Study of the Decay
B
0s!
D
sD
sV. 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
J. 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,19G. 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,21S. 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
S. Cihangir,50D. Claes,67B. Cle´ment,18C. Cle´ment,40Y. Coadou,5M. Cooke,80W. E. Cooper,50M. Corcoran,80 F. Couderc,17M.-C. Cousinou,14S. Cre´pe´-Renaudin,13D. Cutts,77M. C´ wiok,29H. da Motta,2A. Das,62G. Davies,43 K. De,78P. de Jong,33S. J. de Jong,34E. De La Cruz-Burelo,64C. De Oliveira Martins,3J. D. Degenhardt,64F. De´liot,17 M. Demarteau,50R. Demina,71D. Denisov,50S. P. Denisov,38S. Desai,50H. T. Diehl,50M. Diesburg,50A. Dominguez,67 H. Dong,72L. V. Dudko,37L. Duflot,15S. R. Dugad,28D. Duggan,49A. Duperrin,14J. Dyer,65A. Dyshkant,52M. Eads,67
D. Edmunds,65J. Ellison,48V. D. Elvira,50Y. Enari,77S. Eno,61P. Ermolov,37H. Evans,54A. Evdokimov,36 V. N. Evdokimov,38A. V. Ferapontov,59T. Ferbel,71F. Fiedler,24F. Filthaut,34W. Fisher,50H. E. Fisk,50M. Ford,44
M. Fortner,52H. Fox,22S. Fu,50S. Fuess,50T. Gadfort,82C. F. Galea,34E. Gallas,50E. Galyaev,55C. Garcia,71 A. Garcia-Bellido,82V. Gavrilov,36P. Gay,12W. Geist,18D. Gele´,18C. E. Gerber,51Y. Gershtein,49D. Gillberg,5 G. Ginther,71N. Gollub,40B. Go´mez,7A. Goussiou,55P. D. Grannis,72H. Greenlee,50Z. D. Greenwood,60E. M. Gregores,4
G. Grenier,19Ph. Gris,12J.-F. Grivaz,15A. Grohsjean,24S. Gru¨nendahl,50M. W. Gru¨newald,29F. Guo,72J. Guo,72 G. Gutierrez,50P. Gutierrez,75A. Haas,70N. J. Hadley,61P. Haefner,24S. Hagopian,49J. Haley,68I. Hall,75R. E. Hall,47 L. Han,6K. Hanagaki,50P. Hansson,40K. Harder,44A. Harel,71R. Harrington,63J. M. Hauptman,57R. Hauser,65J. Hays,43 T. Hebbeker,20D. Hedin,52J. G. Hegeman,33J. M. Heinmiller,51A. P. Heinson,48U. Heintz,62C. Hensel,58K. Herner,72 G. Hesketh,63M. D. Hildreth,55R. Hirosky,81J. D. Hobbs,72B. Hoeneisen,11H. Hoeth,25M. Hohlfeld,15S. J. Hong,30
R. Hooper,77P. Houben,33Y. Hu,72Z. Hubacek,9V. Hynek,8I. Iashvili,69R. Illingworth,50A. S. Ito,50S. Jabeen,62 M. Jaffre´,15S. Jain,75K. Jakobs,22C. Jarvis,61R. Jesik,43K. Johns,45C. Johnson,70M. Johnson,50A. Jonckheere,50 P. Jonsson,43A. Juste,50D. Ka¨fer,20S. Kahn,73E. Kajfasz,14A. M. Kalinin,35J. M. Kalk,60J. R. Kalk,65S. Kappler,20 D. Karmanov,37J. Kasper,62P. Kasper,50I. Katsanos,70D. Kau,49R. Kaur,26V. Kaushik,78R. Kehoe,79S. Kermiche,14 N. Khalatyan,38A. Khanov,76A. Kharchilava,69Y. M. Kharzheev,35D. Khatidze,70H. Kim,31T. J. Kim,30M. H. Kirby,34 B. Klima,50J. M. Kohli,26J.-P. Konrath,22M. Kopal,75V. M. Korablev,38J. Kotcher,73B. Kothari,70A. Koubarovsky,37 A. V. Kozelov,38D. Krop,54A. Kryemadhi,81T. Kuhl,23A. Kumar,69S. Kunori,61A. Kupco,10T. Kurcˇa,19J. Kvita,8 D. Lam,55S. Lammers,70G. Landsberg,77J. Lazoflores,49P. Lebrun,19W. M. Lee,50A. Leflat,37F. Lehner,41V. Lesne,12
J. Leveque,45P. Lewis,43J. Li,78L. Li,48Q. Z. Li,50S. M. Lietti,4J. G. R. Lima,52D. Lincoln,50J. Linnemann,65 V. V. Lipaev,38R. Lipton,50Z. Liu,5L. Lobo,43A. Lobodenko,39M. Lokajicek,10A. Lounis,18P. Love,42H. J. Lubatti,82 M. Lynker,55A. L. Lyon,50A. K. A. Maciel,2R. J. Madaras,46P. Ma¨ttig,25C. Magass,20A. Magerkurth,64N. Makovec,15 P. K. Mal,55H. B. Malbouisson,3S. Malik,67V. L. Malyshev,35H. S. Mao,50Y. Maravin,59B. Martin,13R. McCarthy,72 A. Melnitchouk,66A. Mendes,14L. Mendoza,7P. G. Mercadante,4M. Merkin,37K. W. Merritt,50A. Meyer,20J. Meyer,21 M. Michaut,17H. Miettinen,80T. Millet,19J. Mitrevski,70J. Molina,3R. K. Mommsen,44N. K. Mondal,28J. Monk,44
R. W. Moore,5T. Moulik,58G. S. Muanza,19M. Mulders,50M. Mulhearn,70O. Mundal,21L. Mundim,3E. Nagy,14 M. Naimuddin,50M. Narain,77N. A. Naumann,34H. A. Neal,64J. P. Negret,7P. Neustroev,39H. Nilsen,22C. Noeding,22
A. Nomerotski,50S. F. Novaes,4T. Nunnemann,24V. O’Dell,50D. C. O’Neil,5G. Obrant,39C. Ochando,15V. Oguri,3 N. Oliveira,3D. Onoprienko,59N. Oshima,50J. Osta,55R. Otec,9G. J. Otero y Garzo´n,51M. Owen,44P. Padley,80
G. Pawloski,80P. M. Perea,48K. Peters,44Y. Peters,25P. Pe´troff,15M. Petteni,43R. Piegaia,1J. Piper,65M.-A. Pleier,21 P. L. M. Podesta-Lerma,32,†V. M. Podstavkov,50Y. Pogorelov,55M.-E. Pol,2A. Pomposˇ,75B. G. Pope,65A. V. Popov,38 C. Potter,5W. L. Prado da Silva,3H. B. Prosper,49S. Protopopescu,73J. Qian,64A. Quadt,21B. Quinn,66M. S. Rangel,2 K. J. Rani,28K. Ranjan,27P. N. Ratoff,42P. Renkel,79S. Reucroft,63M. Rijssenbeek,72I. Ripp-Baudot,18F. Rizatdinova,76
S. Robinson,43R. F. Rodrigues,3C. Royon,17P. Rubinov,50R. Ruchti,55G. Sajot,13A. Sa´nchez-Herna´ndez,32 M. P. Sanders,16A. Santoro,3G. Savage,50L. Sawyer,60T. Scanlon,43D. Schaile,24R. D. Schamberger,72Y. Scheglov,39
H. Schellman,53P. Schieferdecker,24C. Schmitt,25C. Schwanenberger,44A. Schwartzman,68R. Schwienhorst,65 J. Sekaric,49S. Sengupta,49H. Severini,75E. Shabalina,51M. Shamim,59V. Shary,17A. A. Shchukin,38R. K. Shivpuri,27
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M. Wobisch,50D. R. Wood,63T. R. Wyatt,44Y. Xie,77S. Yacoob,53R. Yamada,50M. Yan,61T. Yasuda,50 Y. A. Yatsunenko,35K. Yip,73H. D. Yoo,77S. W. Youn,53C. Yu,13J. Yu,78A. Yurkewicz,72A. Zatserklyaniy,52
C. Zeitnitz,25D. Zhang,50T. Zhao,82B. Zhou,64J. Zhu,72M. Zielinski,71D. Zieminska,54A. Zieminski,54 V. Zutshi,52and E. G. Zverev37
(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 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 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 23Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 24
Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany
25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany 26
27Delhi University, Delhi, India
28Tata Institute of Fundamental Research, Mumbai, India 29University College Dublin, Dublin, Ireland 30Korea Detector Laboratory, Korea University, Seoul, Korea
31
SungKyunKwan 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 37Moscow State University, Moscow, Russia
38
Institute 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 43Imperial College, London, United Kingdom 44University of Manchester, Manchester, United Kingdom
45University of Arizona, Tucson, Arizona 85721, USA 46
Lawrence 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 52Northern Illinois University, DeKalb, Illinois 60115, USA
53
Northwestern 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 59Kansas State University, Manhattan, Kansas 66506, USA 60Louisiana Tech University, Ruston, Louisiana 71272, USA 61University of Maryland, College Park, Maryland 20742, USA
62
Boston 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 66University of Mississippi, University, Mississippi 38677, USA
67University of Nebraska, Lincoln, Nebraska 68588, USA 68Princeton University, Princeton, New Jersey 08544, USA 69
State 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 75University of Oklahoma, Norman, Oklahoma 73019, USA 76Oklahoma State University, Stillwater, Oklahoma 74078, USA
77Brown University, Providence, Rhode Island 02912, USA 78
University 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
(Received 1 March 2007; published 12 December 2007)
We report a study of the decay B0
Tevatron collider. OneDs meson was partially reconstructed in the decayDs!, and the otherDs meson was identified using the decayDs!where no attempt was made to distinguishDsandDs states. For the branching fraction BrB0
s !Ds Ds we obtain a 90% C.L. range 0:002;0:080 and central value0:0390:019
0:017stat00::016015syst. This was subsequently used to make the most precise estimate
of the width differenceCPs in theB0sBs0system:CPs =s0:07900::038035stat00::031030syst.
DOI:10.1103/PhysRevLett.99.241801 PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Ff, 13.20.Fc
In the standard model (SM), mixing in theB0
ssystem is
expected to produce a large decay width differences LH between the light and heavy mass eigenstates
with a smallCP-violating phases [1]. New phenomena could produce a significantCP-violating phase leading to a reduction in the observed value ofscompared with the
SM prediction of s=s0:127 0:024[2]. CPs CPeven
s CPs odd (sCPs coss) can be estimated
from the branching fractionBrB0
s !Ds Ds . This decay
is predominantly CP even and is related to CP s [1,3]: 2BrB0
s!Ds Ds CPs =s1Os=s, where
contributions of charmonium final states have been ignored. Only one measurement of BrB0
s !Ds Ds
has previously been published, by the ALEPH [4] experi-ment at the CERN LEP collider from the study of corre-lated production ofinZ0decays.
In this Letter we present a study of the decay chainB0
s ! Ds Ds where one Ds decays to , the other Ds
decays toDs !, and where eachmeson decays
toKK. We denote the final states as
1and2,
respectively. A semileptonic decay of oneDs meson was required to trigger on selected events. Charge conjugate reactions are implied throughout. No attempt was made to reconstruct the photon or 0 from the decay D
s ! Ds=0and thus the stateD
s Ds contains contributions
from DsDs, D
sDs, and DsDs. To reduce systematic
ef-fects, BrB0
s!Ds Ds was normalized to the decay B0
s !Ds X.
We use a sample of events collected by the D0 experi-ment at Fermilab inpp collisions atps
1:96 TeV. The D0 detector is described in detail elsewhere [5]. The data used in this analysis correspond to an integrated luminosity of approximately1:3 fb1 and were selected without any
explicit trigger requirement, although most events satisfied inclusive single-muon triggers.
The analysis began with the reconstruction of the decay chainDs!1,1!KK, from events containing
an identified muon. Muons were required to have trans-verse momentum pT>2 GeV=c, total momentum p >
3 GeV=c, and to have measurements in at least two layers of the muon system. Two oppositely charged particles with
pT>0:8 GeV=cwere selected from the remaining parti-cles in the event and were assigned the mass of a kaon. An invariant mass of 1:01< MKK<1:03 GeV=c2 was
required, to be consistent with the mass of ameson. Each pair of kaons satisfying these criteria was combined with a third particle with pT>1:0 GeV=c, which was assigned
the mass of a pion. The three tracks were required to form a
Ds vertex using the algorithm described in Ref. [6]. The cosine of the angle between the Ds momentum and the direction from the pp collision point (primary vertex) to the Dsvertex was required to be greater than 0.9. TheDs
vertex was required to have a displacement from the pri-mary vertex in the plane perpendicular to the beam with at least4significance. The helicity angleis defined as the angle between the momenta of the Ds and a kaon in the (KK) center of mass system. The decay ofDs!
follows acos2distribution, while for backgroundcosis
expected to be flat. Therefore, to enhance the signal, the criterion jcosj>0:35was applied. The muon and pion were required to have opposite charge. The events passing these selections, referred to as the preselection sample, were used to produce the samples of (2Ds) and the normalizing sample (Ds) defined below.
To construct a (Ds) candidate from the preselection sample, the Ds candidate and the muon were required to originate from a commonB0
svertex. The mass of the (Ds)
system was required to be less than 5:2 GeV=c2. The
number of tracks near the B0
s meson tends to be small;
thus, to reduce the background from combinatorics, an isolation criterion was applied. The isolation is defined as the sum of the momenta of the tracks used to reconstruct the signal divided by the total momentum of tracks
con-tained within a cone of radiusR
2 2
p
0:5 centered on the direction of the B0
s candidate. We
required the isolation to exceed 0.6. To suppress back-ground, the visible proper decay length (VPDL), defined as MB0
sL~Tp~T=p2T, was required to exceed 150m.
HereL~Tis the displacement from the primary vertex to the
B0
s decay vertex in the transverse plane, andMB0sis the
mass of theB0
smeson [7]. These data are referred to as the
(Ds) sample; the resulting mass spectrum of the (KK) system is shown in Fig. 1(a), where the D
s
and D mass peaks are described by single Gaussians
with a second-order polynomial used to parametrize the background. Figure 1(b) shows the mass spectrum of the (KK) system, where a double Gaussian describes the
mass peak, and a second-order polynomial is used to parametrize the background.
To construct a (2Ds) candidate from the
preselec-tion sample, a secondmeson, from Ds!2, was required. The selection criteria to reconstruct the second
distri-bution under the 2 meson to be estimated. This 2
meson and muon were required to form a Ds vertex. To suppress background, the mass of the (2) system was
required to be 1:2< M2<1:85 GeV=c2. The
Ds1 andDs2 mesons were required to form
a B0
s vertex. The mass of the (2Ds) system, i.e.,
the combined mass of Ds!2 and Ds!1
candidates, was required to be 4:3< M2Ds< 5:2 GeV=c2. An isolation value exceeding 0.6 and VPDL
greater than150mwere required for theB0
smeson.
To reduce the effect of systematic uncertainties, we calculated the ratio RBrB0
s !Ds Ds BrDs! =BrB0
s !Ds X. We extracted BrB0s ! Ds Ds fromRusing the known values [7] forBrDs! , BrB0
s !Ds X, andBrDs!.R can be
expressed in terms of experimental observables:
R N2DsNbkg ND
sfB
0
s!Ds X
1
2Br!KK
"B
0
s !Ds X "B0
s !Ds Ds
; (1)
whereNDsis the number of (Ds) events,N2Ds is the number of (2Ds) events,Nbkg is the number of
back-ground events in the (2Ds) sample that are not
pro-duced byB0
s !Ds Ds decays, andfB0s !Ds Xis
the fraction of events in (Ds) coming from B0
s ! Ds X. The ratio of efficiencies "Bs0 !Ds Ds = "B0
s !Ds X to reconstruct the two processes was
determined from simulation. All processes involving b
hadrons were simulated with EVTGEN [8] interfaced to
PYTHIA [9], followed by full modeling of the detector response with GEANT[10] and event reconstruction as in
data. The number of (Ds) events was estimated from a
binned fit to the (KK) mass distribution shown in
Fig.1(a)from the 145 000 candidates passing the selection criteria. The resulting fit is superimposed in Fig.1(a)as a solid line and givesNDs 17 670 230statevents.
The number of (2Ds) events was extracted using
a unbinned log-likelihood fit to the two-dimensional dis-tribution of the invariant masses MD of the (1)
sys-tem andM2of the two additional kaons from the (2)
system. All candidates from the (2Ds) sample with 1:7< MD<2:3 GeV=c2 and0:99< M
2<1:07 GeV=c
2
were included in the fit. In the fit, the masses and widths for both Ds andsignals were fixed to the values extracted from a fit to the (Ds) data sample. Extracted from the fit were the numbers ofN2Dsevents from correlated (joint) signal production of (1) and2, events with a recon-structed (1) in the mass peak of Ds1 without
joint production of 2from (2) (i.e., uncorrelated),
events with a reconstructed2from (2) without joint
production of (1) in the mass peak of theDs1
(i.e., also uncorrelated), and combinatorial background. The results of the fit are displayed in Fig.2. The fit gives
N2Ds 13:4
6:6
6:0 events from the 340 candidates
in-cluded in the fit, with a statistical significance of2:2. The fraction fB0
s!Ds X was determined
simi-larly to [11], assuming that in addition to the decaysB0
s! Ds XandB0s !Ds !X, the following decays
contribute to the (Ds) sample: B!DsDX, B0s! Ds Ds , and B0s !DsDX. The branching fractions for B!DsDXandB0s!Ds Ds are taken from Ref. [7].
There is no experimental information for the BrB0
s! DsDX; therefore, we used the value 15.4% provided by Ref. [8] with an assigned uncertainty of 100%.
In addition, the (Ds) sample includes the processes
cc!Ds X, bb!Ds X, and events with a
mis-]
2
[GeV/c
π φ
m
1.8 2 2.2
)
2
Events/(12 MeV/c
0 2 4 6
3 10 ×
-1
DØ, L=1.3 fb
a)
]
2
[GeV/c
KK
m
0.98 1 1.02 1.04 1.06
)
2
Events/(1.5 MeV/c
0 1 2 3 4
3 10 ×
b)
DØ, L=1.3 fb
-1FIG. 1. (a) The (KK) invariant mass spectrum of the (D
s) sample in the mass window1:01< MKK<1:03 GeV=c2. The
D and Ds mass peaks are clearly visible. (b) Mass spectrum of the (KK) system of the (Ds) sample in the mass window
identified muon, etc., with a contribution estimated in Ref. [12] as 10 5%, without any requirement on the VPDL. When the requirement of VPDL >150m is included, we estimate the contribution as2 1%in the (Ds) signal. In total, we estimate that the fraction of events in the (Ds) signal coming from B0s !Ds X
isfB0
s !Ds X 0:82 0:05.
We considered the number of eventsN2Ds from the
(2Ds) sample to contain contributions from (1) the
main signalB0
s !Ds Ds and the following background
processes (2) B!Ds Ds KX, (3) B0s!Ds Ds X,
(4)B0
s !Ds , (5)cc!DsXandbb!DsX,
and (6) B0
s !Ds combined with a meson from
fragmentation. There is no experimental information for most of the processes; therefore, their contributions were estimated by counting events in different regions of the (2Ds) phase space and comparing the obtained
num-bers with the expected mass distribution for each back-ground process.
The mass of the (2Ds) system for the second and third processes is much less than that for the main decay
B0
s !Ds Ds because of the additional particles, and the
requirement M2Ds>4:3 GeV=c2 strongly
sup-presses them. The contribution of B0
s !Ds Ds X is
much less than B!Ds Ds KX because of higher
pro-duction rates ofBandB0 compared toB0
s. Compared to
the B!Ds Ds KX process, the final state in the decay B0
s !Ds Ds X includes at least two pions due to isospin
considerations. At least two gluons are required to pro-duce this state [similar to 2S !J= ]; it is there-fore additionally suppressed and its contribution was ne-glected. Simulation shows that for theB!Ds Ds KX
de-cay, the fraction of events withM2Ds>4:3 GeV=c2
is 0.05. RequiringM2Ds<4:3 GeV=c2and keeping
all other selections, we observe 2:811:2
2:8 events in data.
Assuming that all these events are due to B! Ds Ds KX, we estimate their contribution to the signal
(2Ds) as0:1400::5614events.
The fourth process produces a high mass for both the (2) and (2Ds) systems and requiringM2< 1:85 GeV=c2strongly suppresses it. Simulation shows that
for this process, the fraction of events with M2< 1:85 GeV=c2is 0.14. RequiringM
2>1:85 GeV=c2
and keeping all other selections, we observe 13 11
events. Assuming that all these events are due to the fourth background process, we estimate its contribution to the (2Ds) signal as1:88 1:51events.
We estimate the total number of background events from the above contributions asNbkg 2:0 1:6stat.
The contribution of the fifth process is strongly sup-pressed by the event selection, and we estimate an upper limit of 0.4 events. We therefore included this contribution as an additional uncertainty in the number of background events.
The fitting procedure accounts for the possible back-ground contribution of the decay B0
s !Ds together
with the uncorrelated production of ameson from frag-mentation. In addition, an attempt was made to reconstruct (2Ds) events in the B0s!Ds X simulation
con-taining approximately 9200 reconstructed (Ds) events, and no such events were found. Therefore the contribution from this process was neglected.
In determination of efficiencies, the final states in the (Ds) and (2Ds) samples differ only by the two kaons
from the additional 2 meson. All other applied selec-tions are the same, so many detector-related systematic uncertainties cancel. The muon pT spectrum in B0
s! Ds X decay differs between data and simulation due
to trigger effects, reconstruction efficiencies, and the un-certainties inBmeson production in simulation. To correct for this difference, we normalized the MC calculations to
]
2
[GeV/c
π φ
m
1.8 2 2.2
)
2
Events/(30 MeV/c
0 5 10 15 20
-1
DØ, L=1.3 fb a)
]
2
[GeV/c
KK
m
0.98 1 1.02 1.04 1.06
)
2
Events/(4.5 MeV/c
0 5 10 15
b) DØ, L=1.3 fb-1
FIG. 2. Invariant mass distributions of (a)Ds1events in the signal
win-dow 1:01< M2<1:03 GeV=c
2 and
(b) (KK) events from D
the data by applying weighting functions to all MC events, which were obtained from the ratio of simulated and data events for pT distributions of the B0
s meson and muon.
With this correction, the ratio of efficiencies is "B0
s ! Ds Ds ="B0s !Ds X 0:055 0:001stat. The
systematic uncertainty of this ratio is discussed below. Using all these inputs and taking the value Br! KK 0:492 0:006 [7], we obtain R0:015
0:007stat. The statistical uncertainty shown includes only the uncertainty in N2Ds. All other uncertainties
are included in the systematics. The experimental extrac-tion of both BrB0
s !Ds X andBrDs!
de-pend on BrDs!. Factorizing the dependence on
BrDs!, we obtain from [7] BrB0
s! Ds XBrDs! 2:84 0:49103, BrDs! 0:55 0:04 BrDs!. Using these numbers, we finally obtain from (1)BrB0
s!Ds Ds 0:0390:019
0:018stat.
The systematic uncertainties in the measured value of
BrB0
s !Ds Ds were estimated as follows. All external
branching fractions [7] were varied within one standard deviation. A 100% uncertainty in the number of back-ground eventsNbkgin the (2Ds) sample was assumed.
The uncertainty on the reconstruction efficiency of two additional kaons from meson decay was estimated to be 14%, following the results of a previous study [12]. For the ratio of efficiencies, a 15% uncertainty was assigned for the reweighting procedure, which reflects the difference in efficiency between weighted and unweighted estimates and includes all effects of modeling the production and decays ofB0
s mesons. The dependence of the number of
(2Ds) events on the fitting procedure was estimated by
adding a possible signal contribution from D events
which decreased the correlated signal by 3%, which we assigned as a systematic uncertainty.
Using these numbers, we obtain BrB0
s!Ds Ds
0:03900::019017stat 0:014syst0:044=BrDs!2.
UsingBrDs! 0:044 0:006[7], we find
BrB0
s !Ds Ds 0:03900::019017stat00::016015syst; (2)
which yields a 90% C.L. interval forBrB0
s !Ds Ds of
0:002;0:080. The result is consistent with, and more precise than, the ALEPH measurement BrB0
s ! Ds Ds 0:077 0:03400::038026 [4,13], where the value
has been recalculated using the current value ofBrDs! [7]. We calculateCP
s [1] assuming that the decay B0
s !Ds Ds is mainly CP even and gives the primary
contribution to the width difference between theCP-even andCP-oddB0
s states [3]:
CPs
s
0:07900::038035stat0:031
0:030syst: (3)
Assuming CP violation in B0
s mixing is small [2], this
estimate is in good agreement with the SM prediction
s=s0:127 0:024[2] and with the direct
measure-ment of this parameter by the D0 experimeasure-ment in B0
s! J= decays [14]. The agreement with the CDF measure-ment of s=s, also performed inB0
s !J= [15], is
not as good, although still within two standard deviations. 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.
*Visiting scientist from Augustana College, Sioux Falls, SD, USA.
†Visiting scientist from ICN-UNAM, Mexico City, Mexico.
‡Visiting scientist from Helsinki Institute of Physics,
Helsinki, Finland.
xVisiting scientist from Universita¨t Zu¨rich, Zu¨rich,
Switzerland.
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486, 286 (2000).
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