Direct Limits on the
B
0sOscillation Frequency
V. M. Abazov,36B. Abbott,76M. Abolins,66B. S. Acharya,29M. Adams,52T. Adams,50M. Agelou,18J.-L. Agram,19 S. H. Ahn,31M. Ahsan,60G. D. Alexeev,36G. Alkhazov,40A. Alton,65G. Alverson,64G. A. Alves,2M. Anastasoaie,35
T. Andeen,54S. Anderson,46B. Andrieu,17M. S. Anzelc,54Y. Arnoud,14M. Arov,53A. Askew,50B. A˚ sman,41 A. C. S. Assis Jesus,3O. Atramentov,58C. Autermann,21C. Avila,8C. Ay,24F. Badaud,13A. Baden,62L. Bagby,53 B. Baldin,51D. V. Bandurin,36P. Banerjee,29S. Banerjee,29E. Barberis,64P. Bargassa,81P. Baringer,59C. Barnes,44 J. Barreto,2J. F. Bartlett,51U. Bassler,17D. Bauer,44A. Bean,59M. Begalli,3M. Begel,72C. Belanger-Champagne,5 A. Bellavance,68J. A. Benitez,66S. B. Beri,27G. Bernardi,17R. Bernhard,42L. Berntzon,15I. Bertram,43M. Besanc¸on,18 R. Beuselinck,44V. A. Bezzubov,39P. C. Bhat,51V. Bhatnagar,27M. Binder,25C. Biscarat,43K. M. Black,63I. Blackler,44 G. Blazey,53F. Blekman,44S. Blessing,50D. Bloch,19K. Bloom,68U. Blumenschein,23A. Boehnlein,51O. Boeriu,56 T. A. Bolton,60F. Borcherding,51G. Borissov,43K. Bos,34T. Bose,78A. Brandt,79R. Brock,66G. Brooijmans,71A. Bross,51
D. Brown,79N. J. Buchanan,50D. Buchholz,54M. Buehler,82V. Buescher,23S. Burdin,51S. Burke,46T. H. Burnett,83 E. Busato,17C. P. Buszello,44J. M. Butler,63S. Calvet,15J. Cammin,72S. Caron,34W. Carvalho,3B. C. K. Casey,78 N. M. Cason,56H. Castilla-Valdez,33S. Chakrabarti,29D. Chakraborty,53K. M. Chan,72A. Chandra,49D. Chapin,78 F. Charles,19E. Cheu,46F. Chevallier,14D. K. Cho,63S. Choi,32B. Choudhary,28L. Christofek,59D. Claes,68B. Cle´ment,19
C. Cle´ment,41Y. Coadou,5M. Cooke,81W. E. Cooper,51D. Coppage,59M. Corcoran,81M.-C. Cousinou,15B. Cox,45 S. Cre´pe´-Renaudin,14D. Cutts,78M. C´ wiok,30H. da Motta,2A. Das,63M. Das,61B. Davies,43G. Davies,44G. A. Davis,54 K. De,79P. de Jong,34S. J. de Jong,35E. De La Cruz-Burelo,65C. De Oliveira Martins,3J. D. Degenhardt,65F. De´liot,18 M. Demarteau,51R. Demina,72P. Demine,18D. Denisov,51S. P. Denisov,39S. Desai,73H. T. Diehl,51M. Diesburg,51
M. Doidge,43A. Dominguez,68H. Dong,73L. V. Dudko,38L. Duflot,16S. R. Dugad,29A. Duperrin,15J. Dyer,66 A. Dyshkant,53M. Eads,68D. Edmunds,66T. Edwards,45J. Ellison,49J. Elmsheuser,25V. D. Elvira,51S. Eno,62 P. Ermolov,38J. Estrada,51H. Evans,55A. Evdokimov,37V. N. Evdokimov,39S. N. Fatakia,63L. Feligioni,63 A. V. Ferapontov,60T. Ferbel,72F. Fiedler,25F. Filthaut,35W. Fisher,51H. E. Fisk,51I. Fleck,23M. Ford,45M. Fortner,53
H. Fox,23S. Fu,51S. Fuess,51T. Gadfort,83C. F. Galea,35E. Gallas,51E. Galyaev,56C. Garcia,72A. Garcia-Bellido,83 J. Gardner,59V. Gavrilov,37A. Gay,19P. Gay,13D. Gele´,19R. Gelhaus,49C. E. Gerber,52Y. Gershtein,50D. Gillberg,5 G. Ginther,72N. Gollub,41B. Go´mez,8K. Gounder,51A. Goussiou,56P. D. Grannis,73H. Greenlee,51Z. D. Greenwood,61
E. M. Gregores,4G. Grenier,20Ph. Gris,13J.-F. Grivaz,16S. Gru¨nendahl,51M. W. Gru¨newald,30F. Guo,73J. Guo,73 G. Gutierrez,51P. Gutierrez,76A. Haas,71N. J. Hadley,62P. Haefner,25S. Hagopian,50J. Haley,69I. Hall,76R. E. Hall,48
L. Han,7K. Hanagaki,51K. Harder,60A. Harel,72R. Harrington,64J. M. Hauptman,58R. Hauser,66J. Hays,54 T. Hebbeker,21D. Hedin,53J. G. Hegeman,34J. M. Heinmiller,52A. P. Heinson,49U. Heintz,63C. Hensel,59G. Hesketh,64
M. D. Hildreth,56R. Hirosky,82J. D. Hobbs,73B. Hoeneisen,12M. Hohlfeld,16S. J. Hong,31R. Hooper,78P. Houben,34 Y. Hu,73V. Hynek,9I. Iashvili,70R. Illingworth,51A. S. Ito,51S. Jabeen,63M. Jaffre´,16S. Jain,76V. Jain,74K. Jakobs,23 C. Jarvis,62A. Jenkins,44R. Jesik,44K. Johns,46C. Johnson,71M. Johnson,51A. Jonckheere,51P. Jonsson,44A. Juste,51 D. Ka¨fer,21S. Kahn,74E. Kajfasz,15A. M. Kalinin,36J. M. Kalk,61J. R. Kalk,66S. Kappler,21D. Karmanov,38J. Kasper,63
I. Katsanos,71D. Kau,50R. Kaur,27R. Kehoe,80S. Kermiche,15S. Kesisoglou,78A. Khanov,77A. Kharchilava,70 Y. M. Kharzheev,36D. Khatidze,71H. Kim,79T. J. Kim,31M. H. Kirby,35B. Klima,51J. M. Kohli,27J.-P. Konrath,23
M. Kopal,76V. M. Korablev,39J. Kotcher,74B. Kothari,71A. Koubarovsky,38A. V. Kozelov,39J. Kozminski,66 A. Kryemadhi,82S. Krzywdzinski,51T. Kuhl,24A. Kumar,70S. Kunori,62A. Kupco,11T. Kurcˇa,20,*J. Kvita,9S. Lager,41
S. Lammers,71G. Landsberg,78J. Lazoflores,50A.-C. Le Bihan,19P. Lebrun,20W. M. Lee,53A. Leflat,38F. Lehner,42 C. Leonidopoulos,71V. Lesne,13J. Leveque,46P. Lewis,44J. Li,79Q. Z. Li,51J. G. R. Lima,53D. Lincoln,51J. Linnemann,66 V. V. Lipaev,39R. Lipton,51Z. Liu,5L. Lobo,44A. Lobodenko,40M. Lokajicek,11A. Lounis,19P. Love,43H. J. Lubatti,83 M. Lynker,56A. L. Lyon,51A. K. A. Maciel,2R. J. Madaras,47P. Ma¨ttig,26C. Magass,21A. Magerkurth,65A.-M. Magnan,14 N. Makovec,16P. K. Mal,56H. B. Malbouisson,3S. Malik,68V. L. Malyshev,36H. S. Mao,6Y. Maravin,60M. Martens,51
S. E. K. Mattingly,78R. McCarthy,73R. McCroskey,46D. Meder,24A. Melnitchouk,67A. Mendes,15L. Mendoza,8 M. Merkin,38K. W. Merritt,51A. Meyer,21J. Meyer,22M. Michaut,18H. Miettinen,81T. Millet,20J. Mitrevski,71J. Molina,3
S. K. Park,31J. Parsons,71R. Partridge,78N. Parua,73A. Patwa,74G. Pawloski,81P. M. Perea,49E. Perez,18K. Peters,45 P. Pe´troff,16M. Petteni,44R. Piegaia,1M.-A. Pleier,22P. L. M. Podesta-Lerma,33V. M. Podstavkov,51Y. Pogorelov,56 M.-E. Pol,2A. Pomposˇ,76B. G. Pope,66A. V. Popov,39W. L. Prado da Silva,3H. B. Prosper,50S. Protopopescu,74J. Qian,65
A. Quadt,22B. Quinn,67K. J. Rani,29K. Ranjan,28P. A. Rapidis,51P. N. Ratoff,43P. Renkel,80S. Reucroft,64 M. Rijssenbeek,73I. Ripp-Baudot,19F. Rizatdinova,77S. Robinson,44R. F. Rodrigues,3C. Royon,18P. Rubinov,51 R. Ruchti,56V. I. Rud,38G. Sajot,14A. Sa´nchez-Herna´ndez,33M. P. Sanders,62A. Santoro,3G. Savage,51L. Sawyer,61
T. Scanlon,44D. Schaile,25R. D. Schamberger,73Y. Scheglov,40H. Schellman,54P. Schieferdecker,25C. Schmitt,26 C. Schwanenberger,45A. Schwartzman,69R. Schwienhorst,66S. Sengupta,50H. Severini,76E. Shabalina,52M. Shamim,60 V. Shary,18A. A. Shchukin,39W. D. Shephard,56R. K. Shivpuri,28D. Shpakov,64V. Siccardi,19R. A. Sidwell,60V. Simak,10 V. Sirotenko,51P. Skubic,76P. Slattery,72R. P. Smith,51G. R. Snow,68J. Snow,75S. Snyder,74S. So¨ldner-Rembold,45
X. Song,53L. Sonnenschein,17A. Sopczak,43M. Sosebee,79K. Soustruznik,9M. Souza,2B. Spurlock,79J. Stark,14 J. Steele,61K. Stevenson,55V. Stolin,37A. Stone,52D. A. Stoyanova,39J. Strandberg,41M. A. Strang,70M. Strauss,76 R. Stro¨hmer,25D. Strom,54M. Strovink,47L. Stutte,51S. Sumowidagdo,50A. Sznajder,3M. Talby,15P. Tamburello,46 W. Taylor,5P. Telford,45J. Temple,46B. Tiller,25M. Titov,23V. V. Tokmenin,36M. Tomoto,51T. Toole,62I. Torchiani,23 S. Towers,43T. Trefzger,24S. Trincaz-Duvoid,17D. Tsybychev,73B. Tuchming,18C. Tully,69A. S. Turcot,45P. M. Tuts,71
R. Unalan,66L. Uvarov,40S. Uvarov,40S. Uzunyan,53B. Vachon,5P. J. van den Berg,34R. Van Kooten,55 W. M. van Leeuwen,34N. Varelas,52E. W. Varnes,46A. Vartapetian,79I. A. Vasilyev,39M. Vaupel,26P. Verdier,20
L. S. Vertogradov,36M. Verzocchi,51F. Villeneuve-Seguier,44P. Vint,44J.-R. Vlimant,17E. Von Toerne,60 M. Voutilainen,68,†M. Vreeswijk,34H. D. Wahl,50L. Wang,62J. Warchol,56G. Watts,83M. Wayne,56M. Weber,51 H. Weerts,66N. Wermes,22M. Wetstein,62A. White,79D. Wicke,26G. W. Wilson,59S. J. Wimpenny,49M. Wobisch,51 J. Womersley,51D. R. Wood,64T. R. Wyatt,45Y. Xie,78N. Xuan,56S. Yacoob,54R. Yamada,51M. Yan,62T. Yasuda,51
Y. A. Yatsunenko,36K. Yip,74H. D. Yoo,78S. W. Youn,54C. Yu,14J. Yu,79A. Yurkewicz,73A. Zatserklyaniy,53 C. Zeitnitz,26D. Zhang,51T. Zhao,83Z. Zhao,65B. Zhou,65J. Zhu,73M. Zielinski,72D. Zieminska,55A. Zieminski,55
V. Zutshi,53and E. G. Zverev38
(D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2
LAFEX, 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 6
Institute 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 9
Center for Particle Physics, Charles University, Prague, Czech Republic 10Czech Technical University, Prague, Czech Republic
11
Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 12Universidad San Francisco de Quito, Quito, Ecuador
13
Laboratoire 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 18
DAPNIA/Service de Physique des Particules, CEA, Saclay, France
19IReS, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France, and Universite´ de Haute Alsace, Mulhouse, France 20
Institut de Physique Nucle´aire de Lyon, IN2P3-CNRS, Universite´ Claude Bernard, Villeurbanne, France 21III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany
22
Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 23Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany
24Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 25
Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 26Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
27
28Delhi University, Delhi, India
29Tata Institute of Fundamental Research, Mumbai, India 30University College Dublin, Dublin, Ireland 31Korea Detector Laboratory, Korea University, Seoul, Korea
32
SungKyunKwan University, Suwon, Korea 33CINVESTAV, Mexico City, Mexico 34
FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 35Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
36
Joint Institute for Nuclear Research, Dubna, Russia 37Institute for Theoretical and Experimental Physics, Moscow, Russia
38Moscow State University, Moscow, Russia 39
Institute for High Energy Physics, Protvino, Russia 40Petersburg Nuclear Physics Institute, St. Petersburg, Russia 41
Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden
42
Physik Institut der Universita¨t Zu¨rich, Zu¨rich, Switzerland 43Lancaster University, Lancaster, United Kingdom
44Imperial College, London, United Kingdom 45University of Manchester, Manchester, United Kingdom
46University of Arizona, Tucson, Arizona 85721, USA 47
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA and University of California, Berkeley, California 94720, USA
48
California State University, Fresno, California 93740, USA 49University of California, Riverside, California 92521, USA 50
Florida State University, Tallahassee, Florida 32306, USA 51Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
52University of Illinois at Chicago, Chicago, Illinois 60607, USA 53
Northern Illinois University, DeKalb, Illinois 60115, USA 54Northwestern University, Evanston, Illinois 60208, USA
55
Indiana University, Bloomington, Indiana 47405, USA 56University of Notre Dame, Notre Dame, Indiana 46556, USA
57
Purdue University Calumet, Hammond, Indiana 46323, USA 58Iowa State University, Ames, Iowa 50011, USA 59University of Kansas, Lawrence, Kansas 66045, USA 60Kansas State University, Manhattan, Kansas 66506, USA 61Louisiana Tech University, Ruston, Louisiana 71272, USA 62
University of Maryland, College Park, Maryland 20742, USA 63Boston University, Boston, Massachusetts 02215, USA 64
Northeastern University, Boston, Massachusetts 02115, USA 65University of Michigan, Ann Arbor, Michigan 48109, USA 66Michigan State University, East Lansing, Michigan 48824, USA
67University of Mississippi, University, Mississippi 38677, USA 68University of Nebraska, Lincoln, Nebraska 68588, USA 69
Princeton University, Princeton, New Jersey 08544, USA 70State University of New York, Buffalo, New York 14260, USA
71
Columbia University, New York, New York 10027, USA 72University of Rochester, Rochester, New York 14627, USA 73
State University of New York, Stony Brook, New York 11794, USA 74Brookhaven National Laboratory, Upton, New York 11973, USA
75Langston University, Langston, Oklahoma 73050, USA 76University of Oklahoma, Norman, Oklahoma 73019, USA 77Oklahoma State University, Stillwater, Oklahoma 74078, USA
78
Brown University, Providence, Rhode Island 02912, USA 79University of Texas, Arlington, Texas 76019, USA 80
Southern Methodist University, Dallas, Texas 75275, USA 81Rice University, Houston, Texas 77005, USA 82
University of Virginia, Charlottesville, Virginia 22901, USA 83University of Washington, Seattle, Washington 98195, USA
(Received 15 March 2006; published 14 July 2006)
We report results of a study of theB0
the Fermilab Tevatron Collider in 2002 – 2006. The amplitude method gives a lower limit on theB0 s oscillation frequency at14:8 ps1at the 95% C.L. Atm
s19 ps1, the amplitude deviates from the hypothesisA0(1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%). A likelihood scan over the oscillation frequency,ms, gives a most probable value of19 ps1and a range of 17<ms<21 ps1at the 90% C.L., assuming Gaussian uncertainties. This is the first direct two-sided bound measured by a single experiment. Ifms lies above22 ps1, then the probability that it would produce a likelihood minimum similar to the one observed in the interval16–22 ps1 is5:00:3%.
DOI:10.1103/PhysRevLett.97.021802 PACS numbers: 14.40.Nd, 12.15.Ff, 12.15.Hh, 13.20.He
Measurements of flavor oscillations in the B0
d and B0s
systems provide important constraints on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle and the source of CP violation in the standard model (SM) [1]. The phenomenon ofB0
doscillations is well established [2],
with a precisely measured oscillation frequencymd. In the SM, this parameter is proportional to the combination
jV
tbVtdj2 of CKM matrix elements. Since the matrix ele-mentVtsis larger thanVtd, the expected frequencymsis higher. As a result,B0
s oscillations have not been observed
by any previous experiment and the current 95% C.L. lower limit on ms is 16:6 ps1 [2]. A measurement of
ms would yield the ratiojVts=Vtdj, which has a smaller uncertainty than jVtdj alone due to the cancellation of certain theory uncertainties. If the SM is correct, and if current limits on B0
s oscillations are not included, then
global fits to the unitarity triangle favor ms 20:94:5
4:2 ps1 [3] orms21:23:2 ps1 [4].
In this Letter, we present a study ofB0
s-B0s oscillations
carried out using semileptonic B0
s!DsX decays [5]
collected by the D0 experiment at Fermilab in pp colli-sions atps
1:96 TeV. In theB0
s-B0ssystem there are two
mass eigenstates, the heavier (lighter) one having massMH
(ML) and decay width H (L). Denoting msMH ML, sLH, s LH=2, the time-dependent probability Pthat an initial B0
s decays at time
t as B0
s!XPnos or B0s!XPosc is given by
Pnos=oscest1cosm
st=2, assuming that s=s
is small and neglecting CP violation. Flavor tagging ab
(b) on the opposite side from the signal meson establishes the signal meson as aB0
s (B0s) at timet0.
The D0 detector is described in detail elsewhere [6]. Charged particles are reconstructed using the central track-ing system which consists of a silicon microstrip tracker (SMT) and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet. Electrons are identified by the preshower and liquid-argon and uranium calorimeter. Muons are identified by the muon system which consists of a layer of tracking detectors and scintillation trigger counters in front of 1.8 T iron toroids, followed by two similar layers after the toroids [7].
No explicit trigger requirement was made, although most of the sample was collected with single muon trig-gers. The decay chainB0
s !DsX,Ds !,!
KK was then reconstructed. The charged tracks were
required to have signals in both the CFT and SMT. Muons were required to have transverse momentum pT>
2 GeV=cand momentump>3 GeV=c, and to have
measurements in at least two layers of the muon system. All charged tracks in the event were clustered into jets [8], and theDs candidate was reconstructed from three tracks
found in the same jet as the reconstructed muon. Oppositely charged particles with pT>0:7 GeV=c were assigned the kaon mass and were required to have an invariant mass1:004< MKK<1:034 GeV=c2, con-sistent with that of ameson. The third track was required to havepT>0:5 GeV=cand charge opposite to that of the muon charge and was assigned the pion mass. The three tracks were required to form a common D
s vertex using
the algorithm described in Ref. [9]. To reduce combinato-rial background, the D
s vertex was required to have a
positive displacement in the transverse plane, relative to the pp collision point [or primary vertex (PV)], with at least4significance. The cosine of the angle between the
Ds momentum and the direction from the PV to theDs
vertex was required to be greater than 0.9. The trajectories of the muon andD
s candidates were required to originate
from a common B0
s vertex, and the Ds system was
required to have an invariant mass between 2.6 and
5:4 GeV=c2.
To further improveB0
ssignal selection, a likelihood ratio
method [10] was utilized. UsingMKKsideband (B)
and sideband-subtracted signal (S) distributions in the data, probability density functions (PDFs) were found for a number of discriminating variables: the helicity angle be-tween the D
s andK momenta in the center-of-mass
frame, the isolation of theDs system, the2of theD
s
vertex, the invariant masses MDs and MKK,
and pTKK. The final requirement on the combined
selection likelihood ratio variable,ysel, was chosen to max-imize the predicted ratio S=
SB p
. The total number of
D
s candidates after these requirements was Ntot
26 710556stat, as shown in Fig.1(a).
The performance of the opposite-side flavor tagger (OST) [11] is characterized by the efficiency Ntag=Ntot, whereNtag is the number of taggedB0s mesons;
the puritys, defined assNcor=Ntag, whereNcoris the number ofB0
smesons with correct flavor identification; and
the dilution, related to purity as D2s1. Again, a likelihood ratio method was used. In the construction of the flavor discriminating variablesx1;. . .; xnfor each event, an
object, either a lepton ‘ (electron or muon) or a recon-structed secondary vertex (SV), was defined to be on the opposite side from the B0
cos’p~‘orSV; ~pB<0:8, where p~B is the reconstructed
three-momentum of theB0
s meson, and’is the azimuthal
angle about the beam axis. A lepton jet charge was formed as Q‘
J PiqipiT=PipiT, where all charged particles are
summed, including the lepton, inside a cone of R
’2 2
p
<0:5 centered on the lepton. The SV charge was defined as QSVPiqipiL0:6=PipiL0:6,
where all charged particles associated with the SV are summed, andpi
L is the longitudinal momentum of tracki
with respect to the direction of the SV momentum. Finally, event charge is defined as QEVPiqipiT=PipiT, where
the sum is over all tracks withpT>0:5 GeV=coutside a cone ofR >1:5centered on theB0
sdirection. The PDF of
each discriminating variable was found forbandbquarks using a large data sample ofB!D0 events where the initial state is known from the charge of the decay muon.
For an initialb(b) quark, the PDF for a given variablexi
is denotedfb ixi[f
b
ixi], and the combined tagging
vari-able is defined as dtag 1z=1z, where z
Qn i1f
b
ixi=fibxi. The variable dtag varies between
1 and 1. An event with dtag>0<0 is tagged as a b (b) quark.
The OST purity was determined from large samples of
B!D0X (nonoscillating) and B0
d!DX
(slowly oscillating) semileptonic candidates. An average value of D2
2:480:21stat0:08
0:06syst% was ob-tained [11]. The estimated event-by-event dilution as a function of jdtagj was determined by measuring D in bins of jdtagj and parametrizing with a third-order poly-nomial forjdtagj<0:6. Forjdtagj>0:6,Dis fixed to 0.6.
The OST was applied to theB0
s !DsXdata sample,
yielding Ntag 5601102stat candidates having an identified initial state flavor, as shown in Fig. 1(b). The tagging efficiency was20:90:7%.
After flavor tagging, the proper decay time of candidates is needed; however, the undetected neutrino and other missing particles in the semileptonic B0
s decay prevent a
precise determination of the meson’s momentum and Lorentz boost. This represents an important contribution to the smearing of the proper decay length in semileptonic decays, in addition to the resolution effects. A correction factorKwas estimated from a Monte Carlo (MC) simula-tion by finding the distribusimula-tion ofKpTD
s=pTB
for a given decay channel in bins ofMD
s. The proper
decay length of each B0
s meson is then ctB0s lMK,
where lMMB0
s L~Tp~TDs=pTDs2 is
the measured visible proper decay length (VPDL), L~T is
the vector from the PV to the B0
s decay vertex in the
transverse plane andMB0
s 5:3696 GeV=c2 [1].
All flavor-tagged events with 1:72< MKK< 2:22 GeV=c2 were used in an unbinned fitting procedure. The likelihood, L, for an event to arise from a specific source in the sample depends event-by-event on lM, its uncertainty lM, the invariant mass of the candidate
MKK, the predicted dilution Ddtag, and the selection variable ysel. The PDFs for lM, MKK,
Ddtag, andyselwere determined from data. Four sources were considered: the signal Ds!; the
accom-panying peak due to D!; a small (less than
1%) reflection due to D!K, where the
kaon mass is misassigned to one of the pions; and combi-natorial background. The total fractions of the first two categories were determined from the mass fit of Fig.1(b).
The D
s signal sample is composed mostly of B0s
mesons with some contributions fromB0
dandBmesons.
Contributions ofbbaryons to the sample were estimated to be small and were neglected. The data were divided into subsamples with and without oscillation as determined by the OST. The distribution of the VPDLlfor nonoscillated and oscillated cases was modeled appropriately for each type ofBmeson, e.g., forB0
s:
pnoss =oscl; K; dtag
K c B0
s
exp
c Kl
B0
s
1DdtagcosmsKl=c=2: (1)
The world averages [1] of B0
d, B, andmdwere used as
inputs to the fit. The lifetime, B0
s, was allowed to float in
the fit. In the amplitude and likelihood scans described below, B0
s was fixed to this fitted value, which agrees with
expectations.
The total VPDL PDF for the D
s signal is then the
sum over all decay channels, including branching frac-tions, that yield the Ds mass peak. The B0
s!DsX
signal modes (including Ds , D
s0 , and D0s1; and originating from decay) comprise 85:63:3% of our sample, as determined from a MC simulation which included thePYTHIAgenerator v6.2 [12] interfaced with the
EVTGENdecay package [13], followed by fullGEANTv3.15 [14] modeling of the detector response and event recon-struction. Other backgrounds considered were decays via
] [GeV
π
(KK) M ) Events/(0.01 GeV 0 0 400 800 1200 2000 4000 6000 ) b ( ) a (
D Run II 1 fb−1 D Run II 1 fb−1
1.8 1.9 2.0
] [GeV
π
(KK) M
1.8 1.9 2.0
FIG. 1 (color online). KK invariant mass distribution (a) for the untaggedB0
ssample, and (b) for candidates that have been flavor tagged. The left and right peaks correspond toD and D
B0
s !DsDsX andBd0,B !DDs, followed byDs! X, with a real Ds reconstructed in the peak and an
associated real . Another background taken into
ac-count occurs when the D
s meson originates from one b
orcquark and the muon arises from another quark. This background peaks around the PV (peaking backgrounds). The uncertainty in each channel covers possible trigger efficiency biases. Translation from the true VPDL,l, to the measured lM for a given channel, is achieved by a
con-volution of the VPDL detector resolution, ofKfactors over each normalized distribution, and by including the recon-struction efficiency as a function of VPDL. The lifetime-dependent efficiency was found for each channel using MC simulations and, as a cross check, the efficiency was also determined from the data by fixing B0
s and fitting for the
functional form of the efficiency. The shape of the VPDL distribution for peaking backgrounds was found from MC simulation, and the fraction from this source was allowed to float in the fit.
The VPDL uncertainty was determined from the vertex fit using track parameters and their uncertainties. To ac-count for possible mismodeling of these uncertainties, resolution scale factors were introduced as determined by examining the pull distribution of the vertex positions of a sample of J= ! decays. Using these scale
fac-tors, the convolving function for the VPDL resolution was the sum of two Gaussian functions with widths (fractions) of0:998l
M(72%) and1:775lM(28%). A cross check was
performed using a MC simulation with tracking errors tuned according to the procedure described in Ref. [15]. The 7% variation of scale factors found in this cross check was used to estimate systematic uncertainties due to decay length resolution.
Several contributions to the combinatorial backgrounds that have different VPDL distributions were considered. True prompt background was modeled with a Gaussian function with a separate scale factor on the width; back-ground due to fake vertices around the PV was modeled with another Gaussian function; and long-lived back-ground was modeled with an exponential function convo-luted with the resolution, including a component oscil-lating with a frequency of md. The unbinned fit of the
total tagged sample was used to determine the various fractions of signal and backgrounds and the background VPDL parametrizations.
Figure2shows the value of logLas a function of
ms, indicating a favored value of19 ps1, while variation of logL from the minimum indicates an oscillation frequency of 17<ms<21 ps1 at the 90% C.L. The
uncertainties are approximately Gaussian inside this inter-val. The plateau of the likelihood curve shows the region where we do not have sufficient resolution to measure an oscillation, and if the true value of ms>22 ps1, our measured confidence interval does not make any statement about the frequency. Using 100 parametrized MC samples with similar statistics, VPDL resolution, overall tagging
performance, and sample composition of the data sample, it was determined that for a true value ofms19 ps1,
the probability was 15% for measuring a value in the range
16<ms<22 ps1with a logLlower by at least 1.9
than the corresponding value atms25 ps1.
The amplitude method [16] was also used. Equation (1) was modified to include the oscillation amplitudeAas an additional coefficient on thecosmsKl=cterm. The un-binned fit was repeated for fixed input values ofmsand the fitted value ofAand its uncertaintyAfound for each step, as shown in Fig.3. Atms19 ps1 the measured data point deviates from the hypothesis A0(A1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%), and is in agreement with the likelihood results. In the presence of a signal, however, it is more difficult to define a confidence interval using the amplitude than by examining the logLcurve. Since, on average, these two methods give the same results, we chose to quantify our ms interval using the likelihood
curve.
−∆
log(L
)
0 2 4 6
26 22
18 14
10
[ps ]
s
m ∆
30 −1 90% C.L.
(two-sided)
DØ Run II, 1 fb−1
FIG. 2 (color online). Value of logLas a function ofms. Star symbols do not include systematic uncertainties, and the shaded band represents the envelope of alllogLscan curves due to different systematic uncertainties.
] -1 [ps s m
∆
0 5 10 15 20 25
Amplitude
-4 -2 0 2 4
(stat.) σ 1.645 ± data
syst.) ⊕ (stat. σ 1.645 ± data
σ 1 ± data
-1 95% CL limit: 14.8ps
-1 Expected limit: 14.1ps
DØ Run II
-1
1 fb
FIG. 3 (color online). B0
Systematic uncertainties were addressed by varying in-puts, cut requirements, branching ratios, and PDF model-ing. The branching ratios were varied within known uncertainties [1] and large variations were taken for those not yet measured. The K-factor distributions were varied within uncertainties, using measured (or smoothed) instead of generated momenta in the MC simulation. The fractions of peaking and combinatorial backgrounds were varied within uncertainties. Uncertainties in the reflection contri-bution were considered. The functional form to determine the dilutionDdtagwas varied. The lifetime B0
s was fixed
to its world average value, andswas allowed to be
non-zero. The scale factors on the signal and background reso-lutions were varied within uncertainties, and typically gen-erated the largest systematic uncertainty in the region of interest. A separate scan of logLwas taken for each variation, and the envelope of all such curves is indicated as the band in Fig.2. The same systematic uncertainties were considered for the amplitude method using the pro-cedure of Ref. [16], and, when added in quadrature with the statistical uncertainties, represent a small effect, as shown in Fig. 3. Taking these systematic uncertainties into ac-count, we obtain from the amplitude method an expected limit of14:1 ps1 and an observed lower limit ofm
s> 14:8 ps1 at the 95% C.L., consistent with the likelihood scan.
The probability that B0
s-B0s oscillations with the true
value ofms>22 ps1would give a logLminimum in the range 16<ms<22 ps1 with a depth of more than 1.7 with respect to the logL value at ms 25 ps1, corresponding to our observation including sys-tematic uncertainties, was found to be5:00:3%. This range ofmswas chosen to encompass the world average lower limit and the edge of our sensitive region. To deter-mine this probability, an ensemble test using the data sample was performed by randomly assigning a flavor to each candidate while retaining all its other information, effectively simulating a B0
s oscillation with an infinite
frequency. Similar probabilities were found using ensem-bles of parametrized MC events.
In summary, a study of B0
s-B0s oscillations was
per-formed using B0
s !DsX decays, where Ds !
and !KK, an opposite-side flavor tagging
algo-rithm, and an unbinned likelihood fit. The amplitude method gives an expected limit of 14:1 ps1 and an ob-served lower limit ofms>14:8 ps1at the 95% C.L. At
ms19 ps1, the amplitude method yields a result that deviates from the hypothesisA0(A1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%). The likelihood curve is well behaved near a preferred value of 19 ps1 with a 90% C.L. interval of
17<ms<21 ps1, assuming Gaussian uncertainties. The lower edge of the confidence level interval is near the world average 95% C.L. lower limitms>16:6 ps1
[2]. Ensemble tests indicate that if ms lies above the
sensitive region, i.e., above approximately 22 ps1, there is a5:00:3%probability that it would produce a like-lihood minimum similar to the one observed in the interval
16<ms<22 ps1. This is the first report of a direct two-sided bound measured by a single experiment on the
B0
s oscillation frequency.
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.
*On leave from IEP SAS Kosice, Slovakia.
†Visiting scientist from Helsinki Institute of Physics,
Helsinki, Finland.
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[3] J. Charleset al.(CKMfitter Group), Eur. Phys. J. C41, 1 (2005).
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