Measurement of the B− meson lifetime in the decay B− → J/ψ π− c c T. Aaltonen,21 B. A´lvarez Gonz´alezz,9 S. Amerio,40 D. Amidei,32 A. Anastassovx,15 A. Annovi,17 J. Antos,12 G. Apollinari,15 J.A. Appel,15 T. Arisawa,54 A. Artikov,13 J. Asaadi,49 W. Ashmanskas,15 B. Auerbach,57 A. Aurisano,49 F. Azfar,39 W. Badgett,15 T. Bae,25 A. Barbaro-Galtieri,26 V.E. Barnes,44 B.A. Barnett,23 P. Barriahh,42 P. Bartos,12 M. Bauceff,40 F. Bedeschi,42 S. Behari,23 G. Bellettinigg,42 J. Bellinger,56 D. Benjamin,14 A. Beretvas,15 A. Bhatti,46 D. Biselloff,40 I. Bizjak,28 K.R. Bland,5 B. Blumenfeld,23 A. Bocci,14 A. Bodek,45 D. Bortoletto,44 J. Boudreau,43 A. Boveia,11 L. Brigliadoriee,6 C. Bromberg,33 E. Brucken,21 J. Budagov,13 H.S. Budd,45 K. Burkett,15 G. Busettoff,40 P. Bussey,19 A. Buzatu,31 A. Calamba,10 C. Calancha,29 S. Camarda,4 M. Campanelli,28 M. Campbell,32 F. Canelli,11,15 B. Carls,22 D. Carlsmith,56 R. Carosi,42 S. Carrillom,16 S. Carron,15 B. Casalk,9 M. Casarsa,50 A. Castroee,6 P. Catastini,20 D. Cauz,50 V. Cavaliere,22 M. Cavalli-Sforza,4 A. Cerrif,26 L. Cerritos,28 Y.C. Chen,1 M. Chertok,7 G. Chiarelli,42 G. Chlachidze,15 3 F. Chlebana,15 K. Cho,25 D. Chokheli,13 W.H. Chung,56 Y.S. Chung,45 M.A. Cioccihh,42 A. Clark,18 C. Clarke,55 1 G. Compostellaff,40 M.E. Convery,15 J.Conway,7 M.Corbo,15 M.Cordelli,17 C.A. Cox,7 D.J. Cox,7 F. Crescioligg,42 0 J. Cuevasz,9 R. Culbertson,15 D. Dagenhart,15 N. d’Ascenzow,15 M. Datta,15 P. de Barbaro,45 M. Dell’Orsogg,42 2 L. Demortier,46 M. Deninno,6 F. Devoto,21 M. d’Erricoff,40 A. Di Cantogg,42 B. Di Ruzza,15 J.R. Dittmann,5 n M. D’Onofrio,27 S. Donatigg,42 P. Dong,15 M. Dorigo,50 T. Dorigo,40 K. Ebina,54 A. Elagin,49 A. Eppig,32 a R. Erbacher,7 S. Errede,22 N. Ershaidatdd,15 R. Eusebi,49 S. Farrington,39 M. Feindt,24 J.P. Fernandez,29 J R. Field,16 G. Flanaganu,15 R. Forrest,7 M.J. Frank,5 M. Franklin,20 J.C. Freeman,15 Y. Funakoshi,54 I. Furic,16 3 M. Gallinaro,46 J.E. Garcia,18 A.F. Garfinkel,44 P. Garosihh,42 H. Gerberich,22 E. Gerchtein,15 S. Giagu,47 ] V. Giakoumopoulou,3 P. Giannetti,42 K. Gibson,43 C.M. Ginsburg,15 N. Giokaris,3 P. Giromini,17 G. Giurgiu,23 x V. Glagolev,13 D. Glenzinski,15 M. Gold,35 D. Goldin,49 N. Goldschmidt,16 A. Golossanov,15 G. Gomez,9 e - G. Gomez-Ceballos,30 M. Goncharov,30 O. Gonz´alez,29 I. Gorelov,35 A.T. Goshaw,14 K. Goulianos,46 S. Grinstein,4 p C. Grosso-Pilcher,11 R.C. Group53,15 J. Guimaraes da Costa,20 S.R. Hahn,15 E. Halkiadakis,48 A. Hamaguchi,38 e h J.Y. Han,45 F. Happacher,17 K. Hara,51 D. Hare,48 M. Hare,52 R.F. Harr,55 K. Hatakeyama,5 C. Hays,39 M. Heck,24 [ J. Heinrich,41 M. Herndon,56 S. Hewamanage,5 A. Hocker,15 W. Hopkinsg,15 D. Horn,24 S. Hou,1 R.E. Hughes,36 2 M. Hurwitz,11 U. Husemann,57 N. Hussain,31 M. Hussein,33 J. Huston,33 G. Introzzi,42 M. Iorijj,47 A. Ivanovp,7 v E. James,15 D. Jang,10 B. Jayatilaka,14 E.J. Jeon,25 S. Jindariani,15 M. Jones,44 K.K. Joo,25 S.Y. Jun,10 6 T.R. Junk,15 T. Kamon25,49 P.E. Karchin,55 A. Kasmi,5 Y. Katoo,38 W. Ketchum,11 J. Keung,41 V. Khotilovich,49 6 B. Kilminster,15 D.H. Kim,25 H.S. Kim,25 J.E. Kim,25 M.J. Kim,17 S.B. Kim,25 S.H. Kim,51 Y.K. Kim,11 3 2 Y.J. Kim,25 N. Kimura,54 M. Kirby,15 S. Klimenko,16 K. Knoepfel,15 K. Kondo,54 D.J. Kong,25 J. Konigsberg,16 . A.V. Kotwal,14 M. Kreps,24 J. Kroll,41 D. Krop,11 M. Kruse,14 V. Krutelyovc,49 T. Kuhr,24 M. Kurata,51 0 1 S. Kwang,11 A.T. Laasanen,44 S. Lami,42 S. Lammel,15 M. Lancaster,28 R.L. Lander,7 K. Lannony,36 A. Lath,48 2 G. Latinohh,42 T. LeCompte,2 E. Lee,49 H.S. Leeq,11 J.S. Lee,25 S.W. Leebb,49 S. Leogg,42 S. Leone,42 J.D. Lewis,15 1 A. Limosanit,14 C.-J. Lin,26 M. Lindgren,15 E.Lipeles,41 A. Lister,18 D.O. Litvintsev,15 C. Liu,43 H. Liu,53 Q. Liu,44 v: T. Liu,15 S. Lockwitz,57 A. Loginov,57 D. Lucchesiff,40 J. Lueck,24 P. Lujan,26 P. Lukens,15 G. Lungu,46 J. Lys,26 i R. Lysake,12 R. Madrak,15 K. Maeshima,15 P. Maestrohh,42 S. Malik,46 G. Mancaa,27 A. Manousakis-Katsikakis,3 X F. Margaroli,47 C. Marino,24 M. Mart´ınez,4 P. Mastrandrea,47 K. Matera,22 M.E. Mattson,55 A. Mazzacane,15 r a P. Mazzanti,6 K.S. McFarland,45 P. McIntyre,49 R. McNultyj,27 A. Mehta,27 P. Mehtala,21 C. Mesropian,46 T. Miao,15 D. Mietlicki,32 A. Mitra,1 H. Miyake,51 S. Moed,15 N. Moggi,6 M.N. Mondragonm,15 C.S. Moon,25 R. Moore,15 M.J. Morelloii,42 J. Morlock,24 P. Movilla Fernandez,15 A. Mukherjee,15 Th. Muller,24 P. Murat,15 M. Mussiniee,6 J. Nachtmann,15 Y. Nagai,51 J. Naganoma,54 I. Nakano,37 A. Napier,52 J. Nett,49 C. Neu,53 M.S. Neubauer,22 J. Nielsend,26 L. Nodulman,2 S.Y. Noh,25 O. Norniella,22 L. Oakes,39 S.H. Oh,14 Y.D. Oh,25 I. Oksuzian,53 T. Okusawa,38 R. Orava,21 L. Ortolan,4 S. Pagan Grisoff,40 C. Pagliarone,50 E. Palenciaf,9 V. Papadimitriou,15 A.A. Paramonov,2 J. Patrick,15 G. Paulettakk,50 M. Paulini,10 C. Paus,30 D.E. Pellett,7 A. Penzo,50 T.J. Phillips,14 G. Piacentino,42 E. Pianori,41 J. Pilot,36 K. Pitts,22 C. Plager,8 L. Pondrom,56 S. Poprockig,15 K. Potamianos,44 F. Prokoshincc,13 A. Pranko,26 F. Ptohosh,17 G. Punzigg,42 A. Rahaman,43 V. Ramakrishnan,56 N. Ranjan,44 I. Redondo,29 P. Renton,39 M. Rescigno,47 T. Riddick,28 F. Rimondiee,6 L. Ristori42,15 A. Robson,19 T. Rodrigo,9 T. Rodriguez,41 E. Rogers,22 S. Rollii,52 R. Roser,15 F. Ruffinihh,42 A. Ruiz,9 J. Russ,10 V. Rusu,15 A. Safonov,49 W.K. Sakumoto,45 Y. Sakurai,54 L. Santikk,50 K. Sato,51 V. Savelievw,15 A. Savoy-Navarroaa,15 P. Schlabach,15 A. Schmidt,24 E.E. Schmidt,15 T. Schwarz,15 L. Scodellaro,9 A. Scribanohh,42 F. Scuri,42 S. Seidel,35 Y. Seiya,38 A. Semenov,13 F. Sforzahh,42 S.Z. Shalhout,7 T. Shears,27 P.F. Shepard,43 M. Shimojimav,51 M. Shochet,11 I. Shreyber-Tecker,34 A. Simonenko,13 P. Sinervo,31 K. Sliwa,52 J.R. Smith,7 F.D. Snider,15 A. Soha,15 V. Sorin,4 H. Song,43 P. Squillaciotihh,42 M. Stancari,15 R. St. Denis,19 2 B. Stelzer,31 O. Stelzer-Chilton,31 D. Stentzx,15 J. Strologas,35 G.L. Strycker,32 Y. Sudo,51 A. Sukhanov,15 I. Suslov,13 K. Takemasa,51 Y. Takeuchi,51 J. Tang,11 M. Tecchio,32 P.K. Teng,1 J. Thomg,15 J. Thome,10 G.A. Thompson,22 E. Thomson,41 D. Toback,49 S. Tokar,12 K. Tollefson,33 T. Tomura,51 D. Tonelli,15 S. Torre,17 D. Torretta,15 P. Totaro,40 M. Trovatoii,42 F. Ukegawa,51 S. Uozumi,25 A. Varganov,32 F. Va´zquezm,16 G. Velev,15 C. Vellidis,15 M. Vidal,44 I. Vila,9 R. Vilar,9 J. Viza´n,9 M. Vogel,35 G. Volpi,17 P. Wagner,41 R.L. Wagner,15 T. Wakisaka,38 R. Wallny,8 S.M. Wang,1 A. Warburton,31 D. Waters,28 W.C. Wester III,15 D. Whitesonb,41 A.B. Wicklund,2 E. Wicklund,15 S. Wilbur,11 F. Wick,24 H.H. Williams,41 J.S. Wilson,36 P. Wilson,15 B.L. Winer,36 P. Wittichg,15 S. Wolbers,15 H. Wolfe,36 T. Wright,32 X. Wu,18 Z. Wu,5 K. Yamamoto,38 D. Yamato,38 T. Yang,15 U.K. Yangr,11 Y.C. Yang,25 W.-M. Yao,26 G.P. Yeh,15 K. Yin,15 J. Yoh,15 K. Yorita,54 T. Yoshidal,38 G.B. Yu,14 I. Yu,25 S.S. Yu,15 J.C. Yun,15 A. Zanetti,50 Y. Zeng,14 C. Zhou,14 and S. Zucchelliee6 (CDF Collaboration) 1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China 2Argonne National Laboratory, Argonne, Illinois 60439, USA 3University of Athens, 157 71 Athens, Greece 4Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain 5Baylor University, Waco, Texas 76798, USA 6Istituto Nazionale di Fisica Nucleare Bologna, eeUniversity of Bologna, I-40127 Bologna, Italy 7University of California, Davis, Davis, California 95616, USA 8University of California, Los Angeles, Los Angeles, California 90024, USA 9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain 10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA 12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia 13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia 14Duke University, Durham, North Carolina 27708, USA 15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 16University of Florida, Gainesville, Florida 32611, USA 17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy 18University of Geneva, CH-1211 Geneva 4, Switzerland 19Glasgow University, Glasgow G12 8QQ, United Kingdom 20Harvard University, Cambridge, Massachusetts 02138, USA 21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland 22University of Illinois, Urbana, Illinois 61801, USA 23The Johns Hopkins University, Baltimore, Maryland 21218, USA 24Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany 25Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea; Korea Institute of Science and Technology Information, Daejeon 305-806, Korea; Chonnam National University, Gwangju 500-757, Korea; Chonbuk National University, Jeonju 561-756, Korea 26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 27University of Liverpool, Liverpool L69 7ZE, United Kingdom 28University College London, London WC1E 6BT, United Kingdom 29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain 30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 31Institute of Particle Physics: McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6; University of Toronto, Toronto, Ontario, Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3 32University of Michigan, Ann Arbor, Michigan 48109, USA 33Michigan State University, East Lansing, Michigan 48824, USA 34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia 35University of New Mexico, Albuquerque, New Mexico 87131, USA 36The Ohio State University, Columbus, Ohio 43210, USA 37Okayama University, Okayama 700-8530, Japan 38Osaka City University, Osaka 588, Japan 39University of Oxford, Oxford OX1 3RH, United Kingdom 40Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, ffUniversity of Padova, I-35131 Padova, Italy 41University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 3 42Istituto Nazionale di Fisica Nucleare Pisa, ggUniversity of Pisa, hhUniversity of Siena and iiScuola Normale Superiore, I-56127 Pisa, Italy 43University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 44Purdue University, West Lafayette, Indiana 47907, USA 45University of Rochester, Rochester, New York 14627, USA 46The Rockefeller University, New York, New York 10065, USA 47Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, jjSapienza Universita` di Roma, I-00185 Roma, Italy 48Rutgers University, Piscataway, New Jersey 08855, USA 49Texas A&M University, College Station, Texas 77843, USA 50Istituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, kkUniversity of Udine, I-33100 Udine, Italy 51University of Tsukuba, Tsukuba, Ibaraki 305, Japan 52Tufts University, Medford, Massachusetts 02155, USA 53University of Virginia, Charlottesville, Virginia 22906, USA 54Waseda University, Tokyo 169, Japan 55Wayne State University, Detroit, Michigan 48201, USA 56University of Wisconsin, Madison, Wisconsin 53706, USA 57Yale University, New Haven, Connecticut 06520, USA (Dated: January 4, 2013) The lifetime of the B− meson is measured using 272 exclusive B− → J/ψ(→ µ+µ−) π− decays c c reconstructedindatafromproton-antiprotoncollisionscorrespondingtoanintegratedluminosityof 6.7 fb−1 recorded bytheCDF II detector at theFermilab Tevatron. Thelifetime of theB− meson c − is measured to be τ(B ) = 0.452 ± 0.048(stat) ± 0.027(syst) ps. This is the first measurement of c − theB mesonlifetimeinafully-reconstructedhadronicchannel,anditagreeswithpreviousresults c and has comparable precision. PACSnumbers: 14.40.Nd,13.25.Hw − InthestandardmodeltheB mesonistheonlymeson The components of the CDF II detector [8] most rel- c − composed of two distinct heavy quarks. The B meson evant for this analysis are the charged-particle tracking c decaycanbegovernedbythedecayoftheborcspectator and muon identification systems. The tracking system quarks or can proceed through the annihilation of the b is immersed in a uniform 1.4 T solenoidalmagnetic field and c quarks. Various theoretical techniques have been coaxial with the beam line, and consists of single- and − used to predict the B meson lifetime. An operator- double-sidedsilicondetectors[9]anda96-layeropen-cell c − product-expansion calculation [1] predicts a B meson drift chamber (COT) [10]. The muon system is used c lifetime in the range of 0.4 to 0.7 ps. A QCD sum rule to identify the J/ψ →µ+ µ− decay. Two sets of muon approach [2] predicts the lifetime to be 0.48 ± 0.05 ps. chambers [11, 12] are used to cover different pseudora- − Another approach[3], estimating the B meson lifetime pidity regions. c by global fitting of the phenomenological parameters of A three-level event-selection system (trigger) is used all other heavy mesons, gives a result of 0.36 or 0.47 ps, to collect events enriched in J/ψ →µ+ µ− decays [8]. depending on different choices of effective heavy-quark The event reconstruction starts by combining two muon masses. candidatestoformaJ/ψcandidate. Thetriggerrequire- − mentsareconfirmedbyselectingeventsthatcontaintwo The B meson lifetime was measured previously in c oppositelychargedmuoncandidates,eachwithmatching semileptonic decays by CDF [4] and D0 [5]. These COT and muon chamber tracks. The muon-pair mass is measurements have an undetected neutrino in the final − required to be within 80 MeV/c2 of the world-average state and rely on the modeling of the B meson mo- c J/ψ mass [13], where the mass resolution is 13 MeV/c2. mentum to account for unmeasured momentum of the − − − neutrino. Therefore, a measurement of the B meson Both J/ψ K and J/ψ π combinations are recon- c − − lifetime in a fully-reconstructed decay mode is desired structedinthis analysis. The largeB →J/ψ K sam- − − since it does not suffer from this limitation. CDF is pleisusedasareferencedecayforB →J/ψ π . These c − − the first experiment to observe the fully-reconstructed finalstatesareidentifiedbyassigningtheK orπ mass B− →J/ψ(→µ+µ−)π− decaymode[6]andtomeasure to other reconstructed tracks not used in the J/ψ can- c − − − theB mass[7]. Inthispaperwepresentalifetimemea- didates and forming B or B candidates. Each three- c c − surement of the B meson using this decay mode. This track combination must satisfy a kinematic fit in which c measurement is made using data from pp collisions at a the three tracks are required to originate from a com- center-of-mass energy of 1.96 TeV recorded by the CDF mon decay point, and the invariant mass of the muon II detector. The results are basedona data sample with pair is constrained to the world-average J/ψ mass [13]. an integrated luminosity of 6.7 fb−1. TheK− andπ− candidatetrackisnamedthethirdtrack 4 − h . Aminimalselectionismadeonkinematicquantities − after the constrained fit including p (h ) > 1.7 GeV/c T andp (B)>5 GeV/c, where p is the momentum com- 8000 T T ponent transverse to the beam line, and B refers to a − Sideband regions J/ψ h candidate. The selection criteria for the B can- didates are listed in Table I and discussed below. 2V/c 6000 e M 5 per 4000 TABLE I.Selection requirements. es at d Selection variable Requirement ndi pT(h−) >2.0 GeV/c Ca 2000 pT(B) >6.5 GeV/c P(χ2) >0.1% |d(B)|/σd(B) <2.0 05.1 5.2 Mass(J/ψ5 K.3-) [GeV/c2] 5.4 5.5 βT <0.2 radians IB >0.6 σm(B) <40 MeV/c2 − ct >80 µm FIG. 1. Invariant-mass distribution of J/ψ K candidates. σct(B) <max[35,65−3 pT(B)(GeV/c)]µm The hatched areas are the sideband regions and the signal region lies between them. − The h and B candidates are required to have a min- imum pT to suppress combinatorial background events. Becausetheσct(B)distributiondependsonpT(B), we Werejecteventswithpoorlydefineddecaypointsbyim- vary the requirement on σct(B) as a function of pT(B). posing a lower threshold to the chi-square probability For candidates with pT(B) < 10 GeV/c, we require P(χ2) of the constrained fit used to reconstruct the B σct(B) < (65−3 pT(B)) µm for pT(B) measured in candidates. We select B candidates that originate from GeV/c, and σct(B) < 35 µm for pT(B) ≥ 10 GeV/c. theprimaryinteractionpointbyrequiringasmallimpact ThispT-dependentrequirementonσct(B)ischosentobe parameter d(B) (transverse distance of closest approach highly efficient for preserving signalwhile reducing com- to the beam line) in units of its uncertainty σ and a binatorialbackgroundandleadstonomeasurablebiases. d(B) small angle β between L~ and p~ (B), where L~ is the TheresultingB− massdistributionisshowninFig.1. T T T T transverse displacement vector from the primary inter- The signal region lies between two backgroundsideband − action point to the B-decay point, and p~ (B) denotes a regions and has 46 280 B candidates. The two side- T vector in the transverse plane along the momentum di- band regions consist of a lower sideband from 5.18 to rection of the B candidate. The isolation I of the B 5.23 GeV/c2 and an upper sideband from 5.33 to 5.38 B candidate is defined as I ≡ p(B)/(p(B) + | ~p |), GeV/c2, as shown in the hatched areas. B i i − − cwohnesrteruPcteidp~itrisactkhsensoutmusoedf minotmheenJta/ψovhe−r aclolmobtPihneartiroen- samTheepaBrcen→t sJa/mψplπe ascatnhdeidBa−tes→aJre/ψfoKrm−edcafnrodmidatthees within (∆η)2+(∆φ)2 < 0.7, and ∆η and ∆φ are the where the only change to the reconstruction is to assign differenpces in pseudorapidities and azimuthal angles of the pion mass to the third track. We then select events tracks relative to p~(B). We also suppress the promptly for further analysis using the selections in Table I. The − produced combinatorial background by rejecting candi- reconstructedmassdistributionforthe Bc candidatesis dates with small ct, where ct is the decay length of the showninFig.2. Thesignalregionliesbetweentwoback- − B candidate determined by ground sideband regions and has 1496 Bc candidates. − The two sideband regions of B candidates consist of c a lower sideband from 6.16 to 6.21 GeV/c2 and an up- c m(B) per sideband from 6.33 to 6.60 GeV/c2, as shown in the ct ≡ L~ ·~p (B) , (1) T T |p (B)|2 hatched areas. The lower sideband is narrow to avoid T − contamination from semileptonic B decays where the c and m(B) is the reconstructed mass of the B candidate. lepton is misidentified as a pion. Requirements on σ (B) and σ (B) are made to reject We generate Monte Carlo simulations for m ct − − − − poorly reconstructed events, where σ (B) and σ (B) B →J/ψ K and B →J/ψ π decays to study m ct c are the associated uncertainties from the kinematic fit the efficiency of the selection criteria as a function of of m(B) and ct(B), respectively. The optimization of decay length. The Fixed-Order plus Next-to-Leading theselectionrequirementsisobtainedbymaximizingthe Logarithms (FONLL) p spectrum [14] is used for T − quantity S/ (S+B) where the background B is esti- the B production spectrum. We use the calculation − mated frompthe mass sidebands in data andthe signal S of Ref [15] as the spectrum for B simulation. In c − isestimatedfromthesignal-regiondataaftersubtracting comparing the FONLL p spectrum for B production T background contributions as calculated from sidebands. with the experimental data, reasonable consistency is 5 simulation are also p -dependent, and the p thresh- T T old remains the same; the only change is to require 200 σ (B) < (45−2 p (B)) µm for p (B) < 10 GeV/c, ct T T Sideband regions Signal 2eV/c 150 BSiagcnkagl+robuancdkground 1 0 M B- data Candidates per 1 15000 µmer 20 00..68 BB-c- ssiimmuullaattiioonn p ency 0.4 0 Effici 6 6.1 6.2 6.3 6.4 6.5 6.6 Mass(J/ψ π-) [GeV/c2] 0.2 0 FIG. 2. Invariant-mass distribution of J/ψ π− candidates. 0 0.02 0.04 ct(J/ψ0. 0h-6) [cm] 0.08 0.1 0.12 Thehatchedareasarethesidebandregionsandthesignalre- gionliesbetweenthem. Thefitresultisoverlaidinthesignal region, as well as the signal and background components. − − FIG.4. ComparisonofefficiencyforB →J/ψ K obtained from data and the fit result from simulation. Also shown is − − thefit result for B →J/ψ π simulation. c 6000 and σ (B) < 25 µm for p (B) ≥ 10 GeV/c. The ct T Data systematic uncertainty associated with the tuning will Simulation be discussed later. µm1 4000 Theefficiencyoftheselectioncriteriaisfoundbycom- er paring the decay-length distribution after applying the p es selection in Table I to that obtained from the mini- didat mal selection which requires pT(h−) > 1.7 GeV/c and Can2000 pT(B) > 5 GeV/c. The efficiency determined from sim- ulation is then fit to a function of the form 0 0 0.002 0.004 0.006 0.008 a−ct σ (J/ψ K-) [cm] ǫ(ct)=C 1−exp , (2) ct (cid:20) (cid:18) b (cid:19)(cid:21) FIG.3. Theσct distribution of J/ψ K− candidatesobtained where C, a, b are parameters to b−e fit. Figure−4 shows the efficiency determined from B →J/ψ K experi- from the simulation is compared with data. mental data as well as the fit result from simulation. The parameter C in Eq. (2) is not necessary in the life- time fit because only the relative shape of the efficiency observedforp >6GeV/c,andanyresidualdiscrepancy function matters. The requirement on β leads to an T T gives a negligible systematic uncertainty. To further efficiency that is not constant as a function of decay − − validate the B →J/ψ K simulation, we compare the length. This variable is very effective in rejecting back- distributions of the selection variables listed in Table I ground events, especially for events with small ct. The for experimental data and simulation. Generally, good goodagreementbetweenthesimulatedefficiencyandthe agreement is observed for all selection variables except data-determined efficiency supports the use of this ap- for σ (B), whose comparison is shown in Fig. 3. The proach in the ct-dependent efficiency. The efficiency for ct − − disagreement in the σ (B) distribution arises from the B →J/ψ π decay as a function of decay time de- ct c mis-modeling of the silicon tracking detector in the termined from simulation is fit and also shown in Fig. 4. simulation, giving a smaller σ (B) compared with We use a maximum log-likelihood simultaneous fit to ct experimental data for a given p (B). Consequently, the the unbinned mass and decay-lengthdistributions of the T − selection requirement made on σ (B) for simulation is B candidates. Thelikelihoodfunctionconsistsofsignal ct c tuned in order to allow the same efficiency as in the andbackgroundparts,andeachparthasamasstermand experimental data. These σ (B) selection values for a decay length term. The log-likelihood function is ct 6 lnL= ln[f M (m ) T (ct )+(1−f ) M (m ) T (ct )], (3) s s i s i s b i b i Xi where f is the signal fraction, m and ct are the re- s i i constructed mass and decay length for event i. M (m ) s i and T (ct ) are the normalized probability density func- 103 s i tions for mass and decay length of the signalmodel, and Signal M (m ) and T (ct ) are the corresponding functions of Background theb baickgroundb miodel. The signal mass model M (m ) m 102 Signal+background s i µ is described by a Gaussian distribution with mean m0 er 20 and width σm, whose values are determined by the fit. es p 10 The signal decay length model Ts(cti) is an exponential dat di distributionwithcharacteristiclifetimeτ,smearedbythe n a C detector resolutionandmultiplied by the efficiency func- 1 tion given in Eq. (2). The detector resolution, which is modeledasaGaussiandistributioncenteredatzerowith 10-1 a width of 20 µm, is chosen to be consistent with cali- 0.02 0.04 0.06 0.08 0.1 0.12 ct(J/ψ π-) [cm] brationusingpromptlydecayingbackgroundevents[16]. The background mass model M (m ) is described by a b i linear distribution, and Tb(cti) is described by a linear FIG.5. Decay-lengthdistributionofJ/ψ π−candidates. The combination of three exponential distributions. fit projection, along individualcontributions from signal and A two-step process is used to extract the lifetime of background,is overlaid. − the B meson. The first step includes the efficiency c fit and the sideband fit. The efficiency fit is performed on the simulated events using Eq. (2), and the result is andalternatemodelsseparately. Thedistributionsofthe shown in Fig. 4. The sideband fit consists of two sepa- sample-by-sample lifetime differences between different rate fits in the sideband regions. The first fit determines models are obtained and compared with the differences the background mass model parameters, and the second observedinexperimentaldata. Toassesstheeffectofthe fitdeterminesthebackgrounddecay-timemodelparame- choice of the linear model for the mass-fit background, ters. Thesignalregionisfitwiththeefficiencyandback- we compare to the result of a fit using a bilinear model groundparametersGaussian-constrainedto the resultof thatallowsthe backgrounddistributionto havedifferent the earlier fits. The signal fraction and the signal model slopesatmasseslowerandhigherthantheB− polemass, c parameters are allowed to float freely in maximizing the withtheconstraintthatthese twodistributions intersect log-likelihood function given in Eq. (3). at the fit B− mass value. The fit lifetime with this bi- c Tovalidatethisfittingtechnique,thefitisfirstapplied linear model has a shift of –0.009 ps compared with the to the B− candidates shown in Fig. 1 to extract the B− default linear model. The pseudoexperiments suggests meson lifetime. The B− lifetime which is found to be up to a 0.017 ps difference from this variation. We con- τ(B−) = 1.637 ± 0.010 (stat) ps is in agreement with clude that the shift between the data fits is consistent theworld-averagevalueof1.641±0.008ps[13]. TheB− with the spread among the pseudoexperiments, and we signal yield returned from the fit is 43 308 ± 171. The use that larger difference as the systematic uncertainty fit is then applied to the B− candidates shownin Fig. 2, from the background mass model. c − resultinginalifetimeofτ(B ) = 0.452±0.048(stat)ps To assess a possible systematic uncertainty due to c − for the B meson, which is taken as our central result, the modeling of the long tail in the background decay- c − withaB signalyieldof272±61(stat)candidates. The length distribution, we test an alternate model of the c B− meson mass of 6274.6 ± 2.9 (stat) MeV/c2 returned background decay time which uses a linear distribu- c fromthe fit is ingoodagreementwiththe previousCDF tion to replace the component with the largest charac- determination [7]. Figures 2 and 5 show the distribution teristic lifetime in the three exponential distributions. − oftheJ/ψ π massanddecaylength. Thefitprojections This variation gives a lifetime result that changes by are overlaid. –0.0007 pscomparedwiththedefaultbackgrounddecay- We have considered several sources of systematic un- timemodel. However,fitresultsfrompseudoexperiments certainty and evaluated their contributions. To evaluate suggestthedifferencebetweenthesetwomodelscouldbe possible systematic uncertainties with the models in the 0.013ps, whichisincludedasthe systematicuncertainty likelihoodfunction,wegenerate400simulateddatasam- due to the choice of the background decay-time model. ples (pseudoexperiments) whose distributions are based Thesignaldecay-timemodelincludestheefficiencyde- on the fit results determined by the experimental data. termined from the simulation. We have performed sev- These pseudoexperiments are then fit with the default eral studies to estimate the associated systematic un- 7 certainty. First, the fit is repeated using an efficiency variation. function obtained without tuning the σct(B) difference The systematic uncertainty from the fitting technique between data and simulation. The difference in the es- itself is tested by generating pseudoexperiments, and timated lifetime is 0.003 ps. Second, the efficiency func- comparing the fit lifetimes with the input lifetime. The tion is shifted toward lower and higher decay length by bias on the lifetime returned by the fit is found to be 20µm to accountfor a possible uncertaintyin determin- no greater than 0.003 ps which we take as systematic ing the efficiency function parameters; this 20 µm shift uncertainty. Table II summarizes the systematic uncer- is equivalent to three standard deviations of the param- tainties,whichareaddedinquadraturetodetermine the eter a in Eq. (2). This variation gives a difference of total systematic uncertainty. –0.010(+0.007)ps for shifting towardlower(higher) de- cay lengths. The distribution of the difference between the resulting lifetimes in the pseudoexperiments is fit by TABLE II.Summary of systematic uncertainties. a Gaussiandistribution that centersat –0.006(0.004)ps Source Uncertainty [ps] withawidthof0.002(0.001)psforshiftingtowardlower Background mass model 0.017 (higher) decay lengths. Third, the systematic uncer- Background decay-timemodel 0.013 − tainty associated with the Bc production spectrum has Signal decay-timemodel 0.010 been assessed. We vary the relative fraction of different Correlation 0.010 contributions to the production spectrum; the difference Misalignment 0.007 in the corresponding efficiency is negligible and no sys- Signal mass model 0.003 tematic uncertainty is assigned to it. Finally, to further Fitting technique 0.003 Total 0.027 studythesystematicuncertaintyassociatedwiththepro- duction spectrum, we use the efficiency parameters ob- − − − tainedfromtheB →J/ψ K simulation. SincetheB Given that the efficiency is not uniform over decay − production spectrum is quite different from that of B , c length, our result relies on the accuracy of the simula- the fit lifetime difference of 0.007 ps indicates that the tion in determining the efficiency. We check our result productionspectrum does not contribute significantly to − by measuring the B lifetime using a different set of se- the systematic uncertainty. Thus, the total systematic c lection criteria, each of which has uniform efficiency in uncertainty associated with the signal decay-time model − − the B →J/ψ K decay. The most important differ- is taken to be 0.010 ps. ences between these selection criteria and those listed in Correlations between the lifetime and other parame- Table I are removing the β requirement and using a T ters of the analysis are consideredas possible systematic larger minimum ct requirement. The alternate selection uncertainties. The list of parameters includes the min- criteria gives 6538 B− candidates between 6.0 and 6.6 c imum and maximum decay length for events in the fi- GeV/c2 which is roughly the same number as obtained nalfit, adding aparameterto the efficiencymodel, small from the selections in Table I (6368 candidates), while variationsinthesidebanddefinitions,smallmodifications only 2578 candidates are common to both samples. in the selection requirements, the use of an alternate fit The consistency check also uses an unbinned maxi- procedure which fits the sideband and the signal regions mum log-likelihoodfit to extract the B− mesonlifetime. c simultaneously, the mass resolution in the signal model, The signal mass model consists of a Gaussian distribu- the background fraction, and the three terms describing tion centered at the B− meson mass and a Cabibbo- c the exponentials in the background decay time model. suppressed B− →J/ψ K− Gaussian distribution cen- c No systematic effect was found to significantly exceed teredat60MeV/c2 belowthe B− mesonmasswitha 30 c thevariationsexpectedfromstatisticaluncertainties. We MeV/c2 width. The signaldecay-time model is an expo- assign an additional uncertainty of 0.010 ps as a conser- nential distribution convoluted with the detector resolu- vative approachto account for possible small systematic tion. Thebackgroundmassmodelisdescribedbyalinear effects. distribution, and the backgrounddecay-time model con- The systematic uncertainty due to tracking detector sists of two prompt Gaussian distributions, two positive misalignmentsisevaluatedbygeneratingsimulatedsam- exponential distributions, and one negative exponential ples with radial displacements of individual sensors as distribution. well as translation and rotation of the silicon detec- A similar two-step fit is used in the consistency tor relative to the COT [17]. A systematic uncertainty check. The first step is to determine the background of 0.007 ps is assigned to the misalignment based on parameters from the sideband fit, where the sideband − these simulated samples. The systematic uncertainty is defined as the J/ψ π invariant-mass region between from the signal mass model is evaluated by including 6.4 and 6.5 GeV/c2. The sideband fit is performed on − a contribution to the total B signal yield from the events with decay length between –1000 µm and 1000 c − − Cabibbo-suppressed decay B →J/ψ K in the signal µm and the resulting background parameters are fixed c mass shape. The Cabibbo-suppressed contribution is in the second step. In the second step we fit events in fixedtobe 5%ofthetotalB− signalyieldasdetermined the signal region between 6.16 and 6.36 GeV/c2, and c from the Cabibbo angle. This effect results in a 0.003ps only the signal fraction and signal model parameters 8 are allowed to float. The consistency check is first laboration [5] using semileptonic decay channels, τ = performedonthe B− candidates. Thefitresultfindsthe 0.448 +0.038(stat) ± 0.032(syst) ps, and has comparable −0.036 − B lifetime to be τ = 1.647 ± 0.020 (stat) ps, precision. The result also agrees with theoretical cal- − which agrees with the world-average value of culations in which the decay width of the B meson is c 1.641 ± 0.008 ps [13]. The consistency check is dominated by the decay of the charm quark. − − then applied to the B candidates, giving a B meson We thank the Fermilab staff and the technical staffs c c lifetime of τ = 0.450 ± 0.053 (stat) ps which is consis- of the participating institutions for their vital contribu- tent with our central value of 0.452 ± 0.048 (stat) ps. tions. This work was supportedby the U.S. Department − The B signal yield from the consistency check is of Energy and National Science Foundation; the Italian c 308 ± 39 (stat) which is compared with 272 ± 61 (stat) Istituto Nazionale di Fisica Nucleare; the Ministry of fromthecentralresult. Thetotalsystematicuncertainty Education, Culture, Sports, Science and Technology of in the consistency check is 0.033 ps where the largest Japan; the Natural Sciences and Engineering Research uncertainty of 0.027 ps comes from the background Council of Canada; the National Science Council of the decay-time model. Thus, we conclude that our central Republic of China; the Swiss National Science Founda- result obtained from the ct-dependent efficiency is tion; the A.P.SloanFoundation;the Bundesministerium reliable. fu¨rBildungundForschung,Germany;theKoreanWorld Class University Program, the National Research Foun- In conclusion, we have made the first measurement of dation of Korea; the Science and Technology Facilities − the B meson lifetime in a fully-reconstructed hadronic CouncilandtheRoyalSociety,UK;theRussianFounda- c − − decay mode. 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