Measurement of the Ratio of B
and B
0Meson Lifetimes
V. M. Abazov,33B. Abbott,70M. Abolins,61B. S. Acharya,27M. Adams,48T. Adams,46M. Agelou,17J.-L. Agram,18 S. H. Ahn,29M. Ahsan,55G. D. Alexeev,33G. Alkhazov,37A. Alton,60G. Alverson,59G. A. Alves,2M. Anastasoaie,32
S. Anderson,42B. Andrieu,16Y. Arnoud,13A. Askew,74B. A˚ sman,38O. Atramentov,53C. Autermann,20C. Avila,7 F. Badaud,12A. Baden,57B. Baldin,47P. W. Balm,31S. Banerjee,27E. Barberis,59P. Bargassa,74P. Baringer,54C. Barnes,40 J. Barreto,2J. F. Bartlett,47U. Bassler,16D. Bauer,51A. Bean,54S. Beauceron,16M. Begel,66A. Bellavance,63S. B. Beri,26
G. Bernardi,16R. Bernhard,47,* I. Bertram,39M. Besanc¸on,17R. Beuselinck,40V. A. Bezzubov,36P. C. Bhat,47
V. Bhatnagar,26M. Binder,24K. M. Black,58I. Blackler,40G. Blazey,49F. Blekman,31S. Blessing,46D. Bloch,18 U. Blumenschein,22A. Boehnlein,47O. Boeriu,52T. A. Bolton,55F. Borcherding,47G. Borissov,39K. Bos,31T. Bose,65
A. Brandt,72R. Brock,61G. Brooijmans,65A. Bross,47N. J. Buchanan,46D. Buchholz,50M. Buehler,48V. Buescher,22 S. Burdin,47T. H. Burnett,76E. Busato,16J. M. Butler,58J. Bystricky,17W. Carvalho,3B. C. K. Casey,71N. M. Cason,52
H. Castilla-Valdez,30S. Chakrabarti,27D. Chakraborty,49K. M. Chan,66A. Chandra,27D. Chapin,71F. Charles,18 E. Cheu,42L. Chevalier,17D. K. Cho,66S. Choi,45T. Christiansen,24L. Christofek,54D. Claes,63B. Cle´ment,18 C. Cle´ment,38Y. Coadou,5M. Cooke,74W. E. Cooper,47D. Coppage,54M. Corcoran,74J. Coss,19A. Cothenet,14 M.-C. Cousinou,14S. Cre´pe´-Renaudin,13M. Cristetiu,45M. A. C. Cummings,49D. Cutts,71H. da Motta,2B. Davies,39
G. Davies,40G. A. Davis,50K. De,72P. de Jong,31S. J. de Jong,32E. De La Cruz-Burelo,30C. De Oliveira Martins,3 S. Dean,41F. De´liot,17P. A. Delsart,19M. Demarteau,47R. Demina,66P. Demine,17D. Denisov,47S. P. Denisov,36 S. Desai,67H. T. Diehl,47M. Diesburg,47M. Doidge,39H. Dong,67S. Doulas,59L. Duflot,15S. R. Dugad,27A. Duperrin,14
J. Dyer,61A. Dyshkant,49M. Eads,49D. Edmunds,61T. Edwards,41J. Ellison,45J. Elmsheuser,24J. T. Eltzroth,72 V. D. Elvira,47S. Eno,57P. Ermolov,35O. V. Eroshin,36J. Estrada,47D. Evans,40H. Evans,65A. Evdokimov,34 V. N. Evdokimov,36J. Fast,47S. N. Fatakia,58L. Feligioni,58T. Ferbel,66F. Fiedler,24F. Filthaut,32W. Fisher,64 H. E. Fisk,47M. Fortner,49H. Fox,22W. Freeman,47S. Fu,47S. Fuess,47T. Gadfort,76C. F. Galea,32E. Gallas,47 E. Galyaev,52C. Garcia,66A. Garcia-Bellido,76J. Gardner,54V. Gavrilov,34P. Gay,12D. Gele´,18R. Gelhaus,45K. Genser,47
C. E. Gerber,48Y. Gershtein,71G. Ginther,66T. Golling,21B. Go´mez,7K. Gounder,47A. Goussiou,52P. D. Grannis,67 S. Greder,18H. Greenlee,47Z. D. Greenwood,56E. M. Gregores,4Ph. Gris,12J.-F. Grivaz,15L. Groer,65S. Gru¨nendahl,47 M. W. Gru¨newald,28S. N. Gurzhiev,36G. Gutierrez,47P. Gutierrez,70A. Haas,65N. J. Hadley,57S. Hagopian,46I. Hall,70 R. E. Hall,44C. Han,60L. Han,41K. Hanagaki,47K. Harder,55R. Harrington,59J. M. Hauptman,53R. Hauser,61J. Hays,50 T. Hebbeker,20D. Hedin,49J. M. Heinmiller,48A. P. Heinson,45U. Heintz,58C. Hensel,54G. Hesketh,59M. D. Hildreth,52 R. Hirosky,75J. D. Hobbs,67B. Hoeneisen,11M. Hohlfeld,23S. J. Hong,29R. Hooper,71P. Houben,31Y. Hu,67J. Huang,51 I. Iashvili,45R. Illingworth,47A. S. Ito,47S. Jabeen,54M. Jaffre´,15S. Jain,70V. Jain,68K. Jakobs,22A. Jenkins,40R. Jesik,40 K. Johns,42M. Johnson,47A. Jonckheere,47P. Jonsson,40H. Jo¨stlein,47A. Juste,47M. M. Kado,43D. Ka¨fer,20W. Kahl,55 S. Kahn,68E. Kajfasz,14A. M. Kalinin,33J. Kalk,61D. Karmanov,35J. Kasper,58D. Kau,46R. Kehoe,73S. Kermiche,14 S. Kesisoglou,71A. Khanov,66A. Kharchilava,52Y. M. Kharzheev,33K. H. Kim,29B. Klima,47M. Klute,21J. M. Kohli,26
M. Kopal,70V. M. Korablev,36J. Kotcher,68B. Kothari,65A. Koubarovsky,35A. V. Kozelov,36J. Kozminski,61 S. Krzywdzinski,47S. Kuleshov,34Y. Kulik,47S. Kunori,57A. Kupco,17T. Kurcˇa,19S. Lager,38N. Lahrichi,17 G. Landsberg,71J. Lazoflores,46A.-C. Le Bihan,18P. Lebrun,19S. W. Lee,29W. M. Lee,46A. Leflat,35F. Lehner,47,*
C. Leonidopoulos,65P. Lewis,40J. Li,72Q. Z. Li,47J. G. R. Lima,49D. Lincoln,47S. L. Linn,46J. Linnemann,61 V. V. Lipaev,36R. Lipton,47L. Lobo,40A. Lobodenko,37M. Lokajicek,10A. Lounis,18H. J. Lubatti,76L. Lueking,47
M. Lynker,52A. L. Lyon,47A. K. A. Maciel,49R. J. Madaras,43P. Ma¨ttig,25A. Magerkurth,60A.-M. Magnan,13 N. Makovec,15P. K. Mal,27S. Malik,56V. L. Malyshev,33H. S. Mao,6Y. Maravin,47M. Martens,47S. E. K. Mattingly,71
A. A. Mayorov,36R. McCarthy,67R. McCroskey,42D. Meder,23H. L. Melanson,47A. Melnitchouk,62M. Merkin,35 K. W. Merritt,47A. Meyer,20H. Miettinen,74D. Mihalcea,49J. Mitrevski,65N. Mokhov,47J. Molina,3N. K. Mondal,27
H. E. Montgomery,47R. W. Moore,5G. S. Muanza,19M. Mulders,47Y. D. Mutaf,67E. Nagy,14M. Narain,58 N. A. Naumann,32H. A. Neal,60J. P. Negret,7S. Nelson,46P. Neustroev,37C. Noeding,22A. Nomerotski,47S. F. Novaes,4 T. Nunnemann,24E. Nurse,41V. O’Dell,47D. C. O’Neil,5V. Oguri,3N. Oliveira,3N. Oshima,47G. J. Otero y Garzo´n,48 P. Padley,74N. Parashar,56J. Park,29S. K. Park,29J. Parsons,65R. Partridge,71N. Parua,67A. Patwa,68P. M. Perea,45 E. Perez,17O. Peters,31P. Pe´troff,15M. Petteni,40L. Phaf,31R. Piegaia,1P. L. M. Podesta-Lerma,30V. M. Podstavkov,47 Y. Pogorelov,52B. G. Pope,61W. L. Prado da Silva,3H. B. Prosper,46S. Protopopescu,68M. B. Przybycien,50,†J. Qian,60 A. Quadt,21B. Quinn,62K. J. Rani,27P. A. Rapidis,47P. N. Ratoff,39N. W. Reay,55S. Reucroft,59M. Rijssenbeek,67
I. Ripp-Baudot,18F. Rizatdinova,55C. Royon,17P. Rubinov,47R. Ruchti,52G. Sajot,13A. Sa´nchez-Herna´ndez,30 M. P. Sanders,41A. Santoro,3G. Savage,47L. Sawyer,56T. Scanlon,40R. D. Schamberger,67H. Schellman,50 P. Schieferdecker,24C. Schmitt,25A. A. Schukin,36A. Schwartzman,64R. Schwienhorst,61S. Sengupta,46H. Severini,70
E. Shabalina,48M. Shamim,55V. Shary,17W. D. Shephard,52D. Shpakov,59R. A. Sidwell,55V. Simak,9V. Sirotenko,47 P. Skubic,70P. Slattery,66R. P. Smith,47K. Smolek,9G. R. Snow,63J. Snow,69S. Snyder,68S. So¨ldner-Rembold,41 X. Song,49Y. Song,72L. Sonnenschein,58A. Sopczak,39M. Sosebee,72K. Soustruznik,8M. Souza,2B. Spurlock,72 N. R. Stanton,55J. Stark,13J. Steele,56G. Steinbru¨ck,65K. Stevenson,51V. Stolin,34A. Stone,48D. A. Stoyanova,36 J. Strandberg,38M. A. Strang,72M. Strauss,70R. Stro¨hmer,24M. Strovink,43L. Stutte,47S. Sumowidagdo,46A. Sznajder,3
M. Talby,14P. Tamburello,42W. Taylor,5P. Telford,41J. Temple,42S. Tentindo-Repond,46E. Thomas,14B. Thooris,17 M. Tomoto,47T. Toole,57J. Torborg,52S. Towers,67T. Trefzger,23S. Trincaz-Duvoid,16B. Tuchming,17C. Tully,64 A. S. Turcot,68P. M. Tuts,65L. Uvarov,37S. Uvarov,37S. Uzunyan,49B. Vachon,5R. Van Kooten,51W. M. van Leeuwen,31
N. Varelas,48E. W. Varnes,42I. A. Vasilyev,36M. Vaupel,25P. Verdier,15L. S. Vertogradov,33M. Verzocchi,57 F. Villeneuve-Seguier,40J.-R. Vlimant,16E. Von Toerne,55M. Vreeswijk,31T. Vu Anh,15H. D. Wahl,46R. Walker,40 L. Wang,57Z.-M. Wang,67J. Warchol,52M. Warsinsky,21G. Watts,76M. Wayne,52M. Weber,47H. Weerts,61M. Wegner,20 N. Wermes,21A. White,72V. White,47D. Whiteson,43D. Wicke,47D. A. Wijngaarden,32G. W. Wilson,54S. J. Wimpenny,45 J. Wittlin,58M. Wobisch,47J. Womersley,47D. R. Wood,59T. R. Wyatt,41Q. Xu,60N. Xuan,52R. Yamada,47M. Yan,57 T. Yasuda,47Y. A. Yatsunenko,33Y. Yen,25K. Yip,68S. W. Youn,50J. Yu,72A. Yurkewicz,61A. Zabi,15A. Zatserklyaniy,49
M. Zdrazil,67C. Zeitnitz,23D. Zhang,47X. Zhang,70T. Zhao,76Z. Zhao,60B. Zhou,60J. Zhu,57M. Zielinski,66 D. Zieminska,51A. Zieminski,51R. Zitoun,67V. Zutshi,49E. G. Zverev,35and A. Zylberstejn17
(D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil
3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil
5Simon Fraser University, Burnaby, Canada; University of Alberta, Edmonton, Canada, McGill University, Montreal, Canada;
and York University, Toronto, Canada
6Institute of High Energy Physics, Beijing, People’s Republic of China 7Universidad de los Andes, Bogota´, Colombia
8Charles University, Center for Particle Physics, Prague, Czech Republic 9
Czech Technical University, Prague, Czech Republic
10Institute of Physics, Academy of Sciences, Center for Particle Physics, Prague, Czech Republic 11Universidad San Francisco de Quito, Quito, Ecuador
12Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universite´ Blaise Pascal, Clermont-Ferrand, France 13Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
14CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France 15Laboratoire de l’Acce´le´rateur Line´aire, IN2P3-CNRS, Orsay, France
16LPNHE, Universite´s Paris VI and VII, IN2P3-CNRS, Paris, France 17DAPNIA/Service de Physique des Particules, CEA, Saclay, France
18IReS, IN2P3-CNRS, Universite´ Louis Pasteur, Strasbourg, France and Universite´ de Haute Alsace, Mulhouse, France 19Institut de Physique Nucle´aire de Lyon, IN2P3-CNRS, Universite´ Claude Bernard, Villeurbanne, France
20RWTH Aachen, III. Physikalisches Institut A, Aachen, Germany 21Universita¨t Bonn, Physikalisches Institut, Bonn, Germany 22Universita¨t Freiburg, Physikalisches Institut, Freiburg, Germany
23Universita¨t Mainz, Institut fu¨r Physik, Mainz, Germany 24Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
26Punjab University, Chandigarh, India
27Tata Institute of Fundamental Research, Mumbai, India 28University College Dublin, Dublin, Ireland 29Korea Detector Laboratory, Korea University, Seoul, Korea
30CINVESTAV, Mexico City, Mexico
31FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 32University of Nijmegen/NIKHEF, Nijmegen, The Netherlands
33Joint Institute for Nuclear Research, Dubna, Russia 34Institute for Theoretical and Experimental Physics, Moscow, Russia
35Moscow State University, Moscow, Russia 36Institute for High Energy Physics, Protvino, Russia 37Petersburg Nuclear Physics Institute, St. Petersburg, Russia
38Lund University, Lund, Sweden; Royal Institute of Technology and Stockholm University, Stockholm, Sweden;
and Uppsala University, Uppsala, Sweden
39Lancaster University, Lancaster, United Kingdom 40Imperial College, London, United Kingdom 41University of Manchester, Manchester, United Kingdom
42University of Arizona, Tucson, Arizona 85721, USA
43Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 44California State University, Fresno, California 93740, USA
45University of California, Riverside, California 92521, USA 46Florida State University, Tallahassee, Florida 32306, USA 47Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
48University of Illinois at Chicago, Chicago, Illinois 60607, USA 49Northern Illinois University, DeKalb, Illinois 60115, USA
50Northwestern University, Evanston, Illinois 60208, USA 51Indiana University, Bloomington, Indiana 47405, USA 52University of Notre Dame, Notre Dame, Indiana 46556, USA
53Iowa State University, Ames, Iowa 50011, USA 54University of Kansas, Lawrence, Kansas 66045, USA 55Kansas State University, Manhattan, Kansas 66506, USA 56Louisiana Tech University, Ruston, Louisiana 71272, USA 57University of Maryland, College Park, Maryland 20742, USA
58Boston University, Boston, Massachusetts 02215, USA 59Northeastern University, Boston, Massachusetts 02115, USA
60University of Michigan, Ann Arbor, Michigan 48109, USA 61Michigan State University, East Lansing, Michigan 48824, USA
62University of Mississippi, University, Mississippi 38677, USA 63University of Nebraska, Lincoln, Nebraska 68588, USA 64Princeton University, Princeton, New Jersey 08544, USA
65Columbia University, New York, New York 10027, USA 66University of Rochester, Rochester, New York 14627, USA 67State University of New York, Stony Brook, New York 11794, USA
68Brookhaven National Laboratory, Upton, New York 11973, USA 69Langston University, Langston, Oklahoma 73050, USA 70University of Oklahoma, Norman, Oklahoma 73019, USA
71Brown University, Providence, Rhode Island 02912, USA 72University of Texas, Arlington, Texas 76019, USA 73Southern Methodist University, Dallas, Texas 75275, USA
74Rice University, Houston, Texas 77005, USA 75University of Virginia, Charlottesville, Virginia 22901, USA
76University of Washington, Seattle, Washington 98195, USA (Received 20 October 2004; published 11 May 2005)
The ratio of the Band B0meson lifetimes was measured using data collected in 2002 – 2004 by the D0
experiment in Run II of the Fermilab Tevatron Collider. These mesons were reconstructed in B !
DXdecays, which are dominated by B0and B ! D0Xdecays, which are dominated by B.
The ratio of lifetimes is measured to be =0 1:080 0:016stat 0:014syst.
DOI: 10.1103/PhysRevLett.94.182001 PACS numbers: 14.40.Nd
In the last few years, significant progress has been made in the understanding of the lifetimes of hadrons containing heavy quarks. Charm and bottom meson (ex-cept Bc) lifetimes have been measured with precisions ranging from 0.5 to 4%, although lifetimes of heavy baryons are not known as well [1]. Experimentally, ratios of lifetimes have smaller uncertainties, since many com-mon sources of systematics cancel. Theoretical
uncertain-ties for these ratios are also reduced. For instance, the ratio of the B and B0 lifetimes has been predicted to be
1:06 0:02 [2,3].
In this Letter, we present a measurement of the ratio of B and B0 lifetimes using semileptonic decays B ! D0X[4] collected by the D0 experiment at Fermilab
in p pcollisions atps 1:96 TeV. The data correspond to approximately 440 pb1of integrated luminosity.
The D0 detector is described in detail elsewhere [5]. The primary vertex of the p pinteraction was determined for each event with the precision on average about 20 m in the plane perpendicular to the beam pipe and about 40 m along the beam pipe. Events with semimuonic b-hadron decays were selected using a suite of inclusive single-muon triggers in a three-level trigger system. Muons were re-quired to have a transverse momentum pT > 2 GeV=c and total momentum p> 3 GeV=c. D0 candidates were
se-lected using D0 ! Kdecays. All charged particles in
an event were clustered into jets using theDURHAM algo-rithm [6] with a jet pTcutoff parameter of 15 GeV=c [7]. A
D0 candidate was constructed from two particles of
oppo-site charge belonging to the same jet as the muon. Both particles were required to have pT > 0:7 GeV=c and to form a common D0vertex. The pT of the D0was required to exceed 5 GeV=c. To reduce the combinatorial back-ground, we required the D0 vertex to have a positive displacement in the plane perpendicular to the beam pipe, relative to the primary vertex, with at least 4 sig-nificance. The trajectory of the muon and D0 candidates
were required to originate from a common B vertex. The D0 system was required to have an invariant mass
between 2.3 and 5:2 GeV=c2.
The masses of the kaon and pion were assigned to the two tracks according to the charge of the muon, assuming the Kcombination. The mass spectrum of the K system after these selections is shown in Fig. 1(a). The signal in the D0 peak contains 126 073 610 events.
The reconstructed D0 events were classified into
three nonoverlapping samples, based on the presence of an additional pion with pT> 0:18 GeV=c. Defining m m D0 m D0, all events containing a pion with a
charge opposite to (same as) that of the muon and 0:1425 < m < 0:1490 GeV=c2 were included in the DRDW sample. The DW sample contains true D0
but fake D events and gives an estimate of the combi-natorial background for D candidates. All other events were assigned to the D0sample. Figure 1(b) shows the m distributions, when 1:8 < m D0 < 1:9 GeV=c2.
The peak in the sample with opposite charges of muon and pion corresponds to the production of the D system and contains 30 528 200 events.
The classification into these samples was based on the presence of a slow pion from D! D0decay, and was
independent of the B-meson lifetime. Therefore, the ratio of the number of events in the two samples, expressed as a function of the proper decay length, depends mainly on the lifetime difference between the B and B0 mesons. The
influences of the selection criteria, detector properties, and some systematic uncertainties are significantly reduced.
Since the final state has missing particles, including the neutrino, the proper decay length was not determined. Instead, the measured visible proper decay length xM was computed as xM m
BcLT pTD0=jpTD0j2.
LT is the vector from the primary to the D0 vertex in
the plane perpendicular to the beam pipe, pTD0 is the
transverse momentum of the D0 system and m B 5:279 GeV=c2 is the mass of the B meson [1]. To reduce
the difference between the Dand D0 samples, the pion
from the Ddecay was not used for the computation of the transverse momentum and the decay length.
Candidates in each of the samples were divided into eight groups according to their xM values. The number of D0 events NR
i (from the DRsample), NiW(from the DW sample), and N0
i (from the D0 sample) in each interval i (i 1; . . . ; 8) were determined from the fit of the K mass spectrum between 1.72 and 2:16 GeV=c2
with the sum of a Gaussian signal function and a poly-nomial background function. The mean and width of the Gaussian function were fixed to the values obtained from the fit of the overall mass distribution in each sample. The fitting procedure was the same for all samples.
The number of Devents for each interval i of xM was defined as Ni
D NR
i CNiW, where CNiW accounts for the combinatorial background under the D peak as shown in Fig. 1(b). The coefficient C 1:27 0:03 reflects the difference in the combinatorial back-ground between D0 and D0 events. It was determined from the ratio of the numbers of these events in the interval 0:153 < m < 0:160 GeV=c2. The number of D0 events in each interval i in xM was defined as NiD0 N0
i NiW CNiW.
The experimental observable ri is the ratio of D and D0 events in interval i of xM, i.e., r
i NiD=NiD0. Values of riand statistical uncer-tainties are given in Table I. The value of k =0 1
was determined from the minimization of 2"
; kwhich has the following form:
2" ; k X i ri re i"; k2 2r i : (1) Here re
i"; kis the expected ratio of Dand D0 events, and "is the efficiency to reconstruct the slow pion in the D! D0 decay. " was assumed to be
inde-0 20000 40000 1.6 1.8 2 (a) DØ m(Kπ) GeV/c2 Entries/20 MeV/c 2 102 103 104 0.14 0.15 m(D – 0π)-m(D – 0 ) (GeV/c2) E n tries/0.5 M eV/c 2 µ+ D – 0 π -µ+ D – 0 π+ (b) DØ
FIG. 1 (color online). (a) Invariant mass of the K system.
The curve shows the result of the fit of the K mass
distribution with the sum of a signal Gaussian function and polynomial background function. (b) Mass difference m
pendent of xM and, along with k, was a free parameter in the minimization. The sumPiwas taken over all intervals with positive xM.
For the jth B meson decay channel, the distribution of the visible proper decay length (x) is given by Pjx R
dKDjK$xcKj exp
Kx
cj. j is the lifetime of the B
meson, the K factor, K pTD0=pB
T, reflects the differ-ence between the observed and true momentum of the B meson, and $x is the step function. The function DjK is the normalized distribution of the K factor for the jth decay channel.
Transformation from the true value of x to the experi-mentally measured value xM is given by f
jxM R
dxRjx xM"jxPjx, where Rjx xM is the detec-tor resolution, and "jx is the reconstruction efficiency of D0for the jth decay. It does not include "for channels with D. Finally, the expected value re
i"; kis given by rei"; k "F ik Fi0k 1 "Fik : (2) Here F;0i RidxMP
jBrjfjxM with the summation Pj taken over all decays to D D0 for F
iFi0. For the computation of re
i, the world average of the B lifetime [1] was used. The B0 lifetime 0 was
ex-pressed as 0 =1 k. The branching fractions B ! D and B ! D were taken from Ref. [1]. The following branching fractions were derived from experi-mental measurements [1,8–10]: BrB! D0
2:67 0:37%, BrB! D0! DX
1:07 0:25%, and BrB0
s ! Ds 2:32:42:3%. D states include both narrow and wide D resonances and nonresonant DX and DX production. Regarding the possible decays of Ds , there is no experimental data on the BrDs ! DX. Its central value was therefore set to 0.35, and it was varied between 0.0 and 1.0 to estimate the systematic uncertainty from this source. All other branching fractions were derived assuming isospin invariance.
The distributions DjK, Rjx, and "jx were taken from the Monte Carlo simulation. All processes involving bhadrons were simulated using theEVTGEN[11] generator
interfaced toPYTHIA[7] and followed by the full modeling
of the detector response and event reconstruction. The semileptonic b hadron decays were generated using the ISGW2 model [12].
Assuming the given branching fractions and reconstruc-tion efficiencies, the decay B ! DX contains 89 3%B0, 10 3%B, and 1 1%B0
s, while the decay B ! D0X contains 83 3%B, 15 4%B0, and
2 1%B0 s.
Our study showed that the decay B ! D0X ! D0Xadds 5 2%, and the process c c ! D0X
adds 10 7% to the selected D0 sample. The latter
estimate also includes a possible contribution from c c ! hD0X, when hadron h is misidentified as muon. These
processes were taken into account in the analysis. The B !
D0DsX decay was found to be strongly suppressed by the applied kinematic cuts, contributing less than 2.0%, and was neglected.
Using all these inputs, the minimization of the 2
dis-tribution, Eq. (1), gives k =0 1 0:080
0:016stat. The 2 at the minimum is 4.2 for 5 d.o.f., " is 0:864 0:006stat, and the global correlation coeffi-cient between k and "is 0.18. The simulation predicted " 0:877 0:003. The reasonable agreement in " be-tween data and simulation reflects good consistency of input efficiencies and branching fractions with experimen-tal data. Figure 2 presents the ri values together with the result of the fit.
The influence of various sources of systematic uncer-tainty on the final result is summarized in Table II. Different contributions can be divided into three groups. The first part includes uncertainties coming from the ex-perimental measurements, e.g., branching fractions and lifetimes. All inputs were varied by 1 standard deviation. Only the most significant contributions are listed as
indi-TABLE I. Definition of the intervals in visible proper decay
length, xM. For each interval i, the ratio r
i, and the expected
value re
i for =0 1 0:080 are given.
i xM range (cm) r i rei 1 0:1–0:0 0:295 0:015 0.309 2 0.0 – 0.02 0:321 0:007 0.315 3 0.02 – 0.04 0:317 0:007 0.313 4 0.04 – 0.07 0:305 0:006 0.308 5 0.07– 0.10 0:295 0:007 0.300 6 0.10 – 0.15 0:282 0:007 0.291 7 0.15– 0.25 0:283 0:009 0.276 8 0.25– 0.40 0:274 0:019 0.256 0.25 0.3 0.35 -0.1 0 0.1 0.2 0.3 0.4
Visible Proper Decay Length (cm)
N( µ D * X)/N( µ D 0 X) DØ
FIG. 2 (color online). Points with the error bars show the ratio
of the number of events in the Dand D0samples as a
function of the visible proper decay length. The result of the minimization of Eq. (1) with k 0:080 is shown as a histogram.
vidual entries in Table II; all remaining uncertainties are combined into a single entry ‘‘Other contributions.’’
The second group includes uncertainties due to the in-puts taken from the Monte Carlo simulation. The uncer-tainty due to the decay length dependence of the efficiencies "B ! D0X was obtained by repeating
the analysis with decay length independent efficiencies used for all decay modes.
The variation of the efficiency from channel to channel arises from differences in the kinematics of B-meson de-cays and thus depends on their modeling in simulation. To estimate the uncertainty from this source, an alternative model [13] of semileptonic B decays with parameters (2
0:92, R1 1:18, and R2 0:72 was used. In addition, the
selection cuts on the pTof the and D0were varied over a wide range.
The same alternative model and the variation of pT cuts were used to study the model dependence of the K factors. In all cases, the variation of the average value of K factors did not exceed 2%. Distributions of K factors were deter-mined separately for B ! D0, B ! D, B ! D! D0X, and B ! D! DX. To estimate
the uncertainty due to the modeling of D decays, which include both resonant and nonresonant components and are not yet well understood, the analysis was repeated with the distributions of K factors from B ! D! D0 D decays
set to be the same as for B ! D0 D decays.
The selection of the slow pion was made independently of the B lifetime, and the efficiency " was assumed constant in the minimization. A dedicated study of K0
S ! decays showed good stability of the track recon-struction efficiency with the change of decay length over a
wide range. The slope in the efficiency was estimated to be 0:0038 0:0059 cm1. The independence of " and the decay length was also verified in simulation. The impact on the systematic uncertainty in k of the possible lifetime dependence of "was estimated by repeating the analysis with "varying within the simulation statistical error.
The average decay length resolution, approximately 35 m for this measurement, and the fraction of events with larger resolution, modeled by a Gaussian function with resolution of 1700 m, were varied over a wide range, significantly exceeding the estimated difference in resolution between data and simulation. The corresponding change of k was taken as the systematic uncertainty from this source.
The number of events with negative decay length is determined by the resolution; therefore, the difference between the expected and the observed ratios r1 of events with negative decay length (the first row in Table I) could indicate the difference in resolution between D and D0
samples. Supposing that the whole deviation of r1from the expected value is caused by such a difference, and by varying the resolution of D0 sample, while keeping the
resolution of D sample to be the same, it is possible to obtain an exact agreement of observed and expected values of r1. The fit was repeated with this modified resolution and the change of k was used as the estimate of systematic uncertainty due to the difference in resolution between D and D0 samples.
The fitting procedure is another source of systematic uncertainty. To estimate it, different parametrizations of background functions and variation of the fit limits were used. For the signal description, the fit with two Gaussians and the fit with the mean and width allowed to vary were tried. Kaons and pions cannot be separated by the D0 detector, and the decays D0! KK and D0 !
are also present in the K mass spectrum. The fit was repeated with the signal taken as the sum of the Gaussian for the D0 ! K decay and template mK
dis-tributions for the D0! KK and D0 ! decays,
when the particles were assigned the masses of K. These template distributions were taken from simulation. The relative rate of different decay modes was taken from [1]. The maximal variation of the result obtained was taken as the systematic uncertainty due to this source. Finally, the uncertainty in the background level under the Dpeak in Fig. 1(b) was also taken into account.
Various consistency checks of this measurement were also performed. The total sample of events was divided into two parts using different criteria, such as the sign of the muon rapidity, polarity of the solenoid, charge of the muon, pTof the muon, position of the primary interaction, etc. The measurement was repeated independently for each sample. The definition of proper decay length intervals was varied, one more interval, 0.4 – 0.8 cm, was added, and the last interval, 0.25– 0.4 cm, was removed from the fit. In all
TABLE II. Summary of systematic uncertainties.
Source =0 BrB0! D 0.0005 BrB! D0 0.0010 BrB! D0 0.0009 BrB! DX 0.0059 BrB0 s ! DsX 0.0009 Ds ! DX 0.0020 cc ! D0Xcontribution 0.0015 Other contributions 0.0006
"B ! D0X, decay length dependence 0.0014
Modeling B meson decays 0.0030
", decay length dependence 0.0036
Decay length resolution 0.0024
Difference in Dand D0 resolution 0.0053
Kfactors, average value 0.0032
Kfactors, difference between channels 0.0013
Fitting procedure 0.0086
Background level under D 0.0004
cases, the results are consistent within statistical uncertain-ties. Finally, the measurement of the ratio of lifetimes was performed with simulated events. The resulting value kMC 0:084 0:015 agrees well with the generated
life-time ratio kgen 0:070. The whole fitting procedure was
also verified to the precision 0.0005 in k using a fast simulation.
In summary, the ratio of Band B0meson lifetimes was
found to be k
0 1 0:080 0:016stat 0:014syst: (3)
This result is the most precise measurement of this pa-rameter, and agrees well with the world average value k 0:086 0:017 [1]. Improved precision of the ratio of B and B0 lifetimes will allow a better test of theoretical
predictions, especially those inputs to the calculations that rely on lattice QCD or on other nonperturbative meth-ods [2,3].
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 (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), A.P. Sloan Foundation, Research Corpora-tion, Texas Advanced Research Program, Alexander von Humboldt Foundation, and the Marie Curie Fellowships.
*Visitor from University of Zurich, Zurich, Switzerland.
†Visitor from Institute of Nuclear Physics, Krakow, Poland.
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