Measurement of the B
0s
Lifetime in the Exclusive Decay Channel B
0s! J=
V. M. Abazov,33B. Abbott,70M. Abolins,61B. S. Acharya,27D. L. Adams,68M. Adams,48T. Adams,46M. Agelou,17 J.-L. Agram,18S. N. Ahmed,32S. H. Ahn,29G. D. Alexeev,33G. Alkhazov,37A. Alton,60G. Alverson,59G. A. Alves,2 M. Anastasoaie,32S. Anderson,42B. Andrieu,16Y. Arnoud,13A. Askew,73B. A˚ sman,38O. Atramentov,53C. Autermann,20
C. Avila,7L. Babukhadia,67T. C. Bacon,40F. Badaud,12A. Baden,57S. Baffioni,14B. Baldin,47P. W. Balm,31 S. Banerjee,27E. Barberis,59P. Bargassa,73P. Baringer,54C. Barnes,40J. Barreto,2J. F. Bartlett,47U. Bassler,16D. Bauer,51
A. Bean,54S. Beauceron,16F. Beaudette,15M. Begel,66A. Bellavance,63S. B. Beri,26G. Bernardi,16R. Bernhard,47,* I. Bertram,39M. Besanc¸on,17A. Besson,18R. Beuselinck,40V. A. Bezzubov,36P. C. Bhat,47V. Bhatnagar,26 M. Bhattacharjee,67M. Binder,24A. Bischoff,45K. M. Black,58I. Blackler,40G. Blazey,49F. Blekman,31S. Blessing,46
D. Bloch,18U. Blumenschein,22A. Boehnlein,47O. Boeriu,52T. A. Bolton,55P. Bonamy,17F. Borcherding,47 G. Borissov,39K. Bos,31T. Bose,65C. Boswell,45A. Brandt,72G. Briskin,71R. Brock,61G. Brooijmans,65A. Bross,47 N. J. Buchanan,46D. Buchholz,50M. Buehler,48V. Buescher,22S. Burdin,47T. H. Burnett,75E. Busato,16J. M. Butler,58
J. Bystricky,17F. Canelli,66W. Carvalho,3B. C. K. Casey,71D. Casey,61N. M. Cason,52H. Castilla-Valdez,30 S. Chakrabarti,27D. Chakraborty,49K. M. Chan,66A. Chandra,27D. Chapin,71F. Charles,18E. Cheu,42L. Chevalier,17
D. K. Cho,66S. Choi,45S. Chopra,68T. Christiansen,24L. Christofek,54D. Claes,63A. R. Clark,43B. Cle´ment,18 C. Cle´ment,38Y. Coadou,5D. J. Colling,40L. Coney,52B. Connolly,46M. Cooke,73W. E. Cooper,47D. Coppage,54 M. Corcoran,73J. Coss,19A. Cothenet,14M.-C. Cousinou,14S. Cre´pe´-Renaudin,13M. Cristetiu,45M. A. C. Cummings,49
D. Cutts,71H. da Motta,2B. Davies,39G. Davies,40G. A. Davis,50K. De,72P. de Jong,31S. J. de Jong,32 E. De La Cruz-Burelo,30C. De Oliveira Martins,3S. Dean,41K. Del Signore,60F. De´liot,17P. A. Delsart,19 M. Demarteau,47R. Demina,66P. Demine,17D. Denisov,47S. P. Denisov,36S. Desai,67H. T. Diehl,47M. Diesburg,47 M. Doidge,39H. Dong,67S. Doulas,59L. Duflot,15S. R. Dugad,27A. Duperrin,14J. Dyer,61A. Dyshkant,49M. Eads,49
D. Edmunds,61T. Edwards,41J. Ellison,45J. Elmsheuser,24J. T. Eltzroth,72V. D. Elvira,47S. Eno,57P. Ermolov,35 O. V. Eroshin,36J. Estrada,47D. Evans,40H. Evans,65A. Evdokimov,34V. N. Evdokimov,36J. Fast,47S. N. Fatakia,58
D. Fein,42L. Feligioni,58T. Ferbel,66F. Fiedler,24F. Filthaut,32W. Fisher,64H. E. Fisk,47F. Fleuret,16M. Fortner,49 H. Fox,22W. Freeman,47S. Fu,47S. Fuess,47C. F. Galea,32E. Gallas,47E. Galyaev,52M. Gao,65C. Garcia,66 A. Garcia-Bellido,75J. Gardner,54V. Gavrilov,34P. Gay,12D. Gele´,18R. Gelhaus,45K. Genser,47C. E. Gerber,48 Y. Gershtein,71G. Geurkov,71G. Ginther,66K. Goldmann,25T. Golling,21B. Go´mez,7K. Gounder,47A. Goussiou,52
G. Graham,57P. D. Grannis,67S. Greder,18J. A. Green,53H. Greenlee,47Z. D. Greenwood,56E. M. Gregores,4 S. Grinstein,1Ph. Gris,12J.-F. Grivaz,15L. Groer,65S. Gru¨nendahl,47M. W. Gru¨newald,28W. Gu,6S. N. Gurzhiev,36 G. Gutierrez,47P. Gutierrez,70A. Haas,65N. J. Hadley,57H. Haggerty,47S. Hagopian,46I. Hall,70R. E. Hall,44C. Han,60 L. Han,41K. Hanagaki,47P. Hanlet,72K. Harder,55R. Harrington,59J. M. Hauptman,53R. Hauser,61C. Hays,65J. Hays,50 T. Hebbeker,20C. Hebert,54D. Hedin,49J. M. Heinmiller,48A. P. Heinson,45U. Heintz,58C. Hensel,54G. Hesketh,59
M. D. Hildreth,52R. Hirosky,74J. D. Hobbs,67B. Hoeneisen,11M. Hohlfeld,23S. J. Hong,29R. Hooper,71S. Hou,60 P. Houben,31Y. Hu,67J. Huang,51Y. Huang,60I. Iashvili,45R. Illingworth,47A. S. Ito,47S. Jabeen,54M. Jaffre´,15S. Jain,70
V. Jain,68K. Jakobs,22A. Jenkins,40R. Jesik,40Y. Jiang,60K. Johns,42M. Johnson,47P. Johnson,42A. Jonckheere,47 P. Jonsson,40H. Jo¨stlein,47A. Juste,47M. M. Kado,43D. Ka¨fer,20W. Kahl,55S. Kahn,68E. Kajfasz,14A. M. Kalinin,33
J. Kalk,61D. Karmanov,35J. Kasper,58D. Kau,46Z. Ke,6R. Kehoe,61S. Kermiche,14S. Kesisoglou,71A. Khanov,66 A. Kharchilava,52Y. M. Kharzheev,33K. H. Kim,29B. Klima,47M. Klute,21J. M. Kohli,26M. Kopal,70V. M. Korablev,36
J. Kotcher,68B. Kothari,65A. V. Kotwal,65A. Koubarovsky,35O. Kouznetsov,13A. V. Kozelov,36J. Kozminski,61 J. Krane,53M. R. Krishnaswamy,27S. Krzywdzinski,47M. Kubantsev,55S. Kuleshov,34Y. Kulik,47S. Kunori,57 A. Kupco,17T. Kurcˇa,19V. E. Kuznetsov,45S. Lager,38N. Lahrichi,17G. Landsberg,71J. Lazoflores,46A.-C. Le Bihan,18 P. Lebrun,19S. W. Lee,29W. M. Lee,46A. Leflat,35C. Leggett,43F. Lehner,47,* C. Leonidopoulos,65P. Lewis,40J. Li,72
Q. Z. Li,47X. Li,6J. G. R. Lima,49D. Lincoln,47S. L. Linn,46J. Linnemann,61V. V. Lipaev,36R. Lipton,47L. Lobo,40 A. Lobodenko,37M. Lokajicek,10A. Lounis,18J. Lu,6H. J. Lubatti,75A. Lucotte,13L. Lueking,47C. Luo,51M. Lynker,52
A. L. Lyon,47A. K. A. Maciel,49R. J. Madaras,43P. Ma¨ttig,25A. Magerkurth,60A.-M. Magnan,13M. Maity,58 N. Makovec,15P. K. Mal,27S. Malik,56V. L. Malyshev,33V. Manankov,35H. S. Mao,6Y. Maravin,47T. Marshall,51 M. Martens,47M. I. Martin,49S. E. K. Mattingly,71A. A. Mayorov,36R. McCarthy,67R. McCroskey,42T. McMahon,69
D. Meder,23H. L. Melanson,47A. Melnitchouk,62X. Meng,6M. Merkin,35K. W. Merritt,47A. Meyer,20C. Miao,71 H. Miettinen,73D. Mihalcea,49J. Mitrevski,65N. Mokhov,47J. Molina,3N. K. Mondal,27H. E. Montgomery,47
R. W. Moore,5M. Mostafa,1G. S. Muanza,19M. Mulders,47Y. D. Mutaf,67E. Nagy,14F. Nang,42M. Narain,58 V. S. Narasimham,27N. A. Naumann,32H. A. Neal,60J. P. Negret,7S. Nelson,46P. Neustroev,37C. Noeding,22 A. Nomerotski,47S. F. Novaes,4T. Nunnemann,24E. Nurse,41V. O’Dell,47D. C. O’Neil,5V. Oguri,3N. Oliveira,3 B. Olivier,16N. Oshima,47G. J. Otero y Garzo´n,48P. Padley,73K. Papageorgiou,48N. Parashar,56J. Park,29S. K. Park,29
J. Parsons,65R. Partridge,71N. Parua,67A. Patwa,68P. M. Perea,45E. Perez,17O. Peters,31P. Pe´troff,15M. Petteni,40 L. Phaf,31R. Piegaia,1P. L. M. Podesta-Lerma,30V. M. Podstavkov,47Y. Pogorelov,52B. G. Pope,61E. Popkov,58 W. L. Prado da Silva,3H. B. Prosper,46S. Protopopescu,68M. B. Przybycien,50,†J. Qian,60A. Quadt,21B. Quinn,62
K. J. Rani,27P. A. Rapidis,47P. N. Ratoff,39N. W. Reay,55J.-F. Renardy,17S. Reucroft,59J. Rha,45M. Ridel,15 M. Rijssenbeek,67I. Ripp-Baudot,18F. Rizatdinova,55C. Royon,17P. Rubinov,47R. Ruchti,52B. M. Sabirov,33G. Sajot,13
A. Sa´nchez-Herna´ndez,30M. P. Sanders,41A. Santoro,3G. Savage,47L. Sawyer,56T. Scanlon,40R. D. Schamberger,67 H. Schellman,50P. Schieferdecker,24C. Schmitt,25A. A. Schukin,36A. Schwartzman,64R. Schwienhorst,61S. Sengupta,46
H. Severini,70E. Shabalina,48V. Shary,17W. D. Shephard,52D. Shpakov,59R. A. Sidwell,55V. Simak,9V. Sirotenko,47 D. Skow,47P. Skubic,70P. Slattery,66R. P. Smith,47K. Smolek,9G. R. Snow,63J. Snow,69S. Snyder,68
S. So¨ldner-Rembold,41X. Song,49Y. Song,72L. Sonnenschein,58A. Sopczak,39V. Sorı´n,1M. Sosebee,72K. Soustruznik,8 M. Souza,2B. Spurlock,72N. R. Stanton,55J. Stark,13J. Steele,56G. Steinbru¨ck,65K. Stevenson,51V. Stolin,34A. Stone,48
D. A. Stoyanova,36J. Strandberg,38M. A. Strang,72M. Strauss,70R. Stro¨hmer,24M. Strovink,43L. Stutte,47 S. Sumowidagdo,46A. Sznajder,3M. Talby,14P. Tamburello,42W. Taylor,67P. Telford,41J. Temple,42 S. Tentindo-Repond,46E. Thomas,14B. Thooris,17M. Tomoto,47T. Toole,57J. Torborg,52S. Towers,67T. Trefzger,23 S. Trincaz-Duvoid,16T. G. Trippe,43B. Tuchming,17C. Tully,64A. S. Turcot,68P. M. Tuts,65L. Uvarov,37S. Uvarov,37
S. Uzunyan,49B. Vachon,47R. Van Kooten,51W. M. van Leeuwen,31N. Varelas,48E. W. Varnes,42I. A. Vasilyev,36 M. Vaupel,25P. Verdier,15L. S. Vertogradov,33M. Verzocchi,57F. Villeneuve-Seguier,40J.-R. Vlimant,16E. Von Toerne,55
M. Vreeswijk,31T. Vu Anh,15H. D. Wahl,46R. Walker,40N. Wallace,42Z.-M. Wang,67J. Warchol,52M. Warsinsky,21 G. Watts,75M. Wayne,52M. Weber,47H. Weerts,61M. Wegner,20N. Wermes,21A. White,72V. White,47D. Whiteson,43
D. Wicke,47D. A. Wijngaarden,32G. W. Wilson,54S. J. Wimpenny,45J. Wittlin,58T. Wlodek,72M. Wobisch,47 J. Womersley,47D. R. Wood,59Z. Wu,6T. R. Wyatt,41Q. Xu,60N. Xuan,52R. Yamada,47M. Yan,57T. Yasuda,47 Y. A. Yatsunenko,33Y. Yen,25K. Yip,68S. W. Youn,50J. Yu,72A. Yurkewicz,61A. Zabi,15A. Zatserklyaniy,49M. Zdrazil,67
C. Zeitnitz,23B. Zhang,6D. Zhang,47X. Zhang,70T. Zhao,75Z. Zhao,60H. Zheng,52B. Zhou,60Z. Zhou,53J. Zhu,57 M. Zielinski,66D. Zieminska,51A. Zieminski,51R. Zitoun,67V. Zutshi,49E. G. Zverev,35and A. Zylberstejn17
(D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, 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, Canada and Simon Fraser University, Burnaby, Canada
6Institute of High Energy Physics, Beijing, People’s Republic of China 7Universidad de los Andes, Bogota´, Colombia
8Center for Particle Physics, Charles University, Prague, Czech Republic 9Czech Technical University, Prague, Czech Republic
10Institute of Physics, Academy of Sciences, Center for Particle Physics, Prague, Czech Republic 11Universidad San Francisco de Quito, Quito, Ecuador
12Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universite´ Blaise Pascal, Clermont-Ferrand, France 13Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
14CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France 15Laboratoire de l’Acce´le´rateur Line´aire, IN2P3-CNRS, Orsay, France
16LPNHE, Universite´s Paris VI and VII, IN2P3-CNRS, Paris, France 17DAPNIA/Service de Physique des Particules, CEA, Saclay, France
18IReS, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France and Universite´ de Haute Alsace, Mulhouse, France 19Institut de Physique Nucle´aire de Lyon, IN2P3-CNRS, Universite´ Claude Bernard, Villeurbanne, France
20RWTH Aachen, III. Physikalisches Institut A, Aachen, Germany 21Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 22Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany
23Institut fu¨r Physik,Universita¨t Mainz, Mainz, Germany 24Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany
25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany 26Panjab University, Chandigarh, India
27Tata Institute of Fundamental Research, Mumbai, India 28University College Dublin, Dublin, Ireland 29Korea Detector Laboratory, Korea University, Seoul, Korea
30CINVESTAV, Mexico City, Mexico
31FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 32University of Nijmegen/NIKHEF, Nijmegen, The Netherlands
33Joint Institute for Nuclear Research, Dubna, Russia 34Institute for Theoretical and Experimental Physics, Moscow, Russia
35Moscow State University, Moscow, Russia 36Institute for High Energy Physics, Protvino, Russia 37Petersburg Nuclear Physics Institute, St. Petersburg, Russia
38Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden
and Uppsala University, Uppsala, Sweden
39Lancaster University, Lancaster, United Kingdom 40Imperial College, London, United Kingdom 41University of Manchester, Manchester, United Kingdom
42University of Arizona, Tucson, Arizona 85721, USA
43Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 44California State University, Fresno, California 93740, USA
45University of California, Riverside, California 92521, USA 46Florida State University, Tallahassee, Florida 32306, USA 47Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
48University of Illinois at Chicago, Chicago, Illinois 60607, USA 49Northern Illinois University, DeKalb, Illinois 60115, USA
50Northwestern University, Evanston, Illinois 60208, USA 51Indiana University, Bloomington, Indiana 47405, USA 52University of Notre Dame, Notre Dame, Indiana 46556, USA
53Iowa State University, Ames, Iowa 50011, USA 54University of Kansas, Lawrence, Kansas 66045, USA 55Kansas State University, Manhattan, Kansas 66506, USA 56Louisiana Tech University, Ruston, Louisiana 71272, USA 57University of Maryland, College Park, Maryland 20742, USA
58Boston University, Boston, Massachusetts 02215, USA 59Northeastern University, Boston, Massachusetts 02115, USA
60University of Michigan, Ann Arbor, Michigan 48109, USA 61Michigan State University, East Lansing, Michigan 48824, USA
62University of Mississippi, University, Mississippi 38677, USA 63University of Nebraska, Lincoln, Nebraska 68588, USA 64Princeton University, Princeton, New Jersey 08544, USA
65Columbia University, New York, New York 10027, USA 66University of Rochester, Rochester, New York 14627, USA 67State University of New York, Stony Brook, New York 11794, USA
68Brookhaven National Laboratory, Upton, New York 11973, USA 69Langston University, Langston, Oklahoma 73050, USA 70University of Oklahoma, Norman, Oklahoma 73019, USA
71Brown University, Providence, Rhode Island 02912, USA 72University of Texas, Arlington, Texas 76019, USA
73Rice University, Houston, Texas 77005, USA 74University of Virginia, Charlottesville, Virginia 22901, USA
75University of Washington, Seattle, Washington 98195, USA
(Received 22 September 2004; published 2 February 2005) Using the exclusive decay B0
s ! J= KK, we report the most precise single
measure-ment of the B0
s lifetime. The data sample corresponds to an integrated luminosity of approximately
220 pb1collected with the D0 detector at the Fermilab Tevatron Collider in 2002 – 2004. We reconstruct 337 signal candidates, from which we extract the B0
s lifetime, B0s 1:4440:0980:090stat 0:020sys ps.
We also report a measurement for the lifetime of the B0 meson using the exclusive decay B0!
J= K0892K . We reconstruct 1370 signal candidates, obtaining B0
1:4730:0520:050stat 0:023sys ps, and the ratio of lifetimes, B0
DOI: 10.1103/PhysRevLett.94.042001 PACS numbers: 14.40.Nd, 13.25.Hw
Lifetime differences among hadrons containing b quarks can be used to probe decay mechanisms that go beyond the quark-spectator model [1]. In the charm sector, lifetime differences are quite large [2]; however, in the bottom sector, due to the larger b-quark mass, these differences are expected to be smaller. Phenomenological models pre-dict differences of about 5% between the lifetimes of B and B0, but no more than 1% between B0and B0
slifetimes
[1]. These predictions are consistent with previous mea-surements of B-meson lifetimes [2]. It has also been postu-lated [3] that the lifetimes of the two CP eigenstates (of the
B0
s- B0s system) differ. This could be observed as a
differ-ence in lifetime between B0
s semileptonic decays, which
should have an equal mixture of the two CP eigenstates, and the lifetime for B0
s ! J= , which is expected to be
dominated by the CP-even eigenstate [3].
In this Letter, we report a measurement of the lifetime of the B0
s meson using the exclusive decay channel B0s !
J= , followed by J= ! and ! KK. The lifetime is extracted using a simultaneous unbinned maxi-mum likelihood fit to masses and proper decay lengths. We also measure the lifetime of the B0meson in the exclusive
decay [4] B0! J= K0892, followed by J= !
and K0892 ! K
, and extract the ratio of the life-times of the B0
s and B0 mesons. The analysis is based on
data collected with the D0 detector in Run II of the Fermilab Tevatron Collider during the period September 2002 –February 2004, which corresponds to approximately 220 pb1of p pcollisions atps 1:96 TeV.
The D0 detector is described in detail elsewhere [5]. We describe here only the detector components most relevant to this analysis. The central-tracking system consists of a silicon microstrip tracker (SMT) and a central fiber tracker (CFT), both located inside a 2 T superconducting solenoi-dal magnet [5]. The tracking system and solenoid is sur-rounded by a liquid argon calorimeter. The SMT has 800 000 individual strips, with typical pitch of 50–80 m, and a design optimized for tracking and ver-texing capability for jj < 3, where ln tan=2 is the pseudorapidity and is the polar angle measured relative to the proton beam direction. The system has a six-barrel longitudinal structure, each with a set of four layers arranged axially around the beam pipe and inter-spersed with 16 radial disks. The CFT has eight thin coaxial barrels, each supporting two doublets of overlap-ping scintillating fibers of 0.835 mm diameter, one doublet parallel to the beam axis and the other alternating by 3 relative to this axis. Light signals are transferred via clear light fibers to solid-state photon counters that have a quan-tum efficiency of approximately 80%. The muon system resides beyond the calorimeter and consists of a layer of tracking detectors and scintillation trigger counters before 1.8 T toroidal magnets, followed by two similar layers after
the toroids. Muon identification for jj < 1 relies on 10 cm wide drift tubes, while 1 cm wide mini-drift tubes are used for 1 < jj < 2. Coverage for muons is partially compro-mised at the bottom of the detector where the calorimeter is supported mechanically from the ground. Luminosity is measured using plastic scintillator arrays located in front of the end calorimeter cryostat, covering 2:7 < jj < 4:4.
The data collection consists of a three-level trigger system, designed to accommodate the high luminosity of Run II. The first level uses information from the tracking, calorimetry, and muon systems to reduce the rate for accepted events to 1:5 kHz. At the next trigger level, with more refined information, the rate is reduced further to 800 Hz. The third and final level of the trigger, with access to all of the event information, uses software algo-rithms and a computing farm and reduces the output rate to 50 Hz, which is recorded for further analysis. We did not require the presence of any specific trigger in the event selection.
Reconstruction of B0
s ! J= candidates requires a
pair of oppositely charged muons that are identified by extrapolating charged tracks into the muon system and matching them with hits in the muon system. All charged tracks used in this analysis are required to have at least one hit in the SMT. We require that muon candidates each have a minimum transverse momentum pT> 1:5 GeV=c and
that they form a common vertex, according to the algo-rithm described in Ref. [6], which is based on a fit requir-ing a 2 probability greater than 1%. The dimuon
sys-tem was required to have an invariant mass between 2.90 and 3:15 GeV=c2 and transverse momentum above
4:5 GeV=c. The dimuons are then combined with another pair of oppositely charged tracks, each with pT>
0:8 GeV=c, consistent with the decay ! KK. The
candidate was required to have an invariant mass be-tween 1.008 and 1:032 GeV=c2and transverse momentum
greater than 2 GeV=c. A four-track secondary vertex is fitted to the products of the J= and decays, and required to have a 2probability of at least 1%. The mass of the J=
candidate is constrained in the fit to the world average J= mass of 3:097 GeV=c2[2]; the constraint does not take into
account the uncertainty in the J= mass. The resulting B0 s
candidate is required to have pT> 6:5 GeV=c. We allow
only one B0
s candidate per event, and when multiple
can-didates exist, we choose the one with the best vertex probability. The resulting invariant mass distribution of the J= - system is shown in Fig. 1(a).
Each primary vertex is reconstructed using tracks and the mean beam-spot position. The latter is determined for every data run, where a typical run lasts several hours. The initial primary vertex seed is constructed using all available tracks; a track is removed when it causes a change of more than nine units in the 2 for a fit to a
common vertex. The process is repeated until no more tracks can be removed [6].
We take the four-track vertex as the position of the secondary vertex. To determine the distance traveled by each B0
s candidate, we calculate the signed transverse
decay length (in a plane transverse to the direction of the beam), Lxy ~x ~pT=pT, where ~x is the length vector
pointing from the primary to the secondary vertex and ~pT
is the reconstructed transverse momentum vector of the B0 s.
The proper decay length of the B0
scandidate is then defined
as c LxyMB0
s=pT, where MB0s is taken as the world
average mass of the B0
s meson 5:3696 GeV=c2 [2].
Figure 1(b) shows the reconstructed invariant mass dis-tribution of the B0
s candidates after a proper decay-length
significance requirement of c = c > 5 is imposed, where c is the uncertainty on c . The strong suppres-sion of the background by this cut implies that the back-ground is dominated by zero lifetime vertices, as expected. The proper decay length (without any restriction on significance) and the invariant mass distributions for can-didates passing the above criteria are fit simultaneously using an unbinned maximum likelihood method. The
like-lihood functionL is given by
L Y
N
i
fsFi
s 1 fsFib ;
where Fs is the product of probability density functions
for mass and proper decay length for B0
s,Fbis the
equiva-lent for background, fsis the fraction of signal, and N is
the total number of candidate events in the sample. The proper decay length for signal events is modeled by a normalized exponential-decay function convoluted with a Gaussian function of width equal to the uncertainty on the proper decay length, which is typically 25 m. This uncertainty is obtained from the full covariance (error) matrix of tracks at the secondary vertex and the uncertainty in the position of the primary vertex. The uncertainty is multiplied by a scale factor that is a parameter in the fit to allow for a possible misestimate of the decay-length un-certainty. The mass distribution of signal events is modeled by a Gaussian function.
The proper decay length for the background is parame-trized as a sum of a Gaussian function centered at zero and exponential-decay functions, with two short-lived compo-nents and a long-lived term. The long-lived component accounts for heavy-flavor backgrounds, while the other terms account for resolution and prompt contributions to background. The mass distribution for the background is modeled by a first-order polynomial.
To determine the background, we use a wide mass range of 5:078–5:636 GeV=c2 in the fit, corresponding to 4236
B0s candidates. The number of background candidates in
this range is sufficiently large to measure the parameters of the background with high accuracy and therefore extract a good measurement of the signal fraction and c B0
s. The
fit provides the c and mass of the B0
s, the shapes of the
proper decay length and mass distributions for the back-ground, and the signal fraction. Table I lists the fit values of the parameters and their uncertainties. The distribution of proper decay length and fits to the B0
scandidates are shown
in Fig. 2(a).
With a very similar four-track topology in the final state, the exclusive decay B0 ! J= K0892 followed by
J= ! and K0892 ! K is reconstructed TABLE I. Values of the extracted mass MB, resolution on the
reconstructed mass M, the measured c , the signal fractions fs,
and the scale factor s.
Parameter B0
s ! J= B0! J= K0892
Fit Values Fit Values
MB 5357:0 2:5 MeV=c2 5271:2 1:5 MeV=c2 M 32:92:52:3MeV=c2 37:91:41:3MeV=c2 c 4333027m 4421615m fs 0:0796 0:0058 0:0446 0:0018 s 1:142 0:028 1:128 0:009 ) 2
Invariant Mass (GeV/c
5.1 5.2 5.3 5.4 5.5 5.6
2
Candidates per 18 MeV/c 50
100 150 200 250 ) 2
Invariant Mass (GeV/c
5.1 5.2 5.3 5.4 5.5 5.6
2
Candidates per 18 MeV/c 50
100 150 200 250 (a)
DØ
) 2Invariant Mass (GeV/c
5.1 5.2 5.3 5.4 5.5 5.6 2 Candidat e s per 18 MeV/c 10 20 30 40 50 60 70 80 ) 2
Invariant Mass (GeV/c
5.1 5.2 5.3 5.4 5.5 5.6 2 Candidat e s per 18 MeV/c 10 20 30 40 50 60 70 80 (b)
DØ
FIG. 1. (a) Mass distribution for B0
s candidate events. Points
with error bars show the data, and the solid curve represents the result of the fit. The mass distribution for the signal is shown in gray; (b) same distribution after requiring the significance of the lifetime measurement to be c = c > 5.
using the same selection criteria and algorithms as for the
B0
s channel described above. The only differences are the
requirement that the pT of the pion be greater than 0:5 GeV=c, and the selection of the K0892 candidates. The combination of two oppositely charged tracks, assum-ing the pion mass for one and the kaon mass for the other, that gives an invariant mass closest to the mass of the
K0892 [2] is selected for further study. The invariant mass of these combinations is required to be between 0.850 and 0:930 GeV=c2. Using the sample of B0 candidates in
the mass range 4:935–5:610 GeV=c2, corresponding to
30692 candidates, we determine the c and mass of the
B0 using exactly the same procedure as used for B0 s
me-sons. Results are also given in Table I, and the distribution of proper decay length is shown in Fig. 2(b).
Detailed Monte Carlo studies were performed on en-sembles of events comparable to data samples, with similar resolutions, pulls, fitting, and selection criteria. No signifi-cant biases resulting from our analysis procedures were observed. To test the stability of the fit results for B0
sand B0
mesons, we split each data sample into two roughly equal parts in order to study different kinematic and geometric parameters, compared the fit results, and found consistency
within their uncertainties. We varied the selection criteria and mass ranges, and did not observe any significant shifts. Using Monte Carlo samples with different input proper decay lengths in the range 340 to 560 m, we checked the response of our fits to this variation, and found it to be linear in this range. We studied the contamination of our sample from cross feed between B0
s and B0 using Monte
Carlo events. The estimated contamination is 4.4% for B0 s
and 1.1% for B0, with invariant mass spread almost
uni-formly across the entire mass range. Therefore, their con-tributions are included in the long-lived heavy-flavor component of the background. To study possible biases from our fitting procedure, we used toy Monte Carlo ensembles with the same statistics as our data and with distributions matching those in data. These samples were fit, and the resulting means and widths of the distributions of extracted parameters are consistent with the fits to data. Other sources of systematic uncertainty have been con-sidered, and the contributions are listed in Table II. For the
B0
slifetime, there are major contributions from
determina-tion of the background, the model for resoludetermina-tion, and the reconstruction of the secondary vertex. To determine the systematic error due to the uncertainty in the background, we considered different models for the mass and decay-length distributions. In particular, to account for any model dependence on the invariant mass of misreconstructed heavy-flavor hadrons, we fit the probability distributions separately in the lower-mass and higher-mass sideband regions and found the long-lived component to have differ-ent expondiffer-ents. Combining the two lifetime values for the long-lived components, we modified the functional form of the long-lived component for the global background in our fit. The two long-lived components were combined using a weighting parameter w 0:980:020:36. This weighting pa-rameter was varied by its uncertainty. The largest differ-ence in the c B0
s observed in these variations of
background modeling was found to be 4 m, and is taken as the systematic uncertainty due to this source. The effect of uncertainty in the proper decay-length resolution was studied by using an alternative resolution function consist-ing of two Gaussian functions (with the same mean but different width), resulting in a difference in the fitted
c B0s of 3 m. Uncertainty or biases in the determination
of the secondary vertex were estimated using secondary TABLE II. Summary of systematic uncertainties.
c B0
s c B0 B0s= B0
(m) (m)
Alignment 2 2 0.000
J= vertex 3 4 0.002
Model for resolution 3 3 0.000
Background 4 5 0.002
Total 6 7 0.003
Proper Decay Length (cm)
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 mµ Candidates per 50 10-1 1 10 102 103
Proper Decay Length (cm)
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 mµ Candidates per 50 10-1 1 10 102 103 (a)
DØ
Proper Decay Length (cm)
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 mµ Candidates per 50 10-1 1 10 102 103 104
Proper Decay Length (cm)
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 mµ Candidates per 50 10-1 1 10 102 103 104 (b)
DØ
FIG. 2. Proper decay-length distributions for (a) B0
s and (b) B0
candidates. The points with error bars show the data. The solid curve shows the total fit, the dashed curve the background component, and the shaded region the signal.
vertices constructed with the J= tracks only, resulting in a
c B0
s shift of 3 m. The contribution from the
uncer-tainty on the detector alignment is estimated by recon-structing the B0
s candidate events with the position of the
SMT sensors shifted radially outwards by the alignment error in the radial position of the sensors. The resulting difference in fitted proper decay length of 2 m is taken as the systematic uncertainty due to possible misalignment. The total systematic uncertainty from all these sources added in quadrature is 6 m. The systematic uncertainties in the measurement of the c B0 are determined in the
same way as for the B0
s, and each contribution is listed in
Table II.
We determine the lifetimes of the B0
s and B0 mesons,
B0
s 1:4440:0980:090stat 0:020sys ps;
B0 1:4730:052
0:050stat 0:023sys ps:
Both results are consistent with the current world aver-ages of B0
s 1:461 0:057 ps and B0 1:536
0:014 ps [2]. We note that measurements using B0 s
semi-leptonic events, where there is an equal mixture of
CP-even and CP-odd states, dominate the current world average, while B0
s ! J= has a different composition of
CP-even and CP-odd states as discussed earlier [7]. Using our results we determine the ratio of B0
s=B0 life-times to be B0 s B0 0:980 0:076 0:071stat 0:003sys;
where statistical uncertainties were propagated in quadra-ture, and the systematic uncertainty was evaluated by add-ing each contribution to the correspondadd-ing central value, and evaluating a new ratio, with the difference from the nominal value taken as the systematic uncertainty of that source, as shown in Table II. The sum in quadrature of all contributions is reported as the overall systematic uncer-tainty on the ratio of lifetimes including correlations be-tween the two lifetime measurements.
In conclusion, we have measured the B0
sand B0lifetimes
in exclusive decay modes in p pcollisions. The measure-ments are consistent with previous results [2]. The value of the B0
s lifetime obtained in this analysis is the most
precise measurement from any single experiment. The ratio of the lifetimes is also in good agreement with QCD models based on a heavy quark expansion, which
predict a difference between B0
s and B0 lifetimes of the
order of 1% [1].
We thank the staffs at Fermilab and collaborating insti-tutions, and acknowledge support from the Department of Energy and National Science Foundation (USA), Commissariat a` l’Energie Atomique and CNRS/Institut National de Physique Nucle´aire et de Physique des Particules (France), Ministry of Education and Science, Agency for Atomic Energy and RF President Grants Program (Russia), CAPES, CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil), Departments of Atomic Energy and Science and Technology (India), Colciencias (Colombia), CONACyT (Mexico), KRF (Korea), CONICET and UBACyT (Argentina), The Foundation for Fundamental Research on Matter (The Netherlands), PPARC (United Kingdom), Ministry of Education (Czech Republic), Natural Sciences and Engineering Research Council and WestGrid Project (Canada), BMBF and DFG (Germany), A. P. Sloan Foundation, Civilian Research and Development Foundation, Research Corporation, Texas Advanced Research Program, and the Alexander von Humboldt Foundation.
*Visitor from University of Zurich, Zurich, Switzerland.
†Visitor from Institute of Nuclear Physics, Krakow, Poland.
[1] M. B. Voloshin and M. A. Shifman, Sov. Phys. JETP 64, 698 (1986); I. Bigi and N. G. Uraltsev, Phys. Lett. B 280, 271 (1992); I. Bigi, Nuovo Cimento A 109, 713 (1996); F. Gabbiani, A. I. Onishchenko, and A. A. Petrov, Phys. Rev. D 70, 094031 (2004).
[2] Particle Data Group, S. Eidelman et al., Phys. Lett. B 592, 1 (2004).
[3] I. Bigi et al., in B Decays, edited by S. Stone (World Scientific, Singapore, 1994), 2nd ed., p. 13; I. Dunietz, Phys. Rev. D 52, 3048 (1995); M. Beneke, G. Buchalla, and I. Dunietz, Phys. Rev. D 54, 4419 (1996).
[4] Unless explicitly stated, the appearance of a specific charge state will also imply its charge conjugate through-out this Letter.
[5] T. LeCompte and H. T. Diehl, Annu. Rev. Nucl. Part. Sci.
50, 71 (2000); V. Abazov et al., [Nucl. Instrum. Methods
Phys. Res., Sect. A (to be published)].
[6] DELPHI Collaboration, J. Abdallah et al., Eur. Phys. J. C
32, 185 (2004).
[7] The exact fraction of CP-even and CP-odd decays is unknown. In this analysis, from Monte Carlo, the relative efficiency for CP-even and CP-odd states is 0:99 0:01.
