Combined D0 measurements constraining the
CP
-violating phase and width difference
in the
B
0ssystem
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,64,*G. 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
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,32,†V. 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,67,‡M. 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,22,xN. 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)
1
Universidad 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 4
Instituto 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
7
Universidad de los Andes, Bogota´, Colombia
8Center for Particle Physics, Charles University, Prague, Czech Republic 9
Czech Technical University, Prague, Czech Republic
10Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 11
Universidad 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 16
LPNHE, IN2P3-CNRS, Universite´s Paris VI and VII, Paris, France 17DAPNIA/Service de Physique des Particules, CEA, Saclay, France 18
IPHC, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France, and Universite´ de Haute Alsace, Mulhouse, France 19
IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite´ de Lyon, Lyon, France 20III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany
21
Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 22Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany
23
Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 24Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
26
Panjab University, Chandigarh, India 27Delhi University, Delhi, India 28
29University College Dublin, Dublin, Ireland 30Korea Detector Laboratory, Korea University, Seoul, Korea
31SungKyunKwan University, Suwon, Korea 32CINVESTAV, Mexico City, Mexico 33
FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 34Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
35
Joint Institute for Nuclear Research, Dubna, Russia 36Institute for Theoretical and Experimental Physics, Moscow, Russia
37
Moscow State University, Moscow, Russia 38Institute for High Energy Physics, Protvino, Russia 39Petersburg Nuclear Physics Institute, St. Petersburg, Russia 40
Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden
41
Physik Institut der Universita¨t Zu¨rich, Zu¨rich, Switzerland 42Lancaster University, Lancaster, United Kingdom
43
Imperial 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
48
University of California, Riverside, California 92521, USA 49Florida State University, Tallahassee, Florida 32306, USA 50
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 51University of Illinois at Chicago, Chicago, Illinois 60607, USA
52
Northern Illinois University, DeKalb, Illinois 60115, USA 53Northwestern University, Evanston, Illinois 60208, USA
54Indiana University, Bloomington, Indiana 47405, USA 55
University of Notre Dame, Notre Dame, Indiana 46556, USA 56Purdue University Calumet, Hammond, Indiana 46323, USA
57
Iowa State University, Ames, Iowa 50011, USA 58University of Kansas, Lawrence, Kansas 66045, USA 59
Kansas 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
64
University of Michigan, Ann Arbor, Michigan 48109, USA 65Michigan State University, East Lansing, Michigan 48824, USA
66
University 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 71
University of Rochester, Rochester, New York 14627, USA 72State University of New York, Stony Brook, New York 11794, USA
73
Brookhaven National Laboratory, Upton, New York 11973, USA 74Langston University, Langston, Oklahoma 73050, USA 75
University 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
80
Rice University, Houston, Texas 77005, USA 81University of Virginia, Charlottesville, Virginia 22901, USA
82
University of Washington, Seattle, Washington 98195, USA
x
Visitor from Universita¨t Zu¨rich, Zu¨rich, Switzerland.
‡Visitor from Helsinki Institute of Physics, Helsinki, Finland. †Visitor from ICN-UNAM, Mexico City, Mexico.
(Received 21 February 2007; published 17 September 2007)
We combine the D0 measurement of the width difference between the light and heavy B0
s mass eigenstates and of theCP-violating mixing phase determined from the time-dependent angular distribu-tions in theB0
s!J= decays along with the charge asymmetry in semileptonic decays also measured with the D0 detector. With the additional constraint from the world average of the flavor-specificB0
s lifetime, we obtain s LH 0:130:09 ps1 and jsj 0:7000::3947 or s 0:13 0:09 ps1 and j
sj 2:4400::4739. The data sample corresponds to an integrated luminosity of1:1 fb1
accumulated with the D0 detector at the Fermilab Tevatron Collider.
DOI:10.1103/PhysRevD.76.057101 PACS numbers: 13.25.Hw, 11.30.Er
One of the great challenges for elementary particle physics is to trace all possible sources of the violation of
CP symmetry. In the standard model (SM) of particle physics, CP symmetry is violated through the Cabibbo-Kobayashi-Maskawa (CKM) mechanism [1]. Although the SM picture ofCPviolation has so far been confirmed by all laboratory measurements, it has an unsolved problem: the level ofCPviolation in the SM is too small to produce the observed baryon number density in the universe [2]. Sources of CP violation beyond the CKM mechanism must, therefore, exist to account for the deficit. One signal ofCPviolation arises in the mixing of doublets of neutral mesons.
In the SM, the light (L) and heavy (H) mass eigenstates of the mixedB0
ssystem are expected to have sizeable mass and decay width differences: MsMHML and sLH. The two mass eigenstates are expected to be almost pureCPeigenstates. TheCP-violating mixing phase is predicted [3] to bes 4:21:4 103. New phenomena may alter s leading to a reduction of the observed s compared to the SM prediction [3] SMs : sSMs jcossj. While B0s-B0s oscillations have been detected [4] and the mass difference has recently been measured to high precision [5], the CP-violating phase remains unknown. The D0 experiment [6] at the Fermilab Tevatron Collider has conducted a series of stud-ies [7–10] of B0
s mesons produced in proton-antiproton (pp) interactions. This report utilizes these results to ob-tain the best estimate of theCP-violating phase in theB0 s system.
In Ref. [7], we studied the decay sequenceB0
s !J= , J= !, !KK. From a fit to the time-dependent angular distribution of the decay products, we obtained the mean lifetime,s1=s(wheres H L=2), s, and the first direct constraint on s. As discussed in Ref. [7], there is a 4-fold ambiguity in the result fors: s ands. The sign of sins is reversed with the simultaneous reversal of the signs of the cosines of theCP-conserving strong phases1and2. (We adopted the amplitude definition and sign convention of Ref. [11]). The possible solutions are
jsj 0:790:56stat00::0114syst;
s0:170:08stat 0:02systps1;
jsj 2:350:56stat0:14 0:01syst;
s 0:170:08stat 0:02systps1: (1)
The solutions with positivesare consistent with the SM prediction [7].
Flavor-specific decays are those particular decay chan-nels where the flavor of theB0
s(i.e., whetherB0sorB0s) can be determined from the decay products, e.g., from the charge of the lepton in B0
s semileptonic decay. These decays are 50% CP even and 50%CP odd at t0and provide independent constraints on the parameters of the system. An effective mean lifetime, resulting from a single-exponential fit to the decay time distribution,
fs1=fs, is related to the physics parameters s and s through the equation fss s2=2 s Os3=2
s [12] (see Fig.1). We use the world-average value,fs1=fs1:4400:036 ps[13], from a fit in-cluding the recent D0 measurement, fs1=fs 1:3980:044stat0:028
0:025syst ps[8].
Independently, we obtained another constraint on the parameters of the B0
s system from the measurements of the semileptonic charge asymmetry induced byB0
smixing. In general, the semileptonic charge asymmetry for a bq
meson stateB0
qis defined as [14]
AqSLNB 0
q!‘X NB0q !‘X NB0
q!‘X NB0q !‘X
: (2)
It is related to theCPphaseqby [15]
AqSL q
Mq tanq: (3)
In Ref. [9], we measured the same-sign dimuon charge asymmetry defined as
ASL Nbb!
X Nbb!X
BothB0
d and B0s contribute to this quantity [16], and the result of Ref. [9] is given as
Ad SL
fsZs fdZdA
s
SL 0:00920:0044stat
0:0032syst;
Zq 1
1y2 q
1
1x2 q
; xqMq=q;
yqq=2q;
(5)
whereAd
SL andAsSL are the charge asymmetries of theB0d andB0
ssemileptonic decays, andfdandfsare the produc-tion rates ofB0
dandB0smesons in the hadronization of theb quark, respectively. In deriving relation (5), it is assumed that there is no direct CP violation in semileptonic B
decays and that the semileptonic width of allBmesons is the same. Using the world-average values [14] fd 0:3980:012, fs0:1030:014, xd 0:7760:008, andZd0:3760:006, we obtain
fsZs fdZd
0:700:07syst 0:10PDG: (6)
The value ofZswas computed using the measured values ofs[7],s[7], andMs[5]:Zs1:01500::018010. We have tested that propagating the Zs dependence on s has a negligible effect on the final results. The systematic uncer-tainty arises mainly from a conservative estimate of a
possible variation in the reconstruction efficiency of muons from semileptonic decays of differentBmesons [17]. The Particle-Data-Group uncertainty is due to propagating the statistical and systematic errors of the world-average inputs [14] to the uncertainty of the ratio.
The asymmetry Ad
SL has been measured at B factories where onlyB0
dandB
mesons are produced. The average value of Ad
SL is [13]: AdSL 0:00470:0046. Com-bining this value and (5) and (6), and adding statistical and systematic uncertainties in quadrature, we obtain
As
SL 0:00640:0101: (7)
In Ref. [10], we measured As
SL directly by using all events with at least one muon that were consistent with the sequential decay B0
s!Ds with Ds!. The result of this measurement is
As
SL 0:02450:0193stat 0:0035syst: (8)
The measurements (7) and (8) are nearly independent since the fraction of dimuon final states in the sample of semi-leptonic B0
s decays used in Ref. [10] is only about 10% [18], and the fraction of semileptonic decaysB0
s!Ds with Ds! in the dimuon sample used in Ref. [9] is less than 1%. Also, the systematic uncertainties of the two measurements are uncorrelated. The main source of sys-tematic uncertainty in (7) is the correction due to K decays, while in the case of the measurement (8) it is the fitting procedure.
Their combination gives the best estimate of the charge asymmetry in semileptonic B0
s decays: As
SL 0:00010:0090: (9)
(radians)
sφ
-2 -1.5 -1 -0.5 0 0.5 1
(ps)
sτ
1.35 1.4 1.45 1.5 1.55 1.6 1.65 φ ψ J/ → 0 s B -1D , 1.1 fb
Constrained
FIG. 2 (color online). The error ellipse ( lnL 0:5) in the plane (s, s) for the solution with s<0, cos1>0, and
cos2<0of the fit to theB0s !J= data (dashed blue line) and of the fit with both the constraint from the two D0 measure-ments of the charge asymmetry in semileptonic B0
s decay, and from the world-average flavor-specific lifetime (solid red line).
(ps)
s
τ
1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65
(1/ps) s
Γ ∆ -0.1 0 0.1 0.2 0.3 0.4 0.5 φ ψ J/ → 0 s B SM
Flavour DØ , 1.1 fb-1
Constrained
Specific WA Lifetime
FIG. 1 (color online). The error ellipse ( lnL 0:5) in the
planesversuss for the fit to theB0s !J= data (dashed blue line) and for the fit with the constraint from the two D0 measurements of the charge asymmetry in semileptonic B0
s decay, and from the world-average flavor-specific lifetime (solid red line). Also shown is a one-band representing the world-average result [13] forfs(see text) and a one-band
Using relation (3) and the result Ms17:80:1 ps1 from the CDF experiment [5], we obtain:
s tansAsSL Ms0:000:16 ps1: (10)
We have repeated the fit to the B0
s !J= data, in-cluding the constraints from Eq. (10), and from the world-average measurement offsdiscussed earlier. To illustrate the fit results and the impact of the constraints, in Figs.1–3
we present likelihood contours in three planes,sversus
s, s versus s, and s versus s, respectively. The contours indicate error ellipses, lnL 0:5, corre-sponding to the confidence level of 39%. The 4-fold am-biguity remains unresolved. The likelihood profile as a function of s for the first solution listed in Eq. (1) is shown in Fig.4. The extracted value ofs deviates from zero by 1.2 standard deviations.
In summary, for the solution with s<0, cos1>0, andcos2<0, we find the decay width difference and the
CP-violating phase in theB0
ssystem to be
s0:130:09 ps1; s 0:7000::4739: (11)
The measurement uncertainty is dominated by the limited statistics. The systematic uncertainties include a variation of the background model in the analysis of the decayB0
s! J= , detector acceptance, and sensitivity to the details of the track and vertex reconstruction. The results are con-sistent with the SM predictions [3].
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 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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(radians)
s
φ
-1.5 -1.2 -0.9 -0.6 -0.3 0
)
min
-2ln(L/L
0 0.5 1 1.5 2 2.5 3
(radians)
s
φ
likelihood scan:
FIG. 4 (color online). The likelihood scan versus s for the constrained fit (see text).
(radians)
s φ
-3 -2 -1 0 1 2 3
(1/ps) s
Γ
∆
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
φ ψ
J/
→
0 s
B
-1
D , 1.1 fb
Constrained
Combined semileptonic
asymmetry charge
band
)|
s
φ
|cos(
×
SM
Γ ∆
=
Γ ∆
SM
FIG. 3 (color online). The error ellipses ( lnL 0:5) in the plane (s,s) for the four solutions of fit to theB0s!J= data (dashed blue lines) and of the fit with the constraint from the two D0 measurements of the charge asymmetry in semileptonic B0
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