52S. Anderson,44B. Andrieu,17Y. Arnoud,14M. Arov,51A. Askew,48B. A˚ sman,40A. C. S. Assis Jesus,3 O. Atramentov,55C. Autermann,21C. Avila,8F. Badaud,13A. Baden,59L. Bagby,51B. Baldin,49P. W. Balm,33 P. Banerjee,29S. Banerjee,29E. Barberis,61P. Bargassa,76P. Baringer,56C. Barnes,42J. Barreto,2J. F. Bartlett,49 U. Bassler,17D. Bauer,53A. Bean,56S. Beauceron,17M. Begalli,3M. Begel,68A. Bellavance,65S. B. Beri,27G. Bernardi,17

R. Bernhard,49,* I. Bertram,41M. Besanc¸on,18R. Beuselinck,42V. A. Bezzubov,38P. C. Bhat,49V. Bhatnagar,27 M. Binder,25C. Biscarat,41K. M. Black,60I. Blackler,42G. Blazey,51F. Blekman,42S. Blessing,48D. Bloch,19 U. Blumenschein,23A. Boehnlein,49O. Boeriu,54T. A. Bolton,57F. Borcherding,49G. Borissov,41K. Bos,33T. Bose,67

A. Brandt,74R. Brock,63G. Brooijmans,67A. Bross,49N. J. Buchanan,48D. Buchholz,52M. Buehler,50V. Buescher,23 S. Burdin,49S. Burke,44T. H. Burnett,78E. Busato,17C. P. Buszello,42J. M. Butler,60J. Cammin,68S. Caron,33 W. Carvalho,3B. C. K. Casey,73N. M. Cason,54H. Castilla-Valdez,32S. Chakrabarti,29D. Chakraborty,51K. M. Chan,68

A. Chandra,29D. Chapin,73F. Charles,19E. Cheu,44D. K. Cho,60S. Choi,47B. Choudhary,28T. Christiansen,25 L. Christofek,56D. Claes,65B. Cle´ment,19C. Cle´ment,40Y. Coadou,5M. Cooke,76W. E. Cooper,49D. Coppage,56 M. Corcoran,76A. Cothenet,15M.-C. Cousinou,15B. Cox,43S. Cre´pe´-Renaudin,14D. Cutts,73H. da Motta,2M. Das,58

B. Davies,41G. Davies,42G. A. Davis,52K. De,74P. de Jong,33S. J. de Jong,34E. De La Cruz-Burelo,62 C. De Oliveira Martins,3S. Dean,43J. D. Degenhardt,62F. De´liot,18M. Demarteau,49R. Demina,68P. Demine,18

D. Denisov,49S. P. Denisov,38S. Desai,69H. T. Diehl,49M. Diesburg,49M. Doidge,41H. Dong,69S. Doulas,61 L. V. Dudko,37L. Duflot,16S. R. Dugad,29A. Duperrin,15J. Dyer,63A. Dyshkant,51M. Eads,51D. Edmunds,63 T. Edwards,43J. Ellison,47J. Elmsheuser,25V. D. Elvira,49S. Eno,59P. Ermolov,37O. V. Eroshin,38J. Estrada,49H. Evans,67 A. Evdokimov,36V. N. Evdokimov,38J. Fast,49S. N. Fatakia,60L. Feligioni,60A. V. Ferapontov,38T. Ferbel,68F. Fiedler,25 F. Filthaut,34W. Fisher,49H. E. Fisk,49I. Fleck,23M. Fortner,51H. Fox,23S. Fu,49S. Fuess,49T. Gadfort,78C. F. Galea,34 E. Gallas,49E. Galyaev,54C. Garcia,68A. Garcia-Bellido,78J. Gardner,56V. Gavrilov,36A. Gay,19P. Gay,13D. Gele´,19

R. Gelhaus,47K. Genser,49C. E. Gerber,50Y. Gershtein,48D. Gillberg,5G. Ginther,68T. Golling,22N. Gollub,40 B. Go´mez,8K. Gounder,49A. Goussiou,54P. D. Grannis,69S. Greder,3H. Greenlee,49Z. D. Greenwood,58E. M. Gregores,4

Ph. Gris,13J.-F. Grivaz,16L. Groer,67S. Gru¨nendahl,49M. W. Gru¨newald,30S. N. Gurzhiev,38G. Gutierrez,49 P. Gutierrez,72A. Haas,67N. J. Hadley,59S. Hagopian,48I. Hall,72R. E. Hall,46C. Han,62L. Han,7K. Hanagaki,49

K. Harder,57A. Harel,26R. Harrington,61J. M. Hauptman,55R. Hauser,63J. Hays,52T. Hebbeker,21D. Hedin,51 J. M. Heinmiller,50A. P. Heinson,47U. Heintz,60C. Hensel,56G. Hesketh,61M. D. Hildreth,54R. Hirosky,77J. D. Hobbs,69

B. Hoeneisen,12M. Hohlfeld,24S. J. Hong,31R. Hooper,73P. Houben,33Y. Hu,69J. Huang,33V. Hynek,9I. Iashvili,47 R. Illingworth,49A. S. Ito,49S. Jabeen,56M. Jaffre´,16S. Jain,72V. Jain,70K. Jakobs,23A. Jenkins,42R. Jesik,42K. Johns,44 M. Johnson,49A. Jonckheere,49P. Jonsson,42A. Juste,49D. Ka¨fer,21S. Kahn,70E. Kajfasz,15A. M. Kalinin,35J. Kalk,63 D. Karmanov,37J. Kasper,60I. Katsanos,67D. Kau,48R. Kaur,27R. Kehoe,75S. Kermiche,15S. Kesisoglou,73A. Khanov,68 A. Kharchilava,54Y. M. Kharzheev,35H. Kim,74T. J. Kim,31B. Klima,49J. M. Kohli,27J.-P. Konrath,23M. Kopal,72

V. M. Korablev,38J. Kotcher,70B. Kothari,67A. Koubarovsky,37A. V. Kozelov,38J. Kozminski,63A. Kryemadhi,77 S. Krzywdzinski,49Y. Kulik,49A. Kumar,28S. Kunori,59A. Kupco,11T. Kurcˇa,20J. Kvita,9S. Lager,40N. Lahrichi,18

G. Landsberg,73J. Lazoflores,48A.-C. Le Bihan,19P. Lebrun,20W. M. Lee,48A. Leflat,37F. Lehner,49,* C. Leonidopoulos,67J. Leveque,44P. Lewis,42J. Li,74Q. Z. Li,49J. G. R. Lima,51D. Lincoln,49S. L. Linn,48 J. Linnemann,63V. V. Lipaev,38R. Lipton,49L. Lobo,42A. Lobodenko,39M. Lokajicek,11A. Lounis,19P. Love,41 H. J. Lubatti,78L. Lueking,54L. Luo,53M. Lynker,42A. L. Lyon,49A. K. A. Maciel,51R. J. Madaras,45P. Ma¨ttig,26

C. Magass,21A. Magerkurth,62A.-M. Magnan,14N. Makovec,16P. K. Mal,29H. B. Malbouisson,3S. Malik,65 V. L. Malyshev,35H. S. Mao,6Y. Maravin,49M. Martens,49S. E. K. Mattingly,73A. A. Mayorov,38R. McCarthy,69 R. McCroskey,44D. Meder,24A. Melnitchouk,64A. Mendes,15D. Mendoza,8M. Merkin,37K. W. Merritt,49A. Meyer,21

J. Meyer,22M. Michaut,18H. Miettinen,76J. Mitrevski,67J. Molina,3N. K. Mondal,29R. W. Moore,5T. Moulik,56 G. S. Muanza,20M. Mulders,49L. Mundim,3Y. D. Mutaf,69E. Nagy,15M. Naimuddin,28M. Narain,60N. A. Naumann,34 H. A. Neal,62J. P. Negret,8S. Nelson,48P. Neustroev,39C. Noeding,23A. Nomerotski,49S. F. Novaes,4T. Nunnemann,25

E. Nurse,43V. O’Dell,49D. C. O’Neil,5V. Oguri,3N. Oliveira,3N. Oshima,49G. J. Otero y Garzo´n,50P. Padley,76 N. Parashar,58S. K. Park,31J. Parsons,67R. Partridge,73N. Parua,69A. Patwa,70G. Pawloski,76G. Pawloski,76

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P. M. Perea,47E. Perez,18P. Pe´troff,16M. Petteni,42R. Piegaia,1M.-A. Pleier,68P. L. M. Podesta-Lerma,32 V M. Podstavkov,49Y. Pogorelov,54M.-E. Pol,2A. Pomposˇ,72B. G. Pope,63W. L. Prado da Silva,3H. B. Prosper,48

S. Protopopescu,70J. Qian,62A. Quadt,22B. Quinn,64K. J. Rani,29K. Ranjan,28P. A. Rapidis,49P. N. Ratoff,41 S. Reucroft,61M. Rijssenbeek,69I. Ripp-Baudot,19F. Rizatdinova,57S. Robinson,42R. F. Rodrigues,3C. Royon,18 P. Rubinov,49R. Ruchti,54V. I. Rud,37G. Sajot,14A. Sa´nchez-Herna´ndez,32M. P. Sanders,59A. Santoro,3G. Savage,49

L. Sawyer,58T. Scanlon,42D. Schaile,25R. D. Schamberger,69Y. Scheglov,39H. Schellman,52P. Schieferdecker,25 C. Schmitt,26C. Schwanenberger,22A. Schwartzman,66R. Schwienhorst,63S. Sengupta,48H. Severini,72E. Shabalina,50

M. Shamim,57V. Shary,18A. A. Shchukin,38W. D. Shephard,54R. K. Shivpuri,28D. Shpakov,61R. A. Sidwell,57 V. Simak,10V. Sirotenko,49P. Skubic,72P. Slattery,68R. P. Smith,49K. Smolek,10G. R. Snow,65J. Snow,71S. Snyder,70

S. So¨ldner-Rembold,43X. Song,51L. Sonnenschein,17A. Sopczak,41M. Sosebee,74K. Soustruznik,9M. Souza,2 B. Spurlock,74N. R. Stanton,57J. Stark,14J. Steele,58K. Stevenson,53V. Stolin,36A. Stone,50D. A. Stoyanova,38 J. Strandberg,40M. A. Strang,74M. Strauss,72R. Stro¨hmer,25D. Strom,52M. Strovink,45L. Stutte,49S. Sumowidagdo,48

A. Sznajder,3M. Talby,15P. Tamburello,44W. Taylor,5P. Telford,43J. Temple,44M. Titov,23M. Tomoto,49T. Toole,59 J. Torborg,58S. Towers,69T. Trefzger,24S. Trincaz-Duvoid,17D. Tsybychev,69B. Tuchming,18C. Tully,66A. S. Turcot,43

P. M. Tuts,67L. Uvarov,39S. Uvarov,39S. Uzunyan,51B. Vachon,5P. J. van den Berg,33R. Van Kooten,53 W. M. van Leeuwen,33N. Varelas,50E. W. Varnes,44A. Vartapetian,74I. A. Vasilyev,38M. Vaupel,26P. Verdier,20

L. S. Vertogradov,35M. Verzocchi,49F. Villeneuve-Seguier,42J.-R. Vlimant,17E. Von Toerne,57M. Vreeswijk,33 T. Vu Anh,16H. D. Wahl,48L. Wang,59J. Warchol,54G. Watts,78M. Wayne,54M. Weber,49H. Weerts,63N. Wermes,22 M. Wetstein,59A. White,74V. White,49D. Wicke,49D. A. Wijngaarden,34G. W. Wilson,56S. J. Wimpenny,47J. Wittlin,60 M. Wobisch,49J. Womersley,49D. R. Wood,61T. R. Wyatt,43Y. Xie,73Q. Xu,62N. Xuan,54S. Yacoob,52R. Yamada,49

M. Yan,59T. Yasuda,49Y. A. Yatsunenko,35Y. Yen,26K. Yip,70H. D. Yoo,73S. W. Youn,52J. Yu,74A. Yurkewicz,69 A. Zabi,16A. Zatserklyaniy,51M. Zdrazil,69C. Zeitnitz,24D. Zhang,49X. Zhang,72T. Zhao,78Z. Zhao,62

B. Zhou,62J. Zhu,69M. Zielinski,68D. Zieminska,53A. Zieminski,53R. Zitoun,69 V. Zutshi,51and E. G. Zverev37

(D0 Collaboration)

1Universidad de Buenos Aires, Buenos Aires, Argentina 2Centro Brasileiro de Pesquisas Fı´sicas, LAFEX, Rio de Janeiro, Brazil

3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil

5University of Alberta, Edmonton, Alberta, Canada,

Simon Fraser University, Burnaby, British Columbia, Canada, York University, Toronto, Ontario, Canada,

and McGill University, Montreal, Quebec, Canada

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

8Universidad de los Andes, Bogota´, Colombia

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

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

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

15CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France 16IN2P3-CNRS, Laboratoire de l’Acce´le´rateur Line´aire, Orsay, France

17LPNHE, IN2P3-CNRS, Universite´s Paris VI and VII, Paris, France 18DAPNIA/Service de Physique des Particules, CEA, Saclay, France 19IReS, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France

and Universite´ de Haute Alsace, Mulhouse, France

20Institut de Physique Nucle´aire de Lyon, IN2P3-CNRS, Universite´ Claude Bernard, Villeurbanne, France 21III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany

22Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 23Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany

24Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 25Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany

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26Fachbereich Physik, University of Wuppertal, Wuppertal, Germany 27Panjab University, Chandigarh, India

28Delhi University, Delhi, India

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

32CINVESTAV, Mexico City, Mexico

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

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

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

40Lund University, Lund, Sweden,

Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden

41Lancaster University, Lancaster, United Kingdom 42Imperial College, London, United Kingdom 43University of Manchester, Manchester, United Kingdom

44University of Arizona, Tucson, Arizona 85721, USA

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

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

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

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

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

60Boston University, Boston, Massachusetts 02215, USA 61Northeastern University, Boston, Massachusetts 02115, USA

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

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

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

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

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

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

78University of Washington, Seattle, Washington 98195, USA (Received 20 July 2005; published 17 October 2005) We present a study of the decay B0

s ! J= . We obtain the CP-odd fraction in the final state at time zero, R? 0:16  0:10stat  0:02syst, the average lifetime of the (B0s, B0s) system, B0s  1:390:130:16stat0:01

0:02syst ps, and the relative width difference between the heavy and light mass eigen-states, =   L H=   0:240:280:38stat0:030:04syst. With the additional constraint from the world

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average of the B0

s lifetime measurements using semileptonic decays, we find B0s  1:39  0:06 ps and =   0:250:140:15. For the ratio of the B0

s and B0 lifetimes we obtain B

0

s

B0 0:91  0:09stat 

0:003syst.

DOI:10.1103/PhysRevLett.95.171801 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd

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

B0

smesons are expected to mix in such a way that the mass and decay width differences between the heavy and light eigenstates, M  MH ML and   L H, are sizeable. The mixing phase  is predicted to be small and to a good approximation the two mass eigenstates are expected to be CP eigenstates. New phenomena may alter

, leading to a reduction of the observed  compared to the SM prediction [1].

The decay B0

s! J= , 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 compo-nents of the decay B0

s! J= , and thus to measure the lifetime difference, through a simultaneous study of the time evolution and angular distributions of the decay prod-ucts of the J= and  mesons. The angular distribution of the decay B0

s! J= ! ! KK involves three angles. Current statistics are such that the use of all three angles characterizing the final state is not yet bene-ficial. We use a variable particularly sensitive to separating the CP states, the cosine of the transversity polar angle (called ‘‘transversity’’), as defined below.

The analysis of data collected with the D0 detector [2] at the Fermilab Tevatron collider presented in this Letter is an extension of a recently published study [3] done under the single B0s lifetime hypothesis. We perform an unbinned maximum likelihood fit to the data, including the B0

s can-didate mass, lifetime, and transversity, in the decay se-quence B0

s ! J= , J= ! ,  ! KK. We extract three parameters characterizing the B0

s system and its decay: B0

s  1= , where   H L=2; = ; and R?, the relative rate of the decay to the CP-odd states

at time zero. The average lifetimes of B0

sand B0, as defined above, are expected to be equal to within 1% [4], and their ratio is determined by also measuring the lifetime of B0in

the similar decay topology of J= K.

The data were collected between June 2002 and August 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 pb1.

To select the B0

scandidate sample, we apply the follow-ing kinematic and quality cuts. Minimum values of mo-menta in the transverse plane for B0

s, , and K mesons are

set at 6.0 GeV, 1.5 GeV, and 0.7 GeV, respectively. J= candidates are accepted if the invariant mass is in the range 2.90 –3.25 GeV. Successful candidates are constrained to the average reconstructed J= mass of 3.072 GeV. Decay products of the  candidates are required to satisfy a fit to a common vertex and to have an invariant mass in the range 1.01–1.03 GeV. We require the (J= ; ) pair to be con-sistent with coming from a common vertex, and to have an invariant mass in the range 5.0 –5.8 GeV. In case of mul-tiple  meson candidates, we select the one with the highest transverse momentum. Monte Carlo (MC) studies show that the pT spectrum of the  mesons coming from

B0s decay is harder than the spectrum of a pair of random tracks from hadronization. We define the signed decay length of a B0

s meson LBxyas 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 MB0

s is the world average mass of the B

0

smeson [5]. The distribution of the proper decay length uncertainty

ct of B0

s mesons peaks around 25 m. We accept events with ct < 60 m. There are 9699 events satis-fying the above cuts.

The resulting invariant mass distribution of the (J= ; ) system is shown in Fig. 1. The curves are projections of the

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/

s 0

B

D

FIG. 1 (color online). The invariant mass distribution of the (J= ; ) system for B0

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

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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 find 1913 events of the decay sequence

B0 ! J= K, J= ! , K ! K, and update

the B0 lifetime measurement reported in Ref. [4] with

larger statistics.

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

L Y

N

i1 fsigFi

sig 1  fsigFibck ; (1)

where N is the total number of events,Fi

sig(Fibck) is the

product of the mass, proper decay length, and the trans-versity probability density functions for the signal (back-ground), and fsigis the fraction of signal in the sample. The

background is divided into two categories, based on their origin and lifetime characteristics. ‘‘Prompt’’ background is due to directly produced J= mesons accompanied by random tracks arising from hadronization. This back-ground is distinguished from ‘‘nonprompt’’ backback-ground,

where the J= meson is a product of a B-hadron decay while the tracks forming the  candidate emanate from a multibody decay of the same B hadron or from hadroniza-tion. We allow for independent parameters for the two background components in mass, lifetime, and transver-sity. There are 19 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 normal-izations, obtained in a fit to the signal-dominated subset satisfying ct=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 pa-rametrized by an exponential convoluted with a Gaussian function with the width taken from the event-by-event estimate of ct. To allow for the possibility of the life-time uncertainty to be systematically underestimated, we introduce a free scale factor.

The transversity distribution of the signal is determined 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 B0s, expressed in terms of the linear polarization amplitudes jAxtj and their relative phases i is [6]

d3t

d cosd’d cos / 2jA00j

2eLtcos2 1  sin2cos2’  sin2 fjA

k0j2eLt1  sin2sin2’

 jA?0j2eHtsin2g 

1  2

p sin2 jA00jjAk0j cos2 1eLtsin2 sin2’

  1

 2

p jA00jjA?0j cos2sin2 sin2 cos’  jAk0jjA?0j cos1sin2 sin2 sin’

 1

2e

Ht eLt: (2)

In the coordinate system of the J= rest frame (where the

 meson moves in the x direction, the z axis is perpen-dicular to the decay plane of  ! KK, and pyK 

0), the transversity polar and azimuthal angles ; ’ de-scribe the direction of the , and is the angle between

~

pK and  ~pJ= in the  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]. Simulated events were reweighted to match the kine-matic distributions observed in the data.

To obtain the one-angle (transversity) distribution, we integrate the three-angle distribution over the angles and

. The resulting distribution depends on one free pa-rameter, R? jA?0j2. There is a small correction term

due to the nonuniformity of the acceptance in the angle ’, which is proportional to jA00j2 jAk0j2. We use the

CDF Collaboration measurement [9] of this difference, 0:355  0:066.

The lifetime shape of the background is described as a sum of a prompt component, simulated as a Gaussian function centered at zero, and a nonprompt component, simulated as a superposition of one exponential for the negative ct region and two exponentials for the positive ct region, with free slopes and normalization. The mass dis-tributions of the backgrounds are parametrized by first-order polynomials. The transversity distributions of back-grounds are parametrized as 1  a2cos2  a

4cos4.

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 1 standard deviation ( one-) contour for c B0s versus = . It provides the best display of the uncertainty range for these correlated parameters. Our best fit returns R? 0:16  0:10 and =   0:240:280:38 at



B0s  1:390:130:16 ps.

We do a series of alternative fits, at discrete values of 

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and the corresponding value of the likelihood, 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 simulation, event reconstruction, and maximum likelihood fitting. We see no bias in the event reconstruction or in the fitting procedure. The fits reproduce the inputs (c  439 m, =   0, and a range of R? between 0 and 1) correctly within the

statis-tical precision of 2 m for c, 0.01 for R?, and 0.025 for

= . We test the sensitivity of the results to the parame-trization 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 nonprompt background on c and = . We have also tested the sensitivity of the results to the assumption that the lifetime and the transversity distributions of back-ground are independent of mass. The effect of the uncer-tainty of the detector alignment on the lifetime measurement was estimated in Ref. [3]. The effects of systematic uncertainties are listed in Table II.

We also conduct a test with an ensemble of 1000 pseu-doexperiments 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 system. The world average [5] B0

s lifetime is fs 1=fs 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  and = : fs    2=2   O 3= 2. Applying the above constraint to our

mea-surement, we obtain B0

s  1:39  0:06 ps and =   0:250:140:15. This result is consistent with the SM expectation [11] of 0:12  0:05. (cm) τ c (ps) τ 0.037 0.0397 0.0425 0.0452 0.048

Γ

/ Γ

-0.4 -0.2 0.2 0.0 0.4 0.6 0.8 1.0 1.2 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 CDF

D

band σ theor. 1 σ 1 ± Flav. Spec. WA stat.) σ with WA constraint (1 stat. σ default 1 D

FIG. 4 (color online). The D0 default one- (stat) contour [ lnL  0:5] compared to a one- band for the world average (WA) measurement based on flavor-specific decays, fs 1:442  0:066 ps. A simultaneous fit to our data and the WA gives a one- range B0

s  1:39  0:06 ps and =   0:250:140:15. The SM theoretical prediction is shown as the hori-zontal band. 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

) < 5.42 GeV s 0 5.26 < M(B φ ψ J/s 0 B

FIG. 3 (color online). The distribution of the cosine of the transversity polar angle in the signal mass region, for nonprompt events, with the results of the maximum likelihood fit overlaid.

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 s 0 5.26 < M(B

D

φ ψ J/s 0 B

FIG. 2 (color online). The proper decay length ct of the B0 s candidates in the signal mass region. The curves show the signal contribution, dashed (red online); the background, lower solid line (green online); and total, upper solid line (black) in the signal mass region.

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All the results presented above are obtained under a tacit assumption that the CP-violating phase is negligible, as predicted by the SM (  CKM 0:03). Future im-provements on the measurement of =  may exclude models predicting large deviations of  from the SM value.

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

s ! J= , and the correlated parameters of the average lifetime of the (B0

s, B0s) system B0s  1= , and the relative width difference = , or, equivalently, the mean lifetimes of the light and heavy B0

s eigenstates, respectively. We obtain R? 0:16  0:10stat  0:02syst; =   0:240:280:38stat0:03 0:04syst;  B0 s  1:390:130:16stat0:010:02syst ps; L 1:240:140:11stat0:010:02syst ps; H  1:580:390:42stat0:010:02syst ps:

We have updated the measurement of the mean lifetime of the B0 meson with doubled statistics. With the

system-atic uncertainty estimated in Ref. [3], the updated mea-surement is

B0  1:530  0:043stat  0:023syst ps: For the ratio of the average B0

slifetime to the B0lifetime, we obtain



B0s

B0  0:91  0:09stat  0:003syst:

We thank the staffs at Fermilab and collaborating insti-tutions, 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 (Germany); SFI (Ireland); Research Corporation, Alexander von Humboldt Foundation, and the Marie Curie Program.

*Visitor from University of Zurich, Zurich, Switzerland. [1] I. Dunietz, R. Fleischer, and U. Nierste, Phys. Rev. D 63,

114015 (2001).

[2] V. Abazov et al. (D0 Collaboration), (to be published). [3] V. M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett.

94, 042001 (2005).

[4] I. I. Bigi and N. G. Uraltsev, Phys. Lett. B 280, 271 (1992). [5] S. Eidelman et al. (Particle Data Group), Phys. Lett. B

592, 1 (2004); http://pdg.lbl.gov

[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.

[8] T. Sjo¨strand et al., Comput. Phys. Commun. 135, 238 (2001).

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

[10] K. Anikeev et al., Report No. FERMILAB-Pub-01/197, p. 360, 2001.

[11] A. Lenz, hep-ph/0412007.

TABLE II. Sources of systematic uncertainty. The numbers reflect the variation of the fitted central values associated with the one- variation of the corresponding external input parame-ters. The second item includes contributions from the variation of the acceptance as a function of ’ and , as well as from a one- variation of the quantity jA00j2 jAk0j2.

Source cB0 s, m =  R? Acceptance vs cos 0:6 0:001 0:005 Integration over ’, 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 model 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

TABLE I. Fit results for =  at fixed values of B0 s. For each assumed value of B0

s, the likelihood as function of =  is symmetric and parabolic.

 B0 s ps =   lnL 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

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