Measurement of the
0b
Lifetime Using Semileptonic Decays
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,60M. Arthaud,17A. Askew,49 B. A˚ sman,40A. C. S. Assis Jesus,3O. Atramentov,49C. Autermann,20C. Avila,7C. Ay,23F. Badaud,12A. Baden,61 L. Bagby,52B. Baldin,50D. V. Bandurin,59S. Banerjee,28P. Banerjee,28E. Barberis,63A.-F. Barfuss,14P. Bargassa,80
P. Baringer,58J. Barreto,2J. F. Bartlett,50U. Bassler,16D. Bauer,43S. Beale,5A. Bean,58M. Begalli,3M. Begel,71 C. Belanger-Champagne,40L. Bellantoni,50A. Bellavance,50J. 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,26C. Biscarat,19
G. Blazey,52F. Blekman,43S. Blessing,49D. Bloch,18K. Bloom,67A. Boehnlein,50D. Boline,62T. A. Bolton,59 G. Borissov,42K. Bos,33T. Bose,77A. Brandt,78R. Brock,65G. Brooijmans,70A. Bross,50D. Brown,78N. J. Buchanan,49
D. Buchholz,53M. Buehler,81V. Buescher,21S. Burdin,42,†S. Burke,45T. H. Burnett,82C. P. Buszello,43J. M. Butler,62 P. Calfayan,24S. Calvet,14J. Cammin,71S. Caron,33W. Carvalho,3B. C. K. Casey,77N. M. Cason,55H. Castilla-Valdez,32
S. Chakrabarti,17D. Chakraborty,52K. M. Chan,55K. Chan,5A. Chandra,48F. Charles,18E. Cheu,45F. Chevallier,13 D. K. Cho,62S. Choi,31B. Choudhary,27L. Christofek,77T. Christoudias,43S. Cihangir,50D. Claes,67C. Cle´ment,40
B. Cle´ment,18Y. Coadou,5M. Cooke,80W. E. Cooper,50M. Corcoran,80F. Couderc,17M.-C. Cousinou,14 S. Cre´pe´-Renaudin,13D. Cutts,77M. C´ wiok,29H. da Motta,2A. Das,62G. Davies,43K. De,78S. J. de Jong,34P. de Jong,33
E. De La Cruz-Burelo,64C. De Oliveira Martins,3J. D. Degenhardt,64F. De´liot,17M. Demarteau,50R. Demina,71 D. Denisov,50S. P. Denisov,38S. Desai,50H. T. Diehl,50M. Diesburg,50A. Dominguez,67H. Dong,72L. V. Dudko,37 L. Duflot,15S. R. Dugad,28D. Duggan,49A. Duperrin,14J. Dyer,65A. Dyshkant,52M. Eads,67D. Edmunds,65J. Ellison,48 V. D. Elvira,50Y. Enari,77S. Eno,61P. Ermolov,37H. Evans,54A. Evdokimov,73V. N. Evdokimov,38A. V. Ferapontov,59 T. Ferbel,71F. Fiedler,24F. Filthaut,34W. Fisher,50H. E. Fisk,50M. Ford,44M. Fortner,52H. Fox,22S. Fu,50S. Fuess,50 T. Gadfort,82C. F. Galea,34E. Gallas,50E. Galyaev,55C. Garcia,71A. Garcia-Bellido,82V. Gavrilov,36P. Gay,12W. Geist,18
D. Gele´,18C. E. Gerber,51Y. Gershtein,49D. Gillberg,5G. Ginther,71N. Gollub,40B. Go´mez,7A. Goussiou,55 P. D. Grannis,72H. Greenlee,50Z. D. Greenwood,60E. M. Gregores,4G. Grenier,19Ph. Gris,12J.-F. Grivaz,15 A. Grohsjean,24S. Gru¨nendahl,50M. W. Gru¨newald,29J. Guo,72F. Guo,72P. Gutierrez,75G. Gutierrez,50A. Haas,70 N. J. Hadley,61P. Haefner,24S. Hagopian,49J. Haley,68I. Hall,75R. E. Hall,47L. Han,6K. Hanagaki,50P. Hansson,40
K. Harder,44A. Harel,71R. Harrington,63J. M. Hauptman,57R. Hauser,65J. Hays,43T. Hebbeker,20D. Hedin,52 J. G. Hegeman,33J. M. Heinmiller,51A. P. Heinson,48U. Heintz,62C. Hensel,58K. Herner,72G. Hesketh,63 M. D. Hildreth,55R. Hirosky,81J. D. Hobbs,72B. Hoeneisen,11H. Hoeth,25M. Hohlfeld,21S. J. Hong,30R. Hooper,77
S. Hossain,75P. 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. R. Kalk,65J. M. Kalk,60S. 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 M. Kirsch,20B. Klima,50J. M. Kohli,26J.-P. Konrath,22M. Kopal,75V. M. Korablev,38B. Kothari,70A. V. Kozelov,38 D. Krop,54A. Kryemadhi,81T. Kuhl,23A. Kumar,69S. Kunori,61A. Kupco,10T. Kurcˇa,19J. Kvita,8F. Lacroix,12D. Lam,55
S. Lammers,70G. Landsberg,77J. Lazoflores,49P. Lebrun,19W. M. Lee,50A. Leflat,37F. Lehner,41J. Lellouch,16 V. Lesne,12J. Leveque,45M. Lewin,42P. Lewis,43J. Li,78Q. Z. Li,50L. Li,48S. M. Lietti,4J. G. R. Lima,52D. Lincoln,50 J. Linnemann,65V. V. Lipaev,38R. Lipton,50Y. Liu,6Z. Liu,5L. Lobo,43A. Lobodenko,39M. Lokajicek,10A. Lounis,18
P. Love,42H. J. Lubatti,82A. L. Lyon,50A. K. A. Maciel,2D. Mackin,80R. J. Madaras,46P. Ma¨ttig,25C. Magass,20 A. Magerkurth,64N. Makovec,15P. K. Mal,55H. B. Malbouisson,3S. Malik,67V. L. Malyshev,35H. S. Mao,50Y. Maravin,59
B. Martin,13R. McCarthy,72A. Melnitchouk,66A. Mendes,14L. Mendoza,7P. G. Mercadante,4M. Merkin,37 K. W. Merritt,50J. Meyer,21A. Meyer,20M. Michaut,17T. Millet,19J. Mitrevski,70J. Molina,3R. K. Mommsen,44 N. K. Mondal,28R. W. Moore,5T. Moulik,58G. S. Muanza,19M. Mulders,50M. Mulhearn,70O. Mundal,21L. Mundim,3
E. Nagy,14M. Naimuddin,50M. Narain,77N. A. Naumann,34H. A. Neal,64J. P. Negret,7P. Neustroev,39H. Nilsen,22 A. Nomerotski,50S. F. Novaes,4T. Nunnemann,24V. O’Dell,50D. C. O’Neil,5G. Obrant,39C. Ochando,15 D. Onoprienko,59N. Oshima,50J. Osta,55R. Otec,9G. J. Otero y Garzo´n,51M. Owen,44P. Padley,80M. Pangilinan,77 N. Parashar,56S.-J. Park,71S. K. Park,30J. Parsons,70R. Partridge,77N. Parua,54A. Patwa,73G. Pawloski,80B. Penning,22
P. 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,2P. Polozov,36A. 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
A. Rakitine,42M. S. Rangel,2K. J. Rani,28K. Ranjan,27P. N. Ratoff,42P. Renkel,79S. Reucroft,63P. Rich,44 M. Rijssenbeek,72I. Ripp-Baudot,18F. Rizatdinova,76S. Robinson,43R. F. Rodrigues,3C. Royon,17P. Rubinov,50 R. Ruchti,55G. Safronov,36G. Sajot,13A. Sa´nchez-Herna´ndez,32M. P. Sanders,16A. Santoro,3G. Savage,50L. Sawyer,60
T. Scanlon,43D. Schaile,24R. D. Schamberger,72Y. Scheglov,39H. Schellman,53P. Schieferdecker,24T. Schliephake,25 C. Schmitt,25C. Schwanenberger,44A. Schwartzman,68R. Schwienhorst,65J. Sekaric,49S. Sengupta,49H. Severini,75 E. Shabalina,51M. Shamim,59V. Shary,17A. A. Shchukin,38R. K. Shivpuri,27D. Shpakov,50V. Siccardi,18V. Simak,9
V. Sirotenko,50P. Skubic,75P. Slattery,71D. Smirnov,55R. P. Smith,50J. Snow,74G. R. Snow,67S. Snyder,73 S. So¨ldner-Rembold,44L. Sonnenschein,16A. Sopczak,42M. Sosebee,78K. Soustruznik,8M. Souza,2B. Spurlock,78
J. Stark,13J. Steele,60V. Stolin,36A. Stone,51D. A. Stoyanova,38J. Strandberg,64S. Strandberg,40M. A. Strang,69 M. Strauss,75E. Strauss,72R. Stro¨hmer,24D. Strom,53M. Strovink,46L. Stutte,50S. Sumowidagdo,49P. Svoisky,55
A. Sznajder,3M. Talby,14P. Tamburello,45A. Tanasijczuk,1W. Taylor,5P. Telford,44J. Temple,45B. Tiller,24 F. Tissandier,12M. Titov,17V. V. Tokmenin,35M. Tomoto,50T. Toole,61I. Torchiani,22T. Trefzger,23D. Tsybychev,72
B. Tuchming,17C. Tully,68P. M. Tuts,70R. Unalan,65S. Uvarov,39L. Uvarov,39S. Uzunyan,52B. Vachon,5 P. J. van den Berg,33B. van Eijk,33R. Van Kooten,54W. M. van Leeuwen,33N. Varelas,51E. W. Varnes,45A. Vartapetian,78
I. A. Vasilyev,38M. Vaupel,25P. Verdier,19L. S. Vertogradov,35M. Verzocchi,50F. Villeneuve-Seguier,43P. Vint,43 P. Vokac,9E. Von Toerne,59M. Voutilainen,67,xM. Vreeswijk,33R. Wagner,68H. D. Wahl,49L. Wang,61M. H. L. S Wang,50 J. Warchol,55G. Watts,82M. Wayne,55M. Weber,50G. Weber,23H. Weerts,65A. Wenger,22,kN. Wermes,21M. Wetstein,61
A. White,78D. Wicke,25G. W. Wilson,58S. J. Wimpenny,48M. Wobisch,60D. R. Wood,63T. R. Wyatt,44Y. Xie,77 S. Yacoob,53R. Yamada,50M. Yan,61T. Yasuda,50Y. A. Yatsunenko,35K. Yip,73H. D. Yoo,77S. W. Youn,53J. Yu,78 C. Yu,13A. Yurkewicz,72A. Zatserklyaniy,52C. Zeitnitz,25D. Zhang,50T. Zhao,82B. Zhou,64J. Zhu,72M. Zielinski,71
D. Zieminska,54A. Zieminski,54L. Zivkovic,70V. Zutshi,52and E. G. Zverev37 (D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil
3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil
5University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada,
York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada 6University of Science and Technology of China, Hefei, People’s Republic of China
7Universidad de los Andes, Bogota´, Colombia
8Center for Particle Physics, Charles University, Prague, Czech Republic 9Czech Technical University, Prague, Czech Republic
10Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 11Universidad San Francisco de Quito, Quito, Ecuador
12Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universite´ Blaise Pascal, Clermont-Ferrand, France 13Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
14CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France
15Laboratoire de l’Acce´le´rateur Line´aire, IN2P3-CNRS et Universite´ Paris-Sud, Orsay, France 16LPNHE, IN2P3-CNRS, Universite´s Paris VI and VII, Paris, France
17DAPNIA/Service de Physique des Particules, CEA, Saclay, France
18IPHC, Universite´ Louis Pasteur et Universite´ de Haute Alsace, CNRS, IN2P3, Strasbourg, France 19IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite´ de Lyon, Lyon, France
20III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany 21Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 22Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany
23Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 24Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
26Panjab University, Chandigarh, India 27Delhi University, Delhi, India
28Tata Institute of Fundamental Research, Mumbai, India 29University College Dublin, Dublin, Ireland 30Korea Detector Laboratory, Korea University, Seoul, Korea
31SungKyunKwan University, Suwon, Korea 32CINVESTAV, Mexico City, Mexico
33FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 34Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
35Joint Institute for Nuclear Research, Dubna, Russia 36Institute for Theoretical and Experimental Physics, Moscow, Russia
37Moscow State University, Moscow, Russia 38Institute for High Energy Physics, Protvino, Russia 39Petersburg Nuclear Physics Institute, St. Petersburg, Russia
40Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden
41Physik Institut der Universita¨t Zu¨rich, Zu¨rich, Switzerland 42Lancaster University, Lancaster, United Kingdom
43Imperial College, London, United Kingdom 44University of Manchester, Manchester, United Kingdom
45University of Arizona, Tucson, Arizona 85721, USA
46Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 47California State University, Fresno, California 93740, USA
48University of California, Riverside, California 92521, USA 49Florida State University, Tallahassee, Florida 32306, USA 50Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
51University of Illinois at Chicago, Chicago, Illinois 60607, USA 52Northern Illinois University, DeKalb, Illinois 60115, USA
53Northwestern University, Evanston, Illinois 60208, USA 54Indiana University, Bloomington, Indiana 47405, USA 55University of Notre Dame, Notre Dame, Indiana 46556, USA
56Purdue University Calumet, Hammond, Indiana 46323, USA 57Iowa State University, Ames, Iowa 50011, USA 58University of Kansas, Lawrence, Kansas 66045, USA 59Kansas State University, Manhattan, Kansas 66506, USA 60Louisiana Tech University, Ruston, Louisiana 71272, USA 61University of Maryland, College Park, Maryland 20742, USA
62Boston University, Boston, Massachusetts 02215, USA 63Northeastern University, Boston, Massachusetts 02115, USA
64University of Michigan, Ann Arbor, Michigan 48109, USA 65Michigan State University, East Lansing, Michigan 48824, USA
66University of Mississippi, University, Mississippi 38677, USA 67University of Nebraska, Lincoln, Nebraska 68588, USA 68Princeton University, Princeton, New Jersey 08544, USA 69State University of New York, Buffalo, New York 14260, USA
70Columbia University, New York, New York 10027, USA 71University of Rochester, Rochester, New York 14627, USA 72State University of New York, Stony Brook, New York 11794, USA
73Brookhaven National Laboratory, Upton, New York 11973, USA 74Langston University, Langston, Oklahoma 73050, USA 75University of Oklahoma, Norman, Oklahoma 73019, USA 76Oklahoma State University, Stillwater, Oklahoma 74078, USA
77Brown University, Providence, Rhode Island 02912, USA 78University of Texas, Arlington, Texas 76019, USA 79Southern Methodist University, Dallas, Texas 75275, USA
80Rice University, Houston, Texas 77005, USA 81University of Virginia, Charlottesville, Virginia 22901, USA
82University of Washington, Seattle, Washington 98195, USA (Received 18 June 2007; published 30 October 2007) We report a measurement of the 0
blifetime using a sample corresponding to 1:3 fb1of data collected
by the D0 experiment in 2002 – 2006 during run II of the Fermilab Tevatron collider. The 0
b baryon is
reconstructed via the decay 0
b!
lifetime to be 0
b 1:2900:1190:110stat0:0870:091syst ps, which is among the most precise measurements in semileptonic 0
b decays. This result is in good agreement with the world average value.
DOI:10.1103/PhysRevLett.99.182001 PACS numbers: 14.20.Mr, 13.30.Ce
The lifetimes of b hadrons provide an important test of models describing quark interaction within bound states. The experimental measurements of the lifetimes are in reasonable agreement with the theoretical predictions [1– 4], but further improvement in the experimental and theo-retical precision is essential for the development of quan-tum chromodynamics.
The lifetime of b hadrons has recently attracted special interest. The PDG-2006 world average 0
b lifetime is
0
b 1:230 0:074 ps, and the ratio of the 0bbaryon and B0meson lifetimes is 0
b=B0 0:80 0:05 [5], in good agreement with the theoretical prediction
0b=B0 0:86 0:05 [4]. However, the 0
blifetime measurement from the CDF collaboration in the 0
b !
J= decay gives a significantly larger value: 0
b 1:5930:0830:078 0:033 ps [6]. The D0 measurement in the same decay gives a value consistent with the PDG-2006 world average: 0
b 1:2180:1300:115 0:042 ps [7]. These
two results are not included in the quoted world average. Additional 0
b lifetime measurements could provide a potential resolution of this inconsistency.
This Letter presents a measurement of the 0
b lifetime using the semileptonic decay 0
b!
cX, where X is any other particle. Charge conjugated states are implied throughout this Letter. The c baryon is selected in the decay c ! K0
Sp. The sample corresponds to approxi-mately 1:3 fb1 of data collected by the D0 experiment in run II of the Fermilab Tevatron Collider.
The D0 detector is described in detail elsewhere [8]. The components most important to this analysis are the central tracking and muon systems. The central tracking system consists of a silicon microstrip tracker and a central fiber tracker, both located within a 2 T superconducting sole-noidal magnet, with designs optimized for tracking and vertexing at pseudorapidities jj < 3 and jj < 2:5, re-spectively, (where lntan=2 and is the polar angle of the particle with respect to the proton beam direction). The muon system is located outside the calo-rimeters and has pseudorapidity coverage jj < 2. It con-sists 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 [9]. The trigger system identifies events of interest in a high-luminosity environ-ment based on muon identification and charged tracking. Some triggers require a large impact parameter for the muon. Since this condition biases the lifetime measure-ment, the events selected exclusively by these triggers are removed from our sample. All processes and decays re-quired for this analysis are simulated using the EVTGEN
[10] generator interfaced to PYTHIA[11] and followed by full modeling of the detector response using GEANT[12] and event reconstruction.
Reconstruction of the 0
bdecay starts from the selection of a muon, which must have at least two track segments in the muon chambers associated with a central track, with transverse momentum with respect to the beam axis pT>
2:0 GeV=c. All charged particles in the event are clustered into jets using the Durham clustering algorithm [13]. The products of the c decay are then searched for among tracks belonging to the jet containing the identified muon. The primary vertex is determined using the method described in Ref. [14]. The K0
S meson is reconstructed as a combination of two oppositely charged tracks that have a common vertex displaced from the p pinteraction point by at least 4 standard deviations of the measured decay length in the plane perpendicular to the beam direction. Both tracks are assigned the pion mass and the mass of the
system is required to be consistent with the K0
S mass to within 1.8 standard deviations. Any other charged track in the jet with pT> 1:0 GeV=c and at least two hits in the silicon detector is assigned the proton mass and combined with the neutral extrapolated K0
S candidate to form a c candidate. The c candidate is combined with the muon to make a 0
bcandidate, and its invariant mass is required to be between 3.4 and 5:4 GeV=c2. The transverse
distance dbc
T between the 0band
c vertices is calculated and is assigned a positive sign if the 0
bvertex is closer to the primary vertex, and a negative sign otherwise. The 0
b candidate is required to have 3:0 < dbc
T =dbcT < 3:3, where dbc
T is the uncertainty of the dbcT measurement. The upper bound on the distance between the 0
b and
c vertices reduces the background significantly, since the c lifetime is known to be very small: 0:200 0:006 ps [5]. These selection criteria were chosen to optimize the signal to background ratio while avoiding any lifetime bias.
To further improve the 0
bsignal selection, a likelihood ratio method [15] is utilized. This method provides a simple way to combine many discriminating variables into a single variable with an increased power to separate signal and background. The variables chosen for this analy-sis are the 0
b isolation, the transverse momentum of the
K0S, proton and c candidates, and the mass of the c system. The isolation is defined as the fraction of the total momentum of charged particles within a cone around the
c direction carried by the 0b candidate. The cone is defined by the condition p2 2< 0:5, where
and are the difference in pseudorapidity and azimuthal angle from the direction of the 0
Figure 1 shows the invariant mass MK0
Sp for the selected 0
b candidates. The fit to this distribution is per-formed with a signal Gaussian function and a fourth-order polynomial function for the background. The c signal contains 4437 329stat events at a central mass of 2285:8 1:7 MeV=c2. The width of the mass peak is
20:6 1:7 MeV=c2, consistent with that observed in the
simulation.
Simulation shows that the contribution from the Bd !
K0
Sdecay when a pion is assigned the proton mass has a broad MK0
Spdistribution with no excess in the
c mass region.
Since the final state is not fully reconstructed, the 0
b proper decay length cannot be determined. Instead, a mea-sured visible proper decay length, M, is computed as
M mcL
T pTc=jpTcj2. LT is the vector from the primary vertex to the 0
b vertex in the plane perpendicular to the beams, pT
c is the transverse momentum of the c system and m 5:624 GeV=c2
is taken as the 0
b mass [5]. To determine the 0
blifetime, the selected sample is split into a number of Mbins. The mass distribution in each bin is fitted with a signal Gaussian and a fourth-order poly-nomial background. The position and width of the Gaussian are fixed to the values obtained from the fit of the entire sample (see Fig.1). The Gaussian normalization and background parameters are allowed to float in the fit. The range of Mand the number of signal events fitted in each bin nitogether with its statistical uncertainty iare shown in TableI.
The expected number of signal events in each bin, ne i, is given by ne
i Ntot
R
if Md M, where Ntot is the total
number of c events, and f M is the probability density function (PDF) for M. The integration is done within the range of a given bin.
In addition to 0
b!
cXdecays, the c baryon can also be created in c c or b bproduction, along with a muon from the decay of the second c or b hadron. In what
follows, these processes are referred to as peaking
back-ground, since they produce a c peak in the K0
Sp mass spectrum imitating the signal. Such events are recon-structed as 0
b candidates, and have a fake vertex formed by the intersection of the muon and c trajectories. The simulation shows that the distribution of Mfor such a fake vertex has a mean of zero and a standard deviation of 150 m.
The expression for f M takes into account the contri-butions from signal and peaking background: f M 1 rbckfsig M rbckfbck M. Here rbckis the fraction
of peaking background, and fsig M and f
bck M are the
PDFs for signal and background, respectively. The back-ground PDF is taken from the simulation. The signal PDF is expressed as the convolution of the decay probability and the detector resolution: fsig M RdKHK
f K=c expK =c R M ; sg. Here, is the 0
b lifetime, and is the step function. The factor
K pTc=pT0b is a measure of the difference between the measured pT
c and true momentum of the 0bcandidate, and HK is its PDF. The R M ; s is a function modeling the detector resolution. A scale factor
s accounts for the difference between the expected and actual Mresolution.
The HK distribution is obtained from the simulation. The contribution of decays 0
b !
c and 0b!
c with c ! cis taken into account. The con-tributions of 0
b !
cD
s with the Ds decaying semi-leptonically, b ! cX and 0b!
c with
!
are found to be strongly suppressed by the branching fractions and low reconstruction efficiency. To obtain HK, the K factor distribution of each process is weighted with its expected fraction in the selected sample. This is computed taking into account both the reconstruc-tion efficiency and the branching fracreconstruc-tion of each process. The fraction of ‘ c in semileptonic 0b decays has been measured recently to be 0:470:120:10 [5]. We use this result in our analysis.
The resolution function is given by R M ; s R
fresG M ; ; sd, where fres is the PDF
TABLE I. Fitted signal yield in different Mbins.
Mrange (cm) Number of signal candidates n
i i (stat) [0:06, 0:04] 62 48 [0:04, 0:02] 66 69 [0:02, 0.00] 587 156 [0.00, 0.02] 1172 173 [0.02, 0.04] 999 99 [0.04, 0.06] 540 69 [0.06, 0.08] 299 54 [0.08, 0.10] 225 44 [0.10, 0.20] 454 64 [0.20, 0.30] 47 34 ) 2 p) (GeV/c S M(K 2.1 2.2 2.3 2.4 ) 2 Events / (15 MeV/c 12 000 13 000 14 000 -1 L=1.3 fb ∅ D
FIG. 1 (color online). The K0
Spinvariant mass for the selected
0
for the expected resolution of M, and G is a Gaussian function G M ; ; s 1=p2s exp
M
2=22s2. Here, is the decay length uncertainty,
which is determined for each candidate from the track parameter uncertainties propagated to the vertex uncertainties.
To determine fres, signal and background subsamples are defined according to the mass of the K0
Spsystem. All events with 2244:7 < MK0
Sp < 2326:9 MeV=c2 are in-cluded in the signal subsample, and all events with 2183:9 < MK0
Sp < 2225:0 MeV=c2 and 2346:6 <
MK0Sp < 2387:7 MeV=c2 are included in the back-ground subsample. In addition, the events in both subsam-ples are required to have a measured proper decay length exceeding 200 m. This cut reduces the background under the c signal and the contribution of peaking background. The fres distribution is obtained by subtracting the distribution of expected resolution in the background sub-sample from the distribution in the signal subsub-sample, and the integration in the definition of R M ; s is replaced by the sum over the bins of the fres distribution.
The 0
b lifetime is determined by the minimization of
2 PNbins
i ni nei2=2i, where the sum is taken over all bins of measured proper decay length (Table I). The free parameters of the fit are Ntot, 0
b and rbck. A separate
study is performed to measure the resolution scale factor using the decay D ! D0 with D0 ! K0
S
. It
has a similar topology to that of the 0
b!
c decay. Since the D meson comes mainly from c c production, its decay vertex coincides with the primary interaction point. The distribution of the D proper decay length is mainly determined by the detector resolution and can be used to measure the resolution scale factor. A value of 1:19 0:06 is found. The scale factor in the lifetime fit is fixed to this value and varied later in a wide range to estimate an associated systematic uncertainty.
The lifetime fit gives 0
b 1:2900:1190:110stat ps,
and the fraction of peaking background rbck
0:1600:0680:074stat. Figure 2 shows the distribution of the number of cevents versus Mtogether with the result of the lifetime fit superimposed. The lifetime model agrees well with data with a 2=d:o:f: 5:5=7. The dashed line
shows separately the contribution of the peaking background.
The method used to fit the mass distribution in each of the M bins is the most significant source of systematic uncertainty. The fit sensitivity is tested by refitting each M bin for the mass interval between 2.17 and 2:40 GeV=c2
with a linear parametrization of the background. Binning effects of the mass histograms are checked by performing fits to the data with bins of half the nominal width and with the lowest and highest bins excluded. The lifetime fit is performed again for each test. The largest deviation of
0
b is 0.067 ps, which is given as the systematic uncer-tainty due to the mass-fitting procedure. The parameters
describing the peaking background are varied by their uncertainties, giving a shift of 0.012 ps in the 0
blifetime. The selected sample can also contain a contribution from B ! cX decay. Its branching fraction is un-known; only the upper limit BrB ! e cX < 3:2 103 at 90% C.L. is available [5]. The possible contami-nation from this decay would reduce the fitted 0
blifetime, since the K factor for these events is smaller. The upper 90% C.L. limit on the fraction of this decay in the selected sample is estimated to be 5%, which would result in the reduction of the 0
blifetime by 0.027 ps.
The value of the scale factor is varied by 20%, and shifts of approximately 0:036 ps are observed in the fitted lifetime. This value is also included in the systematic uncertainty. The overall systematic uncertainty due to the
Kfactor distribution is estimated to be 0.036 ps. It includes the uncertainty in the fraction of 0
b!
c decay in semileptonic 0
bdecays, the dependence of the K factor on the muon momentum and the uncertainty in generation and decay of 0
b hadrons [16,17]. The effect on lifetime mea-surement due to misalignment of elements of the tracking detector is determined by rescaling the geometrical posi-tion of all detectors within uncertainties of the alignment procedure. The resulting variation of the 0b lifetime is estimated to be 0.018 ps.
The total systematic uncertainty of this measurement is estimated to be0:0870:091 ps.
Extensive consistency checks using the simulation dem-onstrate that this analysis gives an unbiased measurement of the 0b lifetime and the correct statistical uncertainty. We also split the data sample into two roughly equal parts using various criteria and measure the 0
blifetime in each sample independently. The sample is split according to the muon charge, the muon direction, the K0
S decay length or (cm) M λ 0 0.1 0.2 0.3 yield (events/0.02cm)c Λ µ 10 2 10 3 10 D∅ L=1.3 fb-1
FIG. 2 (color online). Measured c yields in the M bins
(points) and the result of the lifetime fit (solid histogram). The dashed histogram shows the contribution of the peaking back-ground. In each of the last two bins, the total yield is as shown in TableI.
the chronological date of data taking. All such tests give statistically consistent values of the 0
blifetime. In conclusion, our measurement of the 0
blifetime using the semileptonic decay 0
b!
cX results in 0b 1:2900:1190:110stat0:087
0:091syst ps. It is consistent with the
current world average 0
b lifetime and with our measure-ment in the exclusive decay 0
b ! J= [7]. These two D0 results are statistically independent and the correlation of known systematic effects between them is small. Their combination results in 0
b 1:2510:1020:096 ps.
We thank the staffs at Fermilab and collaborating institutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); Science and Technology Facilities Council (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research
Council (Sweden); CAS and CNSF (China);
Alexander von Humboldt Foundation; and the Marie Curie Program.
*Visiting scientist from Augustana College, Sioux Falls, SD, USA.
†Visiting scientist from The University of Liverpool,
Liverpool, United Kingdom.
‡Visiting scientist from ICN-UNAM, Mexico City, Mexico.
xVisiting scientist from Helsinki Institute of Physics,
Helsinki, Finland.
k
Visiting scientist from Universita¨t Zu¨rich, Zu¨rich, Switzerland.
[1] M. Neubert and C. T. Sachrajda, Nucl. Phys. B483, 339 (1997).
[2] M. Di Pierro et al., Phys. Lett. B 468, 143 (1999). [3] E. Franco et al., Nucl. Phys. B633, 212 (2002). [4] F. Gabbiani et al., Phys. Rev. D 70, 094031 (2004). [5] W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1
(2006).
[6] A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett.
98, 122001 (2007).
[7] V. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 99, 142001 (2007).
[8] V. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 565, 463 (2006).
[9] V. Abazov et al., Nucl. Instrum. Methods Phys. Res., Sect. A 552, 372 (2005).
[10] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A
462, 152 (2001).
[11] T. Sjo¨strand et al., Comput. Phys. Commun. 135, 238 (2001).
[12] CERN Program Library Long Writeup Report No. W5013, 1993; documentation available at http:// wwwasd.web.cern.ch/wwwasd/geant/.
[13] S. Catani, Yu. L. Dokshitzer, M. Olsson, G. Turnock, and B. R. Webber, Phys. Lett. B 269, 432 (1991).
[14] J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C
32, 185 (2004).
[15] G. Borisov, Nucl. Instrum. Methods Phys. Res., Sect. A
417, 384 (1998).
[16] V. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 94, 182001 (2005).
[17] V. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 97, 021802 (2006).
