Measurement of the �0 b lifetime in the exclusive decay�0 b ! J=c�0 in p �p collisions at ffiffiffi s p ¼ 1:96 TeV V.M. Abazov,32 B. Abbott,70 B. S. Acharya,26 M. Adams,46 T. Adams,44 G. D. Alexeev,32 G. Alkhazov,36 A. Alton,58,* G. Alverson,57 M. Aoki,45 A. Askew,44 S. Atkins,55 K. Augsten,7 C. Avila,5 F. Badaud,10 L. Bagby,45 B. Baldin,45 D.V. Bandurin,44 S. Banerjee,26 E. Barberis,57 P. Baringer,53 J. Barreto,2 J. F. Bartlett,45 U. Bassler,15 V. Bazterra,46 A. Bean,53 M. Begalli,2 L. Bellantoni,45 S. B. Beri,24 G. Bernardi,14 R. Bernhard,19 I. Bertram,39 M. Besançon,15 R. Beuselinck,40 V. A. Bezzubov,35 P. C. Bhat,45 S. Bhatia,60 V. Bhatnagar,24 G. Blazey,47 S. Blessing,44 K. Bloom,61 A. Boehnlein,45 D. Boline,67 E. E. Boos,34 G. Borissov,39 T. Bose,56 A. Brandt,73 O. Brandt,20 R. Brock,59 G. Brooijmans,65 A. Bross,45 D. Brown,14 J. Brown,14 X. B. Bu,45 M. Buehler,45 V. Buescher,21 V. Bunichev,34 S. Burdin,39,† C. P. Buszello,38 E. Camacho-Pérez,29 B. C.K. Casey,45 H. Castilla-Valdez,29 S. Caughron,59 S. Chakrabarti,67 D. Chakraborty,47 K.M. Chan,51 A. Chandra,75 E. Chapon,15 G. Chen,53 S. Chevalier-Théry,15 D. K. Cho,72 S.W. Cho,28 S. Choi,28 B. Choudhary,25 S. Cihangir,45 D. Claes,61 J. Clutter,53 M. Cooke,45 W. E. Cooper,45 M. Corcoran,75 F. Couderc,15 M.-C. Cousinou,12 A. Croc,15 D. Cutts,72 A. Das,42 G. Davies,40 S. J. de Jong,30,31 E. De La Cruz-Burelo,29 F. Déliot,15 R. Demina,66 D. Denisov,45 S. P. Denisov,35 S. Desai,45 C. Deterre,15 K. DeVaughan,61 H. T. Diehl,45 M. Diesburg,45 P. F. Ding,41 A. Dominguez,61 A. Dubey,25 L. V. Dudko,34 D. Duggan,62 A. Duperrin,12 S. Dutt,24 A. Dyshkant,47 M. Eads,61 D. Edmunds,59 J. Ellison,43 V.D. Elvira,45 Y. Enari,14 H. Evans,49 A. Evdokimov,68 V.N. Evdokimov,35 G. Facini,57 L. Feng,47 T. Ferbel,66 F. Fiedler,21 F. Filthaut,30,31 W. Fisher,59 H. E. Fisk,45 M. Fortner,47 H. Fox,39 S. Fuess,45 A. Garcia-Bellido,66 J. A. Garcı́a-González,29 G.A. Garcı́a-Guerra,29,‡ V. Gavrilov,33 P. Gay,10 W. Geng,12,59 D. Gerbaudo,63 C. E. Gerber,46 Y. Gershtein,62 G. Ginther,45,66 G. Golovanov,32 A. Goussiou,77 P. D. Grannis,67 S. Greder,16 H. Greenlee,45 G. Grenier,17 Ph. Gris,10 J.-F. Grivaz,13 A. Grohsjean,15,§ S. Grünendahl,45 M.W. Grünewald,27 T. Guillemin,13 G. Gutierrez,45 P. Gutierrez,70 A. Haas,65,k S. Hagopian,44 J. Haley,57 L. Han,4 K. Harder,41 A. Harel,66 J.M. Hauptman,52 J. Hays,40 T. Head,41 T. Hebbeker,18 D. Hedin,47 H. Hegab,71 A. P. Heinson,43 U. Heintz,72 C. Hensel,20 I. Heredia-De La Cruz,29 K. Herner,58 G. Hesketh,41,{M.D. Hildreth,51 R. Hirosky,76 T. Hoang,44 J. D. Hobbs,67 B. Hoeneisen,9 M. Hohlfeld,21 I. Howley,73 Z. Hubacek,7,15 V. Hynek,7 I. Iashvili,64 Y. Ilchenko,74 R. Illingworth,45 A. S. Ito,45 S. Jabeen,72 M. Jaffré,13 A. Jayasinghe,70 R. Jesik,40 K. Johns,42 E. Johnson,59 M. Johnson,45 A. Jonckheere,45 P. Jonsson,40 J. Joshi,43 A.W. Jung,45 A. Juste,37 K. Kaadze,54 E. Kajfasz,12 D. Karmanov,34 P. A. Kasper,45 I. Katsanos,61 R. Kehoe,74 S. Kermiche,12 N. Khalatyan,45 A. Khanov,71 A. Kharchilava,64 Y. N. Kharzheev,32 I. Kiselevich,33 J.M. Kohli,24 A.V. Kozelov,35 J. Kraus,60 S. Kulikov,35 A. Kumar,64 A. Kupco,8 T. Kurča,17 V. A. Kuzmin,34 S. Lammers,49 G. Landsberg,72 P. Lebrun,17 H. S. Lee,28 S.W. Lee,52 W.M. Lee,45 J. Lellouch,14 H. Li,11 L. Li,43 Q. Z. Li,45 J. K. Lim,28 D. Lincoln,45 J. Linnemann,59 V.V. Lipaev,35 R. Lipton,45 H. Liu,74 Y. Liu,4 A. Lobodenko,36 M. Lokajicek,8 R. Lopes de Sa,67 H. J. Lubatti,77 R. Luna-Garcia,29,** A. L. Lyon,45 A.K. A. Maciel,1 R. Madar,15 R. Magaña-Villalba,29 S. Malik,61 V. L. Malyshev,32 Y. Maravin,54 J. Martı́nez-Ortega,29 R. McCarthy,67 C. L. McGivern,53 M.M. Meijer,30,31 A. Melnitchouk,60 D. Menezes,47 P. G. Mercadante,3 M. Merkin,34 A. Meyer,18 J. Meyer,20 F. Miconi,16 N.K. Mondal,26 M. Mulhearn,76 E. Nagy,12 M. Naimuddin,25 M. Narain,72 R. Nayyar,42 H.A. Neal,58 J. P. Negret,5 P. Neustroev,36 T. Nunnemann,22 G. Obrant,36,§§ J. Orduna,75 N. Osman,12 J. Osta,51 M. Padilla,43 A. Pal,73 N. Parashar,50 V. Parihar,72 S. K. Park,28 R. Partridge,72,k N. Parua,49 A. Patwa,68 B. Penning,45 M. Perfilov,34 Y. Peters,41 K. Petridis,41 G. Petrillo,66 P. Pétroff,13 M.-A. Pleier,68 P. L.M. Podesta-Lerma,29,†† V.M. Podstavkov,45 A.V. Popov,35 M. Prewitt,75 D. Price,49 N. Prokopenko,35 J. Qian,58 A. Quadt,20 B. Quinn,60 M. S. Rangel,1 K. Ranjan,25 P. N. Ratoff,39 I. Razumov,35 P. Renkel,74 I. Ripp-Baudot,16 F. Rizatdinova,71 M. Rominsky,45 A. Ross,39 C. Royon,15 P. Rubinov,45 R. Ruchti,51 G. Sajot,11 P. Salcido,47 A. Sánchez-Hernández,29 M. P. Sanders,22 B. Sanghi,45 A. S. Santos,1,‡‡ G. Savage,45 L. Sawyer,55 T. Scanlon,40 R. D. Schamberger,67 Y. Scheglov,36 H. Schellman,48 S. Schlobohm,77 C. Schwanenberger,41 R. Schwienhorst,59 J. Sekaric,53 H. Severini,70 E. Shabalina,20 V. Shary,15 S. Shaw,59 A.A. Shchukin,35 R. K. Shivpuri,25 V. Simak,7 P. Skubic,70 P. Slattery,66 D. Smirnov,51 K. J. Smith,64 G. R. Snow,61 J. Snow,69 S. Snyder,68 S. Söldner-Rembold,41 L. Sonnenschein,18 K. Soustruznik,6 J. Stark,11 D.A. Stoyanova,35 M. Strauss,70 L. Stutte,45 L. Suter,41 P. Svoisky,70 M. Takahashi,41 M. Titov,15 V. V. Tokmenin,32 Y.-T. Tsai,66 K. Tschann-Grimm,67 D. Tsybychev,67 B. Tuchming,15 C. Tully,63 L. Uvarov,36 S. Uvarov,36 S. Uzunyan,47 R. Van Kooten,49 W.M. van Leeuwen,30 N. Varelas,46 E.W. Varnes,42 I. A. Vasilyev,35 P. Verdier,17 A.Y. Verkheev,32 L. S. Vertogradov,32 M. Verzocchi,45 M. Vesterinen,41 D. Vilanova,15 P. Vokac,7 H. D. Wahl,44 M.H. L. S. Wang,45 J. Warchol,51 G. Watts,77 M. Wayne,51 J. Weichert,21 L. Welty-Rieger,48 A. White,73 D. Wicke,23 M.R. J. Williams,39 G.W. Wilson,53 M. Wobisch,55 D. R. Wood,57 T. R. Wyatt,41 Y. Xie,45 PHYSICAL REVIEW D 85, 112003 (2012) 1550-7998=2012=85(11)=112003(8) 112003-1 � 2012 American Physical Society R. Yamada,45 W.-C. Yang,41 T. Yasuda,45 Y. A. Yatsunenko,32 W. Ye,67 Z. Ye,45 H. Yin,45 K. Yip,68 S.W. Youn,45 J. Zennamo,64 T. Zhao,77 T. G. Zhao,41 B. Zhou,58 J. Zhu,58 M. Zielinski,66 D. Zieminska,49 and L. Zivkovic72 (D0 Collaboration) 1LAFEX, Centro Brasileiro de Pesquisas Fı́sicas, Rio de Janeiro, Brazil 2Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 3Universidade Federal do ABC, Santo André, Brazil 4University of Science and Technology of China, Hefei, People’s Republic of China 5Universidad de los Andes, Bogotá, Colombia 6Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic 7Czech Technical University in Prague, Prague, Czech Republic 8Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 9Universidad San Francisco de Quito, Quito, Ecuador 10LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France 11LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France 12CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 13LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France 14LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France 15CEA, Irfu, SPP, Saclay, France 16IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France 17IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France 18III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany 19Physikalisches Institut, Universität Freiburg, Freiburg, Germany 20II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 21Institut für Physik, Universität Mainz, Mainz, Germany 22Ludwig-Maximilians-Universität München, München, Germany 23Fachbereich Physik, Bergische Universität Wuppertal, Wuppertal, Germany 24Panjab University, Chandigarh, India 25Delhi University, Delhi, India 26Tata Institute of Fundamental Research, Mumbai, India 27University College Dublin, Dublin, Ireland 28Korea Detector Laboratory, Korea University, Seoul, Korea 29CINVESTAV, Mexico City, Mexico 30Nikhef, Science Park, Amsterdam, The Netherlands 31Radboud University Nijmegen, Nijmegen, The Netherlands 32Joint Institute for Nuclear Research, Dubna, Russia 33Institute for Theoretical and Experimental Physics, Moscow, Russia 34Moscow State University, Moscow, Russia 35Institute for High Energy Physics, Protvino, Russia 36Petersburg Nuclear Physics Institute, St. Petersburg, Russia 37Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Fı́sica d’Altes Energies (IFAE), Barcelona, Spain 38Uppsala University, Uppsala, Sweden 39Lancaster University, Lancaster LA1 4YB, United Kingdom 40Imperial College London, London SW7 2AZ, United Kingdom 41The University of Manchester, Manchester M13 9PL, United Kingdom 42University of Arizona, Tucson, Arizona 85721, USA 43University of California Riverside, Riverside, California 92521, USA 44Florida State University, Tallahassee, Florida 32306, USA 45Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 46University of Illinois at Chicago, Chicago, Illinois 60607, USA 47Northern Illinois University, DeKalb, Illinois 60115, USA 48Northwestern University, Evanston, Illinois 60208, USA 49Indiana University, Bloomington, Indiana 47405, USA 50Purdue University Calumet, Hammond, Indiana 46323, USA 51University of Notre Dame, Notre Dame, Indiana 46556, USA 52Iowa State University, Ames, Iowa 50011, USA 53University of Kansas, Lawrence, Kansas 66045, USA 54Kansas State University, Manhattan, Kansas 66506, USA 55Louisiana Tech University, Ruston, Louisiana 71272, USA V.M. ABAZOV et al. PHYSICAL REVIEW D 85, 112003 (2012) 112003-2 56Boston University, Boston, Massachusetts 02215, USA 57Northeastern University, Boston, Massachusetts 02115, USA 58University of Michigan, Ann Arbor, Michigan 48109, USA 59Michigan State University, East Lansing, Michigan 48824, USA 60University of Mississippi, University, Mississippi 38677, USA 61University of Nebraska, Lincoln, Nebraska 68588, USA 62Rutgers University, Piscataway, New Jersey 08855, USA 63Princeton University, Princeton, New Jersey 08544, USA 64State University of New York, Buffalo, New York 14260, 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 71Oklahoma State University, Stillwater, Oklahoma 74078, USA 72Brown University, Providence, Rhode Island 02912, USA 73University of Texas, Arlington, Texas 76019, USA 74Southern Methodist University, Dallas, Texas 75275, USA 75Rice University, Houston, Texas 77005, USA 76University of Virginia, Charlottesville, Virginia 22901, USA 77University of Washington, Seattle, Washington 98195, USA (Received 13 April 2012; published 7 June 2012) We measure the �0 b lifetime in the fully reconstructed decay �0 b ! J=c�0 using 10:4 fb�1 of p �p collisions collected with the D0 detector at ffiffiffi s p ¼ 1:96 TeV. The lifetime of the topologically similar decay channel B0 ! J=cK0 S is also measured. We obtain �ð�0 bÞ ¼ 1:303� 0:075ðstatÞ � 0:035ðsystÞ ps and �ðB0Þ ¼ 1:508� 0:025ðstatÞ � 0:043ðsystÞ ps. Using these measurements, we determine the lifetime ratio of �ð�0 bÞ=�ðB0Þ ¼ 0:864� 0:052ðstatÞ � 0:033ðsystÞ. DOI: 10.1103/PhysRevD.85.112003 PACS numbers: 14.20.Mr, 13.25.Hw, 13.30.Eg, 14.40.Nd Lifetime measurements of particles containing b quarks provide important tests of the significance of strong inter- actions between the constituent partons in the weak decay of b hadrons. These interactions produce measurable dif- ferences between b hadron lifetimes that the heavy quark expansion (HQE) [1] predicts with good accuracy through the calculation of lifetime ratios. While the agreement of the ratios between experimental measurements and HQE is excellent for B mesons [2], there are remaining discrep- ancies between experimental results and theoretical pre- dictions for b baryons. Recently, the CDF Collaboration [3] used the exclusive decay �0 b ! J=c�0 to report the single most precise determination of the �0 b lifetime which is more than 2 standard deviations higher than the world average [4] and slightly higher than the B0 lifetime. The CDF measurement of the lifetime ratio, �ð�0 bÞ=�ðB0Þ, is higher than the HQE calculation including Oð1=m4 bÞ effects, 0:88� 0:05 [5,6]. On the other hand, theoretical predictions are in agreement with measurements by the D0 Collaboration in the J=c�0 [7] and semileptonic [8] channels, by the CDF Collaboration in the �þ c � � final state [9], by the DELPHI, OPAL, and ALEPH Collaborations in semileptonic decays [10–12], and pre- vious measurements also in semileptonic channels by the CDF Collaboration [13]. More measurements of the �0 b lifetime and of the ratio �ð�0 bÞ=�ðB0Þ are required to re- solve this discrepancy. In this article we report a measurement of the �0 b life- time using the exclusive decay �0 b ! J=c�0. The B0 lifetime is also measured in the topologically similar chan- nel B0 ! J=cK0 S. This provides a cross-check of the mea- surement procedure, and allows the lifetime ratio to be determined directly. The data used in this analysis were collected with the D0 detector during the complete Run II of the Tevatron Collider, from 2002 to 2011, and corre- spond to an integrated luminosity of 10:4 fb�1 of p �p collisions at a center-of-mass energy ffiffiffi s p ¼ 1:96 TeV. A detailed description of the D0 detector can be found in Refs. [14–17]. Here, we describe briefly the most relevant detector components used in this analysis. The D0 central *Visitor from Augustana College, Sioux Falls, SD, USA. †Visitor from The University of Liverpool, Liverpool, UK. ‡Visitor from UPIITA-IPN, Mexico City, Mexico. §Visitor from DESY, Hamburg, Germany. kVisitor from SLAC, Menlo Park, CA, USA. {Visitor from University College London, London, UK. **Visitor from Centro de Investigacion en Computacion - IPN, Mexico City, Mexico. ††Visitor from ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico. ‡‡Visitor from Universidade Estadual Paulista, São Paulo, Brazil. §§Deceased. MEASUREMENT OF THE �0 b LIFETIME IN . . . PHYSICAL REVIEW D 85, 112003 (2012) 112003-3 http://dx.doi.org/10.1103/PhysRevD.85.112003 tracking system is composed of a silicon microstrip tracker (SMT) and a central scintillating fiber tracker (CFT) im- mersed in a 2 T solenoidal field. The SMT and the CFT are optimized for tracking and vertexing for the pseudorapidity region j�j< 3:0 and j�j< 2:0, respectively, where � � � ln½tanð�=2Þ� and � is the polar angle with respect to the proton beam direction. Preshower detectors and electro- magnetic and hadronic calorimeters surround the tracker. Amuon spectrometer is located beyond the calorimeter, and consists of three layers of drift tubes and scintillation trigger counters covering j�j< 2:0. A 1.8 T toroidal ironmagnet is located outside the innermost layer of the muon detector. For all Monte Carlo (MC) simulations in this article, we use PYTHIA [18] to simulate the p �p collisions, EVTGEN [19] for modeling the decay of particles containing b and c quarks, and GEANT [20] to model the detector response. Multiple p �p interactions are modeled by overlaying hits from random bunch crossings onto the MC. In order to reconstruct the �0 b and B0 candidates, we start by searching for J=c ! �þ�� candidates, which are collected by single muon and dimuon triggers. The triggers used do not rely on the displacement of tracks from the interaction point. At least one p �p interaction vertex (PV) must be identified in each event. The interaction vertices are found by minimizing a �2 function that depends on all reconstructed tracks in the event and uses the transverse beam position averaged over multiple beam crossings. The resolution of the PV is� 20 �m in the plane perpendicular to the beam (transverse plane). Muon candidates are re- constructed from tracks formed by hits in the central tracking system and with transverse momentum (pT) greater than 1 GeV=c. At least one muon candidate in the event must have hits in the inner layer, and in at least one outer layer of the muon detector. A second muon candidate, with opposite charge, must either be detected in the innermost layer of the muon system or have a calorimeter energy deposit consistent with that of a minimum-ionizing particle along the direction of hits ex- trapolated from the central tracking system. Each muon track is required to have at least two hits in the SMT and two hits in the CFT to ensure a high quality commonvertex. The probability associated with the vertex fit must exceed 1%. The dimuon invariantmass is required to be in the range 2:80–3:35 GeV=c2, consistent with the J=c mass. Events with J=c candidates are reprocessed with a version of the track reconstruction algorithm that identifies with increased efficiency the low pT and high impact parameter tracks resulting from the decay of �0 and K0 S [21], without introducing any biases in the decay time distribution. We then search for �0 ! p�� candidates reconstructed from pairs of oppositely charged tracks. The tracks must form a vertex with a probability associated with the vertex fit greater than 1%. The transverse impact parameter significance (the transverse impact parameter with respect to the PV divided by its uncertainty) for the two tracks forming�0 candidates must exceed 2, and 4 for at least one of them. Each �0 candidate is required to have a mass in the range 1:105–1:127 GeV=c2. The track with the higher pT is assigned the proton mass. MC simulations indicate that this is always the correct assumption, given the track pT detection threshold of 120 MeV=c. To sup- press contamination from decays of more massive baryons such as �0 ! �0� and �0 ! �0�0, the �0 momentum vector must point within 1� back to the J=c vertex. The same selection criteria are applied in the selection of K0 S ! �þ�� candidates, except that the mass window is chosen in the range 0:470–0:525 GeV=c2 and pion mass assign- ments are used. Track pairs simultaneously reconstructed as both�0 andK0 S, due to different mass assignments to the same tracks, are discarded from both samples. This re- quirement rejects 23% (6%) of the �0 b ! J=c�0 (B0 ! J=cK0 S) signal, as estimated from MC, without introduc- ing biases in the lifetime measurement. The fraction of background rejected by this requirement is 58% (48%) as estimated from data. It is important to remove these back- grounds from the samples to avoid the introduction of biases in the lifetime measurements. The �0 b candidates are reconstructed by performing a kinematic fit that constrains the dimuon invariant mass to the world average J=c mass [4], and the�0 and two muon tracks to a common vertex, where the �0 has been ex- trapolated from its decay vertex according to the recon- structed �0 momentum vector. The invariant mass of the �0 b candidate is required to be within the range 5:15–6:05 GeV=c2. The PV is recalculated excluding the �0 b final decay products. The final selection requirements are obtained by maximizing S ¼ S= ffiffiffiffiffiffiffiffiffiffiffiffiffi Sþ B p , where S (B) is the number of signal (background) candidates in the data sample: the decay length of the �0 (measured from the �0 b vertex) and its significance are required to be greater than 0.3 cm and 3.5, respectively; the pT of the J=c ,�0, and�0 daughter tracks are required to be greater than 4.5, 1.8, and 0:3 GeV=c, respectively; and the isolation of the�0 b [22] is required to be greater than 0.35. After this optimization, if more than one candidate is found in the event, which happens in less than 0.3% of the selected events, the candidate with the best �0 b decay vertex fit probability is chosen. We have verified that this selection is unbiased by varying the selection values chosen by the optimization as described in more detail later. The same selection criteria are applied to B0 ! J=cK0 S decays, except that the B0 mass window is chosen in the range 4:9–5:7 GeV=c2. The samples of �0 b and B0 candidates have two primary background contributions: combinatorial background and partially reconstructed b hadron decays. The combinatorial background can be divided in two categories: prompt background, which accounts for � 70% of the total back- ground, primarily due to direct production of J=c mesons; and nonprompt background, mainly produced by random combinations of a J=c meson from a b hadron and a �0 V.M. ABAZOV et al. PHYSICAL REVIEW D 85, 112003 (2012) 112003-4 (K0 S) candidate in the event. Contamination from partially reconstructed b hadrons comes from b baryons (Bmesons) decaying to a J=c meson, a �0 baryon (K0 S meson), and additional decay products that are not reconstructed. We define the transverse proper decay length as � ¼ cMLxy=pT , where M is the mass of the b hadron taken from the PDG [4], and Lxy is the vector pointing from the PV to the b hadron decay vertex projected on the b hadron transverse momentum ( ~pT) direction. Because of the fact that signal and partially reconstructed b hadron decays have similar � distributions that are particularly hard to disentangle in the lifetime fit, we remove partially recon- structed b hadrons by rejecting events with �0 b (B 0) invari- ant mass below 5:42ð5:20Þ GeV=c2 from the �0 b (B0) sample, as shown in Fig. 1. This figure shows the �0 b and B0 invariant mass distributions with results of unbinned maximum likelihood fits superimposed, excluding events in zones contaminated by partially reconstructed b had- rons. The signal peak is modeled by a Gaussian function. The combinatorial background is parametrized by an ex- ponentially decaying function, while partially recon- structed b hadrons are derived from MC. It can be seen from Fig. 1 that partially reconstructed b hadrons contrib- ute minimally to the signal mass region. In order to extract the lifetimes, we perform separate unbinned maximum likelihood fits for �0 b and B0 candi- dates. The likelihood function (L) depends on the proba- bility of reconstructing each candidate event j in the sample with the mass mj, the proper decay length �j, and proper decay length uncertainty � j : L ¼Y j ½fsF sðmj;�j; � j Þþð1�fsÞF bðmj;�j; � j Þ�; (1) where fs is the fraction of signal events, andF s (F b) is the product of the probability distribution functions that model each of the three observables being considered for signal (background) events. The background is further divided into prompt and nonprompt components. For the signal, the mass distribution is modeled by a Gaussian function; the � distribution is parametrized by an exponential decay, e��j=c�=c�, convoluted with a Gaussian function R ¼ e��2 j =2ðs � j Þ2= ffiffiffiffiffiffiffi 2� p s � j that models the detector resolution; the � distribution is obtained from MC simulation and parametrized by a superposition of Gaussian functions. Here � is the lifetime of the b hadron, and the event-by-event uncertainty � j is scaled by a global factor s to take into account a possible underestimation of the uncertainty. The mass distribution of the prompt component of the background is parameterized by a constant function, sincewe observe that the total amount of background is reduced uniformly over the entire mass range when the requirement � > 100 �m is applied. The nonprompt component of the background is modeled by an exponential function, as observed using the data satisfying this requirement. The prompt component of the � distribution is parametrized by the resolution function, and the nonprompt component by the superposition of two exponential decays for� < 0 and two exponential decays for � > 0, as observed from events in the high-mass sideband of the b hadron peak (above 5.80 and 5:45 GeV=c2 for�0 b and B0, respectively). Finally, the background � distribution is modeled by two exponential functions convoluted with a Gaussian function as determined empirically from the high- mass sideband region. All the events, except for those corre- sponding to the invariant mass region contaminated by par- tially reconstructed b hadrons, are used in each likelihood fit to determine a total of 19 parameters: lifetime, mean, and width of the signal mass, signal fraction, prompt background fraction, one nonprompt background mass parameter, seven nonprompt background � parameters, five background � parameters, and one resolution scale factor. ]2c) [GeV/0Λψ/JMass ( 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 2 c C an di da te s pe r 18 M eV / 0 100 200 300 400 500 -1(a) DØ, 10.4 fb Data Data fit Signal Combinatorial Partially recon- hadronsbstructed ]2c) [GeV/0 SKψ/JMass ( 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 2 c C an di da te s pe r 12 M eV / 0 200 400 600 800 1000 1200 -1(b) DØ, 10.4 fb Data Data fit Signal Combinatorial Partially recon- hadronsbstructed FIG. 1 (color online). Invariant mass distributions for (a) �0 b ! J=c�0 and (b) B0 ! J=cK0 S candidates, with fit results super- imposed. Events in mass regions contaminated with partially reconstructed b hadrons (hatched region) are excluded from the maximum likelihood function used to determine the �0 b and B0 lifetimes. MEASUREMENT OF THE �0 b LIFETIME IN . . . PHYSICAL REVIEW D 85, 112003 (2012) 112003-5 The maximum likelihood fits to the data yield c�ð�0 bÞ¼390:7�22:4�m and c�ðB0Þ¼452:2�7:6�m. Figure 2 shows the � distributions for the �0 b and the B0 candidates. Fit results are superimposed. The numbers of signal events, derived from fs, are 755� 49 (�0 b) and 5671� 126 (B0). The ratios of the event yields in this and in the previous measurement [7] do not scale with the integrated luminosity because the most recent D0 data was collected at higher instantaneous luminosities, which required tighter, and less efficient, trigger require- ments and also resulted in a reduction of the reconstruction efficiency caused by the presence of multiple interactions in a single bunch crossing. We investigate possible sources of systematic uncertain- ties on the measured lifetimes related to the models used to describe the mass, �, and � distributions. For the mass we consider a double Gaussian to model the signal peak instead of the nominal single Gaussian, an exponential function for the prompt background in place of a constant function, and a second-order polynomial for the nonprompt background. The alternative mass models are combined in a single maximum likelihood fit to take into account cor- relations between the effects of the different models, and the difference with respect to the result of the nominal fit is quoted as the systematic uncertainty on the mass model. For �we study the following variations: the introduction of a second Gaussian function along with a second scale factor to model the resolution, the exponential functions in the nonprompt background replaced by exponentials convoluted with the resolution function, one nonprompt negative exponential instead of two, and one long positive exponential together with a double-Gaussian resolution as a substitute for two nonprompt exponentials and one Gaussian resolution. All � model changes are combined in a fit, and the difference between the results of this fit and the nominal fit is quoted as the systematic uncertainty due to � parametrization. For � we use two different ap- proaches: we use the distribution extracted from data by background subtraction, parameterized similarly to the nominal background � model, instead of the MC model, and we use � distributions from MC samples generated with different �0 b (B0) lifetimes. The largest variation in the lifetime (with respect to the nominal measurement) between these two alternative approaches is quoted as the systematic uncertainty due to � parametrization. Residual effects due to contamination from partially reconstructed b hadrons in the samples are investigated by changing the requirement on the invariant mass of the �0 b and B0 candidates that are included in the likelihood fits: the threshold is moved to lower (higher) invariant masses by 40ð20Þ MeV=c2, where 40 MeV=c2 is the resolution on the invariant mass of the reconstructed signal. The largest variation in the lifetime is quoted as the systematic uncer- tainty due to possible contamination from partially recon- structed b hadrons. In the lifetime fit the contamination from the fully reconstructed decay B0 s ! J=cK0 S is as- sumed to have little impact on the final result. To test this assumption the B0 s ! J=cK0 S contribution is included in the nonprompt component. The lifetime shift is found to be negligible. The systematic uncertainty due to the alignment of the SMT detector was estimated in a previous study [7] by reconstructing the B0 sample with the positions of the SMT sensors shifted outwards radially by the alignment uncertainty and then fitting for the lifetime. The systematic uncertainties are summarized in Table I. We perform several cross-checks of the lifetime mea- surements. We extract the signal yield in bins of � by fitting the mass distribution in each of these regions. From these measurements, lifetimes are obtained by the �2 minimiza- tion of the signal yield expected in each � bin according to mµ C an di da te s pe r 50 1 10 210 310 -1(a) DØ, 10.4 fb Data Data fit Signal Background ) [cm]0Λψ/J (λ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 da ta σ da ta - fi t -2 0 2 mµ C an di da te s pe r 50 1 10 210 310 -1(b) DØ, 10.4 fb Data Data fit Signal Background ) [cm]0 SKψ/J (λ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 da ta σ da ta - fi t -2 0 2 FIG. 2 (color online). Proper decay length distributions for (a) �0 b ! J=c�0 and (b) B0 ! J=cK0 S candidates, with fit results superimposed. Residuals normalized by the corresponding uncertainty in each bin are given in the bottom panel. V.M. ABAZOV et al. PHYSICAL REVIEW D 85, 112003 (2012) 112003-6 the first term in Eq. (1). While this method is statistically inferior with respect to the maximum likelihood fit, it is also less dependent on the modeling of the different back- ground components. The results of this study are c��0 b ¼ 391:4� 35:8ðstatÞ �m and c�B0 ¼ 458:3� 8:9ðstatÞ �m. The sample is also split into different data taking periods,� regions, and numbers of hits in the SMT detector. All results obtained with these variations are consistent with our measurement. In order to check that the optimization procedure does not give a potential bias to the selection, we verify that our results remain stable when all requirements in variables used in the optimization process are removed one at a time, when looser and tighter requirements are applied to kinematic variables, and when multiple candi- dates that pass all selection requirements per event are allowed. The results also remain stable after removing the high-end tail (above 100 �m) of the � distribution, mainly populated by background events. We also cross- check the fitting procedure and selection criteria by mea- suring the�0 b and B 0 lifetimes in MC events. The lifetimes obtained are consistent with the input values. In summary, using the full data sample collected by the D0 experiment, we measure the lifetime of the �0 b baryon in the J=c�0 final state to be �ð�0 bÞ ¼ 1:303� 0:075ðstatÞ � 0:035ðsystÞ ps; (2) consistent with the world average, 1:425� 0:032 ps [4]. The method to measure the �0 b lifetime is also used for B0 ! J=cK0 S decays, for which we obtain �ðB0Þ ¼ 1:508� 0:025ðstatÞ � 0:043ðsystÞ ps; (3) in good agreement with the world average, 1:519� 0:007 ps [4]. Using these measurements we calculate the ratio of lifetimes, �ð�0 bÞ �ðB0Þ ¼ 0:864� 0:052ðstatÞ � 0:033ðsystÞ; (4) where the systematic uncertainty is determined from the differences between the lifetime ratio obtained for each systematic variation and the ratio of the nominal measure- ments, and combining theses differences in quadrature, as shown in Table I. Our result, 0:86� 0:06, is in good agreement with the HQE prediction of 0:88� 0:05 [5] and compatible with the current world average, 1:00� 0:06 [4], but differs with the latest measurement of the CDF Collaboration, 1:02� 0:03 [3], at the 2.2 standard deviations level. Our measurements supersede the previous D0 results of �ð�0 bÞ, �ðB0Þ, and �ð�0 bÞ=�ðB0Þ [7]. We thank the staffs at Fermilab and collaborating insti- tutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); MON, Rosatom and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); NRF (Korea); FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China). [1] G. Bellini, I. I. Y. Bigi, and P. J. Dornan, Phys. Rep. 289, 1 (1997). [2] A. J. Lenz, AIP Conf. Proc. 1026, 36 (2008). [3] T. 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Individual uncertainties are combined in quadrature to obtain the total uncertainties. Source �0 b (�m) B0 (�m) Ratio Mass model 2.2 6.4 0.008 Proper decay length model 7.8 3.7 0.024 Proper decay length uncertainty 2.5 8.9 0.020 Partially reconstructed b hadrons 2.7 1.3 0.008 B0 s ! J=cK0 S — 0.4 0.001 Alignment 5.4 5.4 0.002 Total 10.4 12.9 0.033 MEASUREMENT OF THE �0 b LIFETIME IN . . . 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[22] Isolation is defined as pðBÞ=½pðBÞ þP <�Rp�, where pðBÞ is the momentum of the b hadron and the sum, excluding the decay products of the b hadron, is over the momentum of all particles from the PV within the larger �Rð��; b hadronÞ cone in pseudorapidity-azimuthal angle space, defined as �R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ��2 þ� 2 p . V.M. ABAZOV et al. 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