Lifetime Difference and CP-Violating Phase in the B
0s
System
V. M. Abazov,35B. Abbott,75M. Abolins,65B. S. Acharya,28M. Adams,51T. Adams,49E. Aguilo,5S. H. Ahn,30 M. Ahsan,59G. D. Alexeev,35G. Alkhazov,39A. Alton,64G. Alverson,63G. A. Alves,2M. Anastasoaie,34L. S. Ancu,34
T. Andeen,53S. Anderson,45B. Andrieu,16M. S. Anzelc,53Y. Arnoud,13M. Arov,52A. Askew,49B. A˚ sman,40 A. C. S. Assis Jesus,3O. Atramentov,49C. Autermann,20C. Avila,7C. Ay,23F. Badaud,12A. Baden,61L. Bagby,52 B. Baldin,50D. V. Bandurin,59P. Banerjee,28S. Banerjee,28E. Barberis,63A.-F. Barfuss,14P. Bargassa,80P. Baringer,58
C. Barnes,43J. Barreto,2J. F. Bartlett,50U. Bassler,16D. Bauer,43S. Beale,5A. Bean,58M. Begalli,3M. Begel,71 C. Belanger-Champagne,40L. Bellantoni,50A. Bellavance,67J. A. Benitez,65S. B. Beri,26G. Bernardi,16R. Bernhard,22 L. Berntzon,14I. Bertram,42M. Besanc¸on,17R. Beuselinck,43V. A. Bezzubov,38P. C. Bhat,50V. Bhatnagar,26M. Binder,24 C. Biscarat,19I. Blackler,43G. Blazey,52F. Blekman,43S. Blessing,49D. Bloch,18K. Bloom,67A. Boehnlein,50D. Boline,62 T. A. Bolton,59G. Borissov,42K. Bos,33T. Bose,77A. Brandt,78R. Brock,65G. Brooijmans,70A. Bross,50D. Brown,78
N. J. Buchanan,49D. Buchholz,53M. Buehler,81V. Buescher,22S. Burdin,50S. Burke,45T. H. Burnett,82E. Busato,16 C. P. Buszello,43J. M. Butler,62P. Calfayan,24S. Calvet,14J. Cammin,71S. Caron,33W. Carvalho,3B. C. K. Casey,77
N. M. Cason,55H. Castilla-Valdez,32S. Chakrabarti,17D. Chakraborty,52K. Chan,5K. M. Chan,71A. Chandra,48 F. Charles,18E. Cheu,45F. Chevallier,13D. K. Cho,62S. Choi,31B. Choudhary,27L. Christofek,77T. Christoudias,43
D. Claes,67B. Cle´ment,18C. Cle´ment,40Y. Coadou,5M. Cooke,80W. E. Cooper,50M. Corcoran,80F. Couderc,17 M.-C. Cousinou,14B. Cox,44S. Cre´pe´-Renaudin,13D. Cutts,77M. C´ wiok,29H. da Motta,2A. Das,62B. Davies,42 G. Davies,43K. De,78P. de Jong,33S. J. de Jong,34E. De La Cruz-Burelo,64C. De Oliveira Martins,3J. D. Degenhardt,64
F. De´liot,17M. Demarteau,50R. Demina,71D. Denisov,50S. P. Denisov,38S. Desai,50H. T. Diehl,50M. Diesburg,50 M. Doidge,42A. Dominguez,67H. Dong,72L. V. Dudko,37L. Duflot,15S. R. Dugad,28D. Duggan,49A. Duperrin,14 J. Dyer,65A. Dyshkant,52M. Eads,67D. Edmunds,65J. Ellison,48V. D. Elvira,50Y. Enari,77S. Eno,61P. Ermolov,37 H. Evans,54A. Evdokimov,36V. N. Evdokimov,38A. V. Ferapontov,59T. Ferbel,71F. Fiedler,24F. Filthaut,34W. Fisher,50 H. E. Fisk,50M. Ford,44M. Fortner,52H. Fox,22S. Fu,50S. Fuess,50T. Gadfort,82C. F. Galea,34E. Gallas,50E. Galyaev,55
C. Garcia,71A. Garcia-Bellido,82V. Gavrilov,36P. Gay,12W. Geist,18D. Gele´,18C. E. Gerber,51Y. Gershtein,49 D. Gillberg,5G. Ginther,71N. Gollub,40B. Go´mez,7A. Goussiou,55P. D. Grannis,72H. Greenlee,50Z. D. Greenwood,60 E. M. Gregores,4G. Grenier,19Ph. Gris,12J.-F. Grivaz,15A. Grohsjean,24S. Gru¨nendahl,50M. W. Gru¨newald,29F. Guo,72 J. Guo,72G. Gutierrez,50P. Gutierrez,75A. Haas,70N. J. Hadley,61P. Haefner,24S. Hagopian,49J. Haley,68I. Hall,75
R. E. Hall,47L. Han,6K. Hanagaki,50P. Hansson,40K. Harder,44A. Harel,71R. Harrington,63J. M. Hauptman,57 R. Hauser,65J. Hays,43T. Hebbeker,20D. Hedin,52J. G. Hegeman,33J. M. Heinmiller,51A. P. Heinson,48U. Heintz,62
C. Hensel,58K. Herner,72G. Hesketh,63M. D. Hildreth,55R. Hirosky,81J. D. Hobbs,72B. Hoeneisen,11H. Hoeth,25 M. Hohlfeld,15S. J. Hong,30R. Hooper,77P. Houben,33Y. Hu,72Z. Hubacek,9V. Hynek,8I. Iashvili,69R. Illingworth,50 A. S. Ito,50S. Jabeen,62M. Jaffre´,15S. Jain,75K. Jakobs,22C. Jarvis,61A. Jenkins,43R. Jesik,43K. Johns,45C. Johnson,70 M. Johnson,50A. Jonckheere,50P. Jonsson,43A. Juste,50D. Ka¨fer,20S. Kahn,73E. Kajfasz,14A. M. Kalinin,35J. M. Kalk,60 J. R. Kalk,65S. Kappler,20D. Karmanov,37J. Kasper,62P. Kasper,50I. Katsanos,70D. Kau,49R. Kaur,26R. Kehoe,79 S. Kermiche,14N. Khalatyan,62A. Khanov,76A. Kharchilava,69Y. M. Kharzheev,35D. Khatidze,70H. Kim,31T. J. Kim,30
M. H. Kirby,34B. Klima,50J. M. Kohli,26J.-P. Konrath,22M. Kopal,75V. M. Korablev,38J. Kotcher,73B. Kothari,70 A. Koubarovsky,37A. V. Kozelov,38D. Krop,54A. Kryemadhi,81T. Kuhl,23A. Kumar,69S. Kunori,61A. Kupco,10 T. Kurcˇa,19J. Kvita,8D. Lam,55S. Lammers,70G. Landsberg,77J. Lazoflores,49P. Lebrun,19W. M. Lee,50A. Leflat,37 F. Lehner,41V. Lesne,12J. Leveque,45P. Lewis,43J. Li,78L. Li,48Q. Z. Li,50S. M. Lietti,4J. G. R. Lima,52D. Lincoln,50 J. Linnemann,65V. V. Lipaev,38R. Lipton,50Z. Liu,5L. Lobo,43A. Lobodenko,39M. Lokajicek,10A. Lounis,18P. Love,42 H. J. Lubatti,82M. Lynker,55A. L. Lyon,50A. K. A. Maciel,2R. J. Madaras,46P. Ma¨ttig,25C. Magass,20A. Magerkurth,64 N. Makovec,15P. K. Mal,55H. B. Malbouisson,3S. Malik,67V. L. Malyshev,35H. S. Mao,50Y. Maravin,59B. Martin,13
R. McCarthy,72A. Melnitchouk,66A. Mendes,14L. Mendoza,7P. G. Mercadante,4M. Merkin,37K. W. Merritt,50 A. Meyer,20J. Meyer,21M. Michaut,17H. Miettinen,80T. Millet,19J. Mitrevski,70J. Molina,3R. K. Mommsen,44 N. K. Mondal,28J. Monk,44R. W. Moore,5T. Moulik,58G. S. Muanza,19M. Mulders,50M. Mulhearn,70O. Mundal,22
L. Mundim,3E. Nagy,14M. Naimuddin,50M. Narain,77N. A. Naumann,34H. A. Neal,64J. P. Negret,7P. Neustroev,39 H. Nilsen,22C. Noeding,22A. Nomerotski,50S. F. Novaes,4T. Nunnemann,24V. O’Dell,50D. C. O’Neil,5G. Obrant,39
C. Ochando,15V. Oguri,3N. Oliveira,3D. Onoprienko,59N. Oshima,50J. Osta,55R. Otec,9G. J. Otero y Garzo´n,51 M. Owen,44P. Padley,80M. Pangilinan,62N. Parashar,56S.-J. Park,71S. K. Park,30J. Parsons,70R. Partridge,77N. Parua,72
A. Patwa,73G. Pawloski,80P. M. Perea,48K. Peters,44Y. Peters,25P. Pe´troff,15M. Petteni,43R. Piegaia,1J. Piper,65 M.-A. Pleier,21P. L. M. Podesta-Lerma,32V. M. Podstavkov,50Y. Pogorelov,55M.-E. Pol,2A. Pomposˇ,75B. G. Pope,65 A. V. Popov,38C. Potter,5W. L. Prado da Silva,3H. B. Prosper,49S. Protopopescu,73J. Qian,64A. Quadt,21B. Quinn,66 M. S. Rangel,2K. J. Rani,28K. Ranjan,27P. N. Ratoff,42P. Renkel,79S. Reucroft,63M. Rijssenbeek,72I. Ripp-Baudot,18
F. Rizatdinova,76S. Robinson,43R. F. Rodrigues,3C. Royon,17P. Rubinov,50R. Ruchti,55G. Sajot,13 A. Sa´nchez-Herna´ndez,32M. P. Sanders,16A. Santoro,3G. Savage,50L. Sawyer,60T. Scanlon,43D. Schaile,24 R. D. Schamberger,72Y. Scheglov,39H. Schellman,53P. Schieferdecker,24C. Schmitt,25C. Schwanenberger,44 A. Schwartzman,68R. Schwienhorst,65J. Sekaric,49S. Sengupta,49H. Severini,75E. Shabalina,51M. Shamim,59V. Shary,17 A. A. Shchukin,38R. K. Shivpuri,27D. Shpakov,50V. Siccardi,18R. A. Sidwell,59V. Simak,9V. Sirotenko,50P. Skubic,75 P. Slattery,71D. Smirnov,55R. P. Smith,50G. R. Snow,67J. Snow,74S. Snyder,73S. So¨ldner-Rembold,44L. Sonnenschein,16 A. Sopczak,42M. Sosebee,78K. Soustruznik,8M. Souza,2B. Spurlock,78J. Stark,13J. Steele,60V. Stolin,36A. Stone,51
D. A. Stoyanova,38J. Strandberg,64S. Strandberg,40M. A. Strang,69M. Strauss,75R. Stro¨hmer,24D. Strom,53 M. Strovink,46L. Stutte,50S. Sumowidagdo,49P. Svoisky,55A. Sznajder,3M. Talby,14P. Tamburello,45W. Taylor,5 P. Telford,44J. Temple,45B. Tiller,24F. Tissandier,12M. Titov,22V. V. Tokmenin,35M. Tomoto,50T. Toole,61I. Torchiani,22 T. Trefzger,23S. Trincaz-Duvoid,16D. Tsybychev,72B. Tuchming,17C. Tully,68P. M. Tuts,70R. Unalan,65L. Uvarov,39 S. Uvarov,39S. Uzunyan,52B. Vachon,5P. J. van den Berg,33B. van Eijk,35R. Van Kooten,54W. M. van Leeuwen,33
N. Varelas,51E. W. Varnes,45A. Vartapetian,78I. A. Vasilyev,38M. Vaupel,25P. Verdier,19L. S. Vertogradov,35 M. Verzocchi,50F. Villeneuve-Seguier,43P. Vint,43J.-R. Vlimant,16E. Von Toerne,59M. Voutilainen,67M. Vreeswijk,33 H. D. Wahl,49L. Wang,61M. H. L. S Wang,50J. Warchol,55G. Watts,82M. Wayne,55G. Weber,23M. Weber,50H. Weerts,65 A. Wenger,22N. Wermes,21M. Wetstein,61A. White,78D. Wicke,25G. W. Wilson,58S. J. Wimpenny,48M. Wobisch,50 D. R. Wood,63T. R. Wyatt,44Y. Xie,77S. Yacoob,53R. Yamada,50M. Yan,61T. Yasuda,50Y. A. Yatsunenko,35K. Yip,73
H. D. Yoo,77S. W. Youn,53C. Yu,13J. Yu,78A. Yurkewicz,72A. Zatserklyaniy,52C. Zeitnitz,25D. Zhang,50T. Zhao,82 B. Zhou,64J. Zhu,72M. Zielinski,71D. Zieminska,54A. Zieminski,54V. Zutshi,52and E. G. Zverev37
(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, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada,
York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada
6University of Science and Technology of China, Hefei, 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
10Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, 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 et Universite´ Paris-Sud, Orsay, France 16LPNHE, IN2P3-CNRS, Universite´s Paris VI and VII, Paris, France
17DAPNIA/Service de Physique des Particules, CEA, Saclay, France 18IPHC, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France,
and Universite´ de Haute Alsace, Mulhouse, France 19IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France
and Universite´ de Lyon, Lyon, France
20III. Physikalisches Institut A, RWTH Aachen, 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 27Delhi University, Delhi, India
28Tata Institute of Fundamental Research, Mumbai, India 29University College Dublin, Dublin, Ireland 30Korea Detector Laboratory, Korea University, Seoul, Korea
31SungKyunKwan University, Suwon, 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
41Physik Institut der Universita¨t Zu¨rich, Zu¨rich, Switzerland 42Lancaster University, Lancaster, United Kingdom
43Imperial College, London, United Kingdom 44University of Manchester, Manchester, United Kingdom
45University of Arizona, Tucson, Arizona 85721, USA
46Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 47California State University, Fresno, California 93740, USA
48University of California, Riverside, California 92521, USA 49Florida State University, Tallahassee, Florida 32306, USA 50Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
51University of Illinois at Chicago, Chicago, Illinois 60607, USA 52Northern Illinois University, DeKalb, Illinois 60115, USA
53Northwestern University, Evanston, Illinois 60208, USA 54Indiana University, Bloomington, Indiana 47405, USA 55University of Notre Dame, Notre Dame, Indiana 46556, USA
56Purdue University Calumet, Hammond, Indiana 46323, USA 57Iowa State University, Ames, Iowa 50011, USA 58University of Kansas, Lawrence, Kansas 66045, USA 59Kansas State University, Manhattan, Kansas 66506, USA 60Louisiana Tech University, Ruston, Louisiana 71272, USA 61University of Maryland, College Park, Maryland 20742, USA
62Boston University, Boston, Massachusetts 02215, USA 63Northeastern University, Boston, Massachusetts 02115, USA
64University of Michigan, Ann Arbor, Michigan 48109, USA 65Michigan State University, East Lansing, Michigan 48824, USA
66University of Mississippi, University, Mississippi 38677, USA 67University of Nebraska, Lincoln, Nebraska 68588, USA 68Princeton University, Princeton, New Jersey 08544, USA 69State University of New York, Buffalo, New York 14260, USA
70Columbia University, New York, New York 10027, USA 71University of Rochester, Rochester, New York 14627, USA 72State University of New York, Stony Brook, New York 11794, USA
73Brookhaven National Laboratory, Upton, New York 11973, USA 74Langston University, Langston, Oklahoma 73050, USA 75University of Oklahoma, Norman, Oklahoma 73019, USA 76Oklahoma State University, Stillwater, Oklahoma 74078, USA
77Brown University, Providence, Rhode Island 02912, USA 78University of Texas, Arlington, Texas 76019, USA 79Southern Methodist University, Dallas, Texas 75275, USA
80Rice University, Houston, Texas 77005, USA 81University of Virginia, Charlottesville, Virginia 22901, USA
82University of Washington, Seattle, Washington 98195, USA (Received 10 January 2007; published 21 March 2007)
From an analysis of the decay B0
s ! J= , we obtain the width difference between the light and heavy
mass eigenstates L H 0:17 0:09stat 0:02syst ps1 and the CP-violating phase
s 0:79 0:56stat0:140:01syst. Under the hypothesis of no CP violation (s 0), we obtain 1=
B0
s 1:52 0:08stat0:010:03syst ps and 0:120:080:10stat 0:02syst ps1. The data sample corresponds to an integrated luminosity of about 1:1 fb1 accumulated with the D0 detector at the Fermilab Tevatron collider. This is the first direct measurement of the CP-violating mixing phase in the B0
s
system.
DOI:10.1103/PhysRevLett.98.121801 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd
In the standard model (SM), the light (L) and heavy (H) eigenstates of the mixed B0
s system are expected to have a
sizable mass and decay width difference M MH ML and L H. The CP-violating phase, defined as
the relative phase of the off-diagonal elements of the mass and decay matrices in the B0
s- B0s basis, is predicted to be
small. Thus, to a good approximation, the two mass eigen-states are expected to be CP eigeneigen-states. New phenomena may alter the CP-violating mixing phase s, leading to a reduction of the observed compared to the SM predic-tion [1] SM: SM coss. While the mass
difference has recently been measured to high precision [2,3], the CP-violating phase remains unknown.
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 study of the time-dependent angular distribution of the decay products of the J= and mesons. Moreover, with a sizable lifetime difference, there is sensitivity to the mixing phase through the interference terms between the CP-even and CP-odd waves.
Previous analyses [4,5] of the decay chain B0
s ! J= ,
J= ! , ! KKextracted the average lifetime of the B0
s system 1= , where H L=2, and
= under the assumption of CP conservation. Here we present new D0 results, based on a twofold increase in statistics. In addition to and , we extract for the first time the CP-violating phase s. We also measure the
magnitudes of the decay amplitudes and their relative phases. The data, collected with the D0 detector [6] be-tween June 2002 and January 2006, correspond to an integrated luminosity of about 1:1 fb1.
Events triggered by the presence of at least one muon are required to include two reconstructed muons of opposite charge, with a momentum in the plane transverse to the beam greater than 1.5 GeV and pseudorapidity jj < 2. ( lntan=2 , and is the polar angle with respect to the proton beam direction.) Each muon is required to be detected as a track segment in at least one of the three layers of the muon system and to be matched to a central track. At least one muon is required to have segments both inside and outside the toroid magnet.
To select the B0
s candidate sample, we set the minimum
values of momenta in the transverse plane for B0
s, , and K
meson candidates at 6.0, 1.5, and 0.7 GeV, respectively.
J= candidates are accepted if the invariant mass of the muon pair is in the range 2.9 –3.3 GeV. Successful candi-dates are constrained to the world average mass of the J= meson [7]. 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 consistent with coming from a common vertex and to have an invariant mass in the range 5.0 –5.8 GeV. In the case of multiple meson candidates, we select the one with the highest transverse momentum. Monte Carlo (MC) studies show that the pTspectrum of the mesons coming
from B0
s decay is harder than the spectrum of a pair of
random tracks from hadronization. We define the signed decay length of a B0
smeson 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 B0
s candidate and apply a constraint
to the average beam spot position. The proper decay length ctis defined by the relation ct LB
xy MB0
s=pT, where MB0s is the measured mass of the B0
scandidate. The distribution
of the proper decay length uncertainty ct of B0
smesons
peaks around 25 m. We accept events with ct < 60 m. The invariant mass distribution of the accepted 23 343 candidates is shown in Fig. 1. The curves are
Mass (GeV)
5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
2
Candidates per 10.0 MeV/c
0 50 100 150 200 250 300 350 400 450 500 Data Total Fit Prompt Bkg non-Prompt Bkg φ ψ J/ → 0 s B -1 DØ , 1.1 fb
FIG. 1 (color online). The invariant mass distribution of the J= ; system for B0
s candidates. The curves are projections of
projections of the maximum likelihood fit, described be-low. The fit assigns 1039 45stat events to the B0
sdecay.
We perform a simultaneous unbinned maximum like-lihood fit to the proper decay length, three decay angles, 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, and fsig is the fraction of signal in the sample. The function Fi
sig de-scribes the distribution of the signal in mass, proper decay length, and the decay angles. For the signal mass distribu-tion, we use a Gaussian function with free mean and width. The proper decay length distribution of the L or H com-ponent of the signal is parametrized by an excom-ponential convoluted with a Gaussian function with the width taken
from the event-by-event estimate of ct. Fi
bck is the product of the background mass, proper decay length, and angular probability density functions. Background is divided into two categories. A ‘‘prompt’’ background is due to directly produced J= mesons accompanied by random tracks arising from hadronization. This back-ground is distinguished from a ‘‘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 hadronization.
The time evolution of the angular distribution of the products of the decay of flavor untagged B0
s mesons, i.e.,
summed over B0
s and B0s, expressed in terms of the linear
polarization amplitudes Ax and their relative phases i is [8]
d3t
d cosd’dcos / 2jA00j 2T
cos2 1 sin2cos2’ sin2 fjAk0j2T1 sin2sin2’ jA?0j2Tsin2g
1 2
p sin2 jA00jjAk0jcos2 1Tsin2sin2’
1 2
p jA00jjA?0jcos2sin2 sin2cos’ jAk0jjA?0jcos1sin2 sin2sin’
1 2e
Ht eLtsin
s; (2)
whereT=121 cosseLt 1 cosseHt .
In the coordinate system of the J= rest frame [where the meson moves in the x direction, the z axis is perpendicular to the decay plane of ! KK, and pyK 0], the transversity polar and azimuthal angles
(, ’) describe the direction of the , and is the angle between ~pK and ~pJ= in the rest frame.
We model the acceptance and resolution in the three angles by fits using polynomial functions, with parameters determined using Monte Carlo simulations. We have used the SVV_HELAMPmodel in the EVTGEN generator [9],
in-terfaced to the PYTHIA program [10]. Simulated events
were reweighted to match the kinematic distributions ob-served in the data.
TABLE I. Maximum likelihood fit results. Sign ambiguities are discussed in the text.
CPconserved Free s Observable L L0 L L0 1:0 ps1 0:120:080:10 0:17 0:09 1 ps 1:52 0:08 1:49 0:08 s 0 0:79 0:56 jA00j2 jAk0j2 0:38 0:05 0:37 0:06 A?0 0:45 0:05 0:46 0:06 1 2 2:6 0:4 2:6 0:4 1 3:3 1:0 2 0:7 1:1 Transversity -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Events per 0.20 0 50 100 150 200 250 Data Total Fit CP-even CP-odd Total Signal Background φ ψ J/ → 0 s B ) <5.46 GeV s 5.26< M(B (ct) > 5 σ ct/ -1 DØ , 1.1 fb
FIG. 2 (color online). The transversity polar angle distribution for the signal-enhanced subsample: ct=ct > 5 and signal mass range. The curves show the total signal contribution [dashed (red) curve], the CP-even (dotted curve) and CP-odd (dashed-dotted curve) contributions of the signal, the back-ground [light solid (green) curve], and the total [solid (blue) curve].
The proper decay length distribution shape of the back-ground 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 normaliza-tion. The mass distributions of the backgrounds are pa-rametrized by first-order polynomials. The distributions in the transversity polar and azimuthal angles are parame-trized as 1 X2xcos2 X4xcos4 and 1 Y1xcos2’ Y2xcos22’, respectively. For the
back-ground dependence on the angle , we use the function 1 Z2xcos2 . We also allow for a background term analogous to the interference term of the CP-even waves, with one free coefficient. For each of the above background functions, we use two separate sets of parameters for the prompt and nonprompt components.
Our results for the hypothesis of CP conservation and for the case of free sare presented in TableI. Figures2–5 show the fit projections on the angular distributions and the
) ψ Cos( -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Events per 0.20 0 50 100 150 200 250 Data Total Fit Total Signal Background φ ψ J/ → 0 s B ) <5.46 GeV s 5.26< M(B (ct) > 5 σ ct/ -1 DØ , 1.1 fb
FIG. 4 (color online). The angle distribution for the signal-enhanced subsample: ct=ct > 5 and signal mass range. The curves show the signal contribution [dashed (red) curve], the background [light solid (green) curve], and the total [solid (blue) curve]. (radians) s φ -5 -4 -3 -2 -1 0 1 2 3 4 5 (1/ps) Γ ∆ -0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5 φ ψ J/ → 0 s B -1 DØ , 1.1 fb )| s φ |cos( × SM Γ ∆ = Γ ∆ SM
FIG. 6 (color online). The lnL 0:5 contour (error el-lipse) in the plane ; s for the fit to the B0s! J= data.
Also shown is the band representing the relation SM jcossj, with SM 0:10 0:03 ps1 [11]. The fourfold ambiguity is discussed in the text.
ct (cm) -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 mµ Candidates per 25.0 -1 10 1 10 2 10 3 10 φ ψ J/ → 0 s B Mass 5.26 - 5.46 GeV -1 DØ , 1.1 fb Data Total Fit Total Signal CP-even CP-odd Background
FIG. 5 (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) curve], the CP-even (dotted curve) and CP-odd (dashed-dotted curve) contributions of the signal, the background [light solid (green) curve], and the total [solid (blue) curve]. φ -3 -2 -1 0 1 2 3 Events per 0.35 0 20 40 60 80 100 120 140 Data Total Fit Total Signal Background φ ψ J/ → 0 s B ) <5.46 GeV s 5.26< M(B (ct) > 5 σ ct/ -1 DØ , 1.1 fb
FIG. 3 (color online). The transversity azimuthal angle distri-bution for the signal-enhanced subsample: ct=ct > 5 and signal mass range. The curves show the signal contribution [dashed (red) curve], the background [light solid (green) curve], and the total [solid (blue) curve].
proper decay length. Figure 6 shows the lnL 0:5 error ellipse contour (corresponding to the confidence level of 39%) in the plane ; s. As seen from Eq. (2), the
sign of sinsis reversed with the simultaneous reversal of
the signs of cos1 and cos2. For the case cos1< 0 and cos2> 0, expected in the absence of final state interac-tions (cf. Table 1 in Ref. [8]), our measurement correlates two possible solutions for s with the two signs of : s 0:79 0:56stat, > 0, and s 2:35 0:56,
< 0. For the case cos1> 0 and cos2< 0, the two solutions are s 0:79 0:56, > 0, and s
2:35 0:56, < 0.
We perform a test using pseudoexperiments with similar statistical sensitivity, generated with the same parameters as obtained in this analysis under the condition of no CP violation. When fits allowing for CP violation are per-formed, 50% of the experiments have a fitted coss
less than the measured value. About 80% of experiments have the statistical uncertainty of s greater than that for
the data.
We verify the procedure by performing fits on MC samples passed through the full chain of detector simu-lation, event reconstruction, and maximum likelihood fit-ting. We assign systematic uncertainties due to the statis-tical precision of this procedure test. We repeat the fits to the data with the parameters describing the acceptance varied by 1. Uncertainties from the data processing reflect the stability of the results with respect to different versions of the track and vertex reconstruction algorithms. The ‘‘interference’’ term in the background model ac-counts for the collective effect of various physics pro-cesses. However, its presence may be partially due to the detector acceptance effects. Therefore, we interpret the difference between fits with and without this term as a systematic uncertainty associated with the background model. Effects of the imperfect detector alignment are estimated using a modified geometry of the silicon micro-strip tracker, with silicon sensors moved within the known uncertainty. The effects of systematic uncertainties are listed in TableII.
From a fit to the CP-conserving time-dependent angular distribution of the untagged decay B0
s ! J= , we obtain
the average lifetime of the B0
s system B0s 1:52
0:08stat0:010:03syst ps and the width difference between
the two mass eigenstates 0:120:080:10stat 0:02syst ps1.
Allowing for CP violation in B0
s mixing, we provide the
first direct constraint on the CP-violating phase s 0:79 0:56stat0:14
0:01syst.
We thank U. Nierste for useful discussions. We thank the staffs at Fermilab and collaborating institutions and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); PPARC (United Kingdom); MSMT (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); Research Corporation; Alexander von Humboldt Foundation; and the Marie Curie Program.
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TABLE II. Sources of systematic uncertainty in the results of the analysis of the decay B0
s ! J= . Source cB0 s m ps1 R? s Procedure test 2:0 0:02 0:01 Acceptance 0:5 0:001 0:003 0:01 Reco. algorithm 8:0, 1:3 0:001 0:01 0:01 Background model 1:0 0:01 0:01 0:14 Alignment 2:0 Total 8:8, 3:3 0:02 0:02 0:01, 0:14
