Determination of the width of the top quark

arXiv:1009.5686v1 [hep-ex] 28 Sep 2010

Determination of the width of the top quark

V.M. Abazov,35 _{B. Abbott,}73 _{M. Abolins,}62 _{B.S. Acharya,}29 _{M. Adams,}48 _{T. Adams,}46 _{G.D. Alexeev,}35 G. Alkhazov,39_{A. Alton}a_,61_{G. Alverson,}60 _{G.A. Alves,}2 _{L.S. Ancu,}34 _{M. Aoki,}47 _{Y. Arnoud,}14 _{M. Arov,}57 A. Askew,46 _{B. ˚Asman,}40 _{O. Atramentov,}65_{C. Avila,}8 _{J. BackusMayes,}80_{F. Badaud,}13_{L. Bagby,}47_{B. Baldin,}47

D.V. Bandurin,46 _{S. Banerjee,}29 _{E. Barberis,}60 _{P. Baringer,}55 _{J. Barreto,}2 _{J.F. Bartlett,}47 _{U. Bassler,}18 V. Bazterra,48 _{S. Beale,}6 _{A. Bean,}55 _{M. Begalli,}3 _{M. Begel,}71 _{C. Belanger-Champagne,}40_{L. Bellantoni,}47 S.B. Beri,27 _{G. Bernardi,}17 _{R. Bernhard,}22 _{I. Bertram,}41_{M. Besan¸con,}18 _{R. Beuselinck,}42 _{V.A. Bezzubov,}38 P.C. Bhat,47 _{V. Bhatnagar,}27 _{G. Blazey,}49 _{S. Blessing,}46_{K. Bloom,}64 _{A. Boehnlein,}47 _{D. Boline,}70 _{T.A. Bolton,}56

E.E. Boos,37_{G. Borissov,}41_{T. Bose,}59 _{A. Brandt,}76 _{O. Brandt,}23 _{R. Brock,}62 _{G. Brooijmans,}68 _{A. Bross,}47 D. Brown,17 _{J. Brown,}17_{X.B. Bu,}7 _{D. Buchholz,}50_{M. Buehler,}79 _{V. Buescher,}24 _{V. Bunichev,}37 _{S. Burdin}b_,41 T.H. Burnett,80 _{C.P. Buszello,}42_{B. Calpas,}15_{E. Camacho-P´erez,}32_{M.A. Carrasco-Lizarraga,}32_{B.C.K. Casey,}47

H. Castilla-Valdez,32 _{S. Chakrabarti,}70 _{D. Chakraborty,}49 _{K.M. Chan,}53 _{A. Chandra,}78 _{G. Chen,}55 S. Chevalier-Th´ery,18 _{D.K. Cho,}75 _{S.W. Cho,}31 _{S. Choi,}31_{B. Choudhary,}28 _{T. Christoudias,}42 _{S. Cihangir,}47 D. Claes,64 _{J. Clutter,}55 _{M. Cooke,}47 _{W.E. Cooper,}47 _{M. Corcoran,}78_{F. Couderc,}18_{M.-C. Cousinou,}15 _{A. Croc,}18

D. Cutts,75 _{M. ´Cwiok,}30_{A. Das,}44 _{G. Davies,}42 _{K. De,}76 _{S.J. de Jong,}34_{E. De La Cruz-Burelo,}32 _{F. D´eliot,}18 M. Demarteau,47 _{R. Demina,}69 _{D. Denisov,}47 _{S.P. Denisov,}38 _{S. Desai,}47 _{K. DeVaughan,}64 _{H.T. Diehl,}47 M. Diesburg,47 _{A. Dominguez,}64 _{T. Dorland,}80 _{A. Dubey,}28 _{L.V. Dudko,}37_{D. Duggan,}65_{A. Duperrin,}15 _{S. Dutt,}27

A. Dyshkant,49 _{M. Eads,}64 _{D. Edmunds,}62 _{J. Ellison,}45 _{V.D. Elvira,}47 _{Y. Enari,}17_{S. Eno,}58 _{H. Evans,}51 A. Evdokimov,71 _{V.N. Evdokimov,}38_{G. Facini,}60 _{T. Ferbel,}58, 69 _{F. Fiedler,}24 _{F. Filthaut,}34 _{W. Fisher,}62 H.E. Fisk,47 _{M. Fortner,}49_{H. Fox,}41 _{S. Fuess,}47 _{T. Gadfort,}71 _{A. Garcia-Bellido,}69 _{V. Gavrilov,}36_{P. Gay,}13 W. Geist,19 _{W. Geng,}15, 62 _{D. Gerbaudo,}66 _{C.E. Gerber,}48 _{Y. Gershtein,}65_{G. Ginther,}47, 69 _{G. Golovanov,}35 A. Goussiou,80 _{P.D. Grannis,}70 _{S. Greder,}19 _{H. Greenlee,}47 _{Z.D. Greenwood,}57_{E.M. Gregores,}4_{G. Grenier,}20

Ph. Gris,13 _{J.-F. Grivaz,}16 _{A. Grohsjean,}18 _{S. Gr¨unendahl,}47 _{M.W. Gr¨unewald,}30 _{F. Guo,}70 _{J. Guo,}70 G. Gutierrez,47 _{P. Gutierrez,}73 _{A. Haas}c_,68 _{S. Hagopian,}46 _{J. Haley,}60 _{L. Han,}7 _{K. Harder,}43_{A. Harel,}69 J.M. Hauptman,54 _{J. Hays,}42 _{T. Head,}43 _{T. Hebbeker,}21 _{D. Hedin,}49_{H. Hegab,}74 _{A.P. Heinson,}45 _{U. Heintz,}75

C. Hensel,23 _{I. Heredia-De La Cruz,}32_{K. Herner,}61 _{G. Hesketh,}60 _{M.D. Hildreth,}53 _{R. Hirosky,}79 _{T. Hoang,}46 J.D. Hobbs,70_{B. Hoeneisen,}12 _{M. Hohlfeld,}24 _{S. Hossain,}73 _{Z. Hubacek,}10_{N. Huske,}17_{V. Hynek,}10 _{I. Iashvili,}67 R. Illingworth,47 _{A.S. Ito,}47 _{S. Jabeen,}75 _{M. Jaffr´e,}16 _{S. Jain,}67 _{D. Jamin,}15_{R. Jesik,}42 _{K. Johns,}44 _{M. Johnson,}47 D. Johnston,64_{A. Jonckheere,}47_{P. Jonsson,}42_{J. Joshi,}27_{A. Juste}d_,47 _{K. Kaadze,}56 _{E. Kajfasz,}15_{D. Karmanov,}37

P.A. Kasper,47_{I. Katsanos,}64_{R. Kehoe,}77 _{S. Kermiche,}15 _{N. Khalatyan,}47_{A. Khanov,}74 _{A. Kharchilava,}67 Y.N. Kharzheev,35 _{D. Khatidze,}75 _{M.H. Kirby,}50 _{J.M. Kohli,}27 _{A.V. Kozelov,}38_{J. Kraus,}62 _{A. Kumar,}67 A. Kupco,11 _{T. Kurˇca,}20 _{V.A. Kuzmin,}37 _{J. Kvita,}9 _{S. Lammers,}51 _{G. Landsberg,}75_{P. Lebrun,}20 _{H.S. Lee,}31 S.W. Lee,54_{W.M. Lee,}47_{J. Lellouch,}17_{L. Li,}45_{Q.Z. Li,}47 _{S.M. Lietti,}5 _{J.K. Lim,}31 _{D. Lincoln,}47_{J. Linnemann,}62

V.V. Lipaev,38 _{R. Lipton,}47 _{Y. Liu,}7 _{Z. Liu,}6 _{A. Lobodenko,}39_{M. Lokajicek,}11 _{P. Love,}41 _{H.J. Lubatti,}80 R. Luna-Garciae_,32 _{A.L. Lyon,}47 _{A.K.A. Maciel,}2 _{D. Mackin,}78_{R. Madar,}18 _{R. Maga˜na-Villalba,}32 _{S. Malik,}64

V.L. Malyshev,35_{Y. Maravin,}56 _{J. Mart´ınez-Ortega,}32 _{R. McCarthy,}70 _{C.L. McGivern,}55 _{M.M. Meijer,}34 A. Melnitchouk,63 _{D. Menezes,}49 _{P.G. Mercadante,}4 _{M. Merkin,}37 _{A. Meyer,}21_{J. Meyer,}23 _{N.K. Mondal,}29

G.S. Muanza,15 _{M. Mulhearn,}79 _{E. Nagy,}15 _{M. Naimuddin,}28 _{M. Narain,}75 _{R. Nayyar,}28 _{H.A. Neal,}61 J.P. Negret,8 _{P. Neustroev,}39 _{S.F. Novaes,}5 _{T. Nunnemann,}25 _{G. Obrant,}39 _{J. Orduna,}32 _{N. Osman,}42 J. Osta,53 _{G.J. Otero y Garz´on,}1 _{M. Owen,}43 _{M. Padilla,}45 _{M. Pangilinan,}75 _{N. Parashar,}52 _{V. Parihar,}75 S.K. Park,31_{J. Parsons,}68_{R. Partridge}c_,75 _{N. Parua,}51_{A. Patwa,}71_{B. Penning,}47_{M. Perfilov,}37 _{K. Peters,}43

Y. Peters,43 _{G. Petrillo,}69 _{P. P´etroff,}16 _{R. Piegaia,}1 _{J. Piper,}62 _{M.-A. Pleier,}71 _{P.L.M. Podesta-Lerma}f_,32 V.M. Podstavkov,47 _{M.-E. Pol,}2 _{P. Polozov,}36 _{A.V. Popov,}38 _{M. Prewitt,}78 _{D. Price,}51 _{S. Protopopescu,}71 J. Qian,61_{A. Quadt,}23 _{B. Quinn,}63 _{M.S. Rangel,}2_{K. Ranjan,}28 _{P.N. Ratoff,}41 _{I. Razumov,}38 _{P. Renkel,}77 P. Rich,43 _{M. Rijssenbeek,}70 _{I. Ripp-Baudot,}19 _{F. Rizatdinova,}74 _{M. Rominsky,}47 _{C. Royon,}18 _{P. Rubinov,}47 R. Ruchti,53 _{G. Safronov,}36 _{G. Sajot,}14_{A. S´anchez-Hern´andez,}32_{M.P. Sanders,}25_{B. Sanghi,}47_{A.S. Santos,}5 G. Savage,47_{L. Sawyer,}57 _{T. Scanlon,}42 _{R.D. Schamberger,}70_{Y. Scheglov,}39 _{H. Schellman,}50 _{T. Schliephake,}26 S. Schlobohm,80 _{C. Schwanenberger,}43_{R. Schwienhorst,}62 _{J. Sekaric,}55 _{H. Severini,}73 _{E. Shabalina,}23 _{V. Shary,}18

A.A. Shchukin,38 _{R.K. Shivpuri,}28 _{V. Simak,}10 _{V. Sirotenko,}47 _{P. Skubic,}73 _{P. Slattery,}69 _{D. Smirnov,}53 K.J. Smith,67 _{G.R. Snow,}64 _{J. Snow,}72 _{S. Snyder,}71_{S. S¨oldner-Rembold,}43_{L. Sonnenschein,}21 _{A. Sopczak,}41 M. Sosebee,76 _{K. Soustruznik,}9_{B. Spurlock,}76 _{J. Stark,}14 _{V. Stolin,}36 _{D.A. Stoyanova,}38 _{E. Strauss,}70_{M. Strauss,}73

D. Strom,48 _{L. Stutte,}47 _{P. Svoisky,}73_{M. Takahashi,}43 _{A. Tanasijczuk,}1 _{W. Taylor,}6_{M. Titov,}18 _{V.V. Tokmenin,}35 D. Tsybychev,70_{B. Tuchming,}18_{C. Tully,}66 _{P.M. Tuts,}68_{L. Uvarov,}39_{S. Uvarov,}39_{S. Uzunyan,}49_{R. Van Kooten,}51 W.M. van Leeuwen,33_{N. Varelas,}48_{E.W. Varnes,}44_{I.A. Vasilyev,}38_{P. Verdier,}20_{L.S. Vertogradov,}35_{M. Verzocchi,}47 M. Vesterinen,43 _{D. Vilanova,}18_{P. Vint,}42 _{P. Vokac,}10 _{H.D. Wahl,}46 _{M.H.L.S. Wang,}69_{J. Warchol,}53 _{G. Watts,}80

M. Wayne,53 _{M. Weber}g_,47 _{L. Welty-Rieger,}50 _{M. Wetstein,}58 _{A. White,}76 _{D. Wicke,}24 _{M.R.J. Williams,}41 G.W. Wilson,55 _{S.J. Wimpenny,}45 _{M. Wobisch,}57 _{D.R. Wood,}60_{T.R. Wyatt,}43_{Y. Xie,}47 _{C. Xu,}61_{S. Yacoob,}50

R. Yamada,47 _{W.-C. Yang,}43 _{T. Yasuda,}47 _{Y.A. Yatsunenko,}35 _{Z. Ye,}47 _{H. Yin,}7 _{K. Yip,}71 _{H.D. Yoo,}75 S.W. Youn,47_{J. Yu,}76 _{S. Zelitch,}79 _{T. Zhao,}80_{B. Zhou,}61_{J. Zhu,}61 _{M. Zielinski,}69_{D. Zieminska,}51_{and L. Zivkovic}68

(The D0 Collaboration∗₎

1_{Universidad de Buenos Aires, Buenos Aires, Argentina} 2_{LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil}

3_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil} 4_{Universidade Federal do ABC, Santo Andr´e, Brazil}

5_{Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil}

6_{Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada} 7_{University of Science and Technology of China, Hefei, People’s Republic of China}

8_{Universidad de los Andes, Bogot´a, Colombia} 9_{Charles University, Faculty of Mathematics and Physics,}

Center for Particle Physics, Prague, Czech Republic

10_{Czech Technical University in Prague, Prague, Czech Republic} 11_{Center for Particle Physics, Institute of Physics,}

Academy of Sciences of the Czech Republic, Prague, Czech Republic

12_{Universidad San Francisco de Quito, Quito, Ecuador} 13_{LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France}

14_{LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,}

Institut National Polytechnique de Grenoble, Grenoble, France

15_{CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France} 16_{LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France} 17_{LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, Paris, France}

18_{CEA, Irfu, SPP, Saclay, France}

19_{IPHC, Universit´e de Strasbourg, CNRS/IN2P3, Strasbourg, France}

20_{IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France} 21_{III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany}

22_{Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany}

23_{II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, G¨ottingen, Germany} 24_{Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany}

25_{Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany} 26_{Fachbereich Physik, Bergische Universit¨at Wuppertal, Wuppertal, Germany}

27_{Panjab University, Chandigarh, India} 28_{Delhi University, Delhi, India}

29_{Tata Institute of Fundamental Research, Mumbai, India} 30_{University College Dublin, Dublin, Ireland}

31_{Korea Detector Laboratory, Korea University, Seoul, Korea} 32_{CINVESTAV, Mexico City, Mexico}

33_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 34_{Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands}

35_{Joint Institute for Nuclear Research, Dubna, Russia} 36_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

37_{Moscow State University, Moscow, Russia} 38_{Institute for High Energy Physics, Protvino, Russia} 39_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia} 40_{Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden}

41_{Lancaster University, Lancaster LA1 4YB, United Kingdom} 42_{Imperial College London, London SW7 2AZ, United Kingdom} 43_{The University of Manchester, Manchester M13 9PL, United Kingdom}

44_{University of Arizona, Tucson, Arizona 85721, USA} 45_{University of California Riverside, Riverside, California 92521, USA}

46_{Florida State University, Tallahassee, Florida 32306, USA} 47_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA}

48_{University of Illinois at Chicago, Chicago, Illinois 60607, USA} 49_{Northern Illinois University, DeKalb, Illinois 60115, USA}

50_{Northwestern University, Evanston, Illinois 60208, USA} 51_{Indiana University, Bloomington, Indiana 47405, USA} 52_{Purdue University Calumet, Hammond, Indiana 46323, USA} 53_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

54_{Iowa State University, Ames, Iowa 50011, USA} 55_{University of Kansas, Lawrence, Kansas 66045, USA} 56_{Kansas State University, Manhattan, Kansas 66506, USA} 57_{Louisiana Tech University, Ruston, Louisiana 71272, USA} 58_{University of Maryland, College Park, Maryland 20742, USA}

59_{Boston University, Boston, Massachusetts 02215, USA} 60_{Northeastern University, Boston, Massachusetts 02115, USA}

61_{University of Michigan, Ann Arbor, Michigan 48109, USA} 62_{Michigan State University, East Lansing, Michigan 48824, USA}

63_{University of Mississippi, University, Mississippi 38677, USA} 64_{University of Nebraska, Lincoln, Nebraska 68588, USA} 65_{Rutgers University, Piscataway, New Jersey 08855, USA} 66_{Princeton University, Princeton, New Jersey 08544, USA} 67_{State University of New York, Buffalo, New York 14260, USA}

68_{Columbia University, New York, New York 10027, USA} 69_{University of Rochester, Rochester, New York 14627, USA} 70_{State University of New York, Stony Brook, New York 11794, USA}

71_{Brookhaven National Laboratory, Upton, New York 11973, USA} 72_{Langston University, Langston, Oklahoma 73050, USA} 73_{University of Oklahoma, Norman, Oklahoma 73019, USA} 74_{Oklahoma State University, Stillwater, Oklahoma 74078, USA}

75_{Brown University, Providence, Rhode Island 02912, USA} 76_{University of Texas, Arlington, Texas 76019, USA} 77_{Southern Methodist University, Dallas, Texas 75275, USA}

78_{Rice University, Houston, Texas 77005, USA} 79_{University of Virginia, Charlottesville, Virginia 22901, USA}

80_{University of Washington, Seattle, Washington 98195, USA}

(Dated: September 28, 2010)

We extract the total width of the top quark, Γt, from the partial decay width Γ(t → W b) measured

using the t-channel cross section for single top quark production and from the branching fraction B(t → W b) measured in t¯tevents using up to 2.3 fb−1_{of integrated luminosity collected by the D0}

Collaboration at the Tevatron p¯pCollider. The result is Γt= 1.99+0.69_−0.55 GeV, which translates to a

top-quark lifetime of τt= (3.3+1.3_−0.9) × 10−25s. Assuming a high mass fourth generation b′quark and

unitarity of the four-generation quark-mixing matrix, we set the first upper limit on |Vtb′| < 0.63 at

95% C.L.

PACS numbers: 14.65.Ha, 14.65.Jk, 12.15.Hh

The total width, or lifetime, of the top quark is a fun-damental property that has not been measured precisely so far. The top quark, like other fermions in the Standard Model (SM), decays through the electroweak interaction. But unlike b and c quarks, which form long-lived hadrons that can be observed through the reconstruction of

dis-∗_{with visitors from} a_{Augustana College, Sioux Falls, SD, USA,}

b_{The University of Liverpool, Liverpool, UK,}c_{SLAC, Menlo Park,}

CA, USA,d_{ICREA/IFAE, Barcelona, Spain,}e_{Centro de}

Investiga-cion en ComputaInvestiga-cion - IPN, Mexico City, Mexico,f_ECFM,

Uni-versidad Autonoma de Sinaloa, Culiac´an, Mexico, andg_{Universit¨at}

Bern, Bern, Switzerland.

placed vertices in a tracking detector, the top quark has an extremely short lifetime.

In the SM, the total decay width of the top quark, Γt, is dominated by the partial decay width Γ(t → W b) which, at next-to-leading order (NLO) in Quantum Chromody-namics (QCD), depends on the top quark mass mt, the W boson mass MW, the b quark mass mb, the Fermi coupling constant GF, the strong coupling constant αs and the strength of the left-handed W tb coupling, Vtb. Neglecting higher order electroweak corrections [1] and terms of order m2 b/m 2 t, α 2 s, and (αs/π)MW2 /m 2 t, the par-tial width becomes [2]

Γ(t → W b) = GFm 3 t 8π√2 |Vtb| 2  1 −M 2 W m2 t 2 1 + 2M 2 W m2 t  ×

×  1 −2α_3πs 2π 2 3 − 5 2  . (1) Setting αs(MZ) = 0.118, GF = 1.16637 × 10−5 GeV−2, MW = 80.399 GeV, |Vtb| = 1, and mt= 170 GeV leads to Γ(t → W b)SM = 1.26 GeV. Equation 1 can be extended to include non-SM W tb couplings [3].

The decay width of an unstable particle can be mea-sured with precision from its mass spectrum when the experimental resolution is similar or smaller than the nat-ural width of the particle. Because Γtis far smaller than the experimental resolution, the analysis of the invariant mass distribution yields only an upper limit on Γt that is limited by the uncertainty on the detector resolution. The first such direct upper bound of Γt< 13.1 GeV was set by CDF at 95% C.L. [4].

Following a suggestion in Ref. [5], we determine the partial width Γ(t → W b) of the top quark indirectly from the single top t-channel (p¯p → tqb+X) cross section mea-surement [6], assuming that the electroweak coupling in top quark production is identical to the coupling in top quark decay. Electroweak single top quark production proceeds via s-channel production and decay of a vir-tual W boson, or through exchange of a virvir-tual W boson in the t-channel [7, 8]. As in the decay of top quarks, both processes involve the W tb vertex and are therefore proportional to the partial width Γ(t → W b). Since con-tributions outside the SM have different effects on the s-channel and t-channel cross sections, the partial width is determined focusing on the single most sensitive chan-nel in single top quark production, the t-chanchan-nel, which is illustrated in Fig. 1. W b t p p

FIG. 1: Representative diagram for t-channel single top quark production.

From the partial decay width and the branching frac-tion B(t → W b) [9], we form the total decay width:

Γt= Γ(t → W b)

B(t → W b). (2)

In addition to the experimental measurements, this method relies on the validity of the NLO QCD calcula-tions of the single top quark cross section and of the top quark partial decay width. In these calculations only the contributions from SM processes are considered. Any de-viation of the measured total width from the theoretical

prediction would therefore indicate physics beyond the SM. One example is the presence of anomalous form fac-tors in the W tb vertex, such as right-handed vector cou-plings [10]. This would change the measured t-channel cross section and therefore the extracted partial width. It would also modify the measurement of B(t → W b) due to the different event kinematics which would lead to dif-ferent event selection efficiencies. Another example is a charged Higgs boson H+ _{with a mass m}

H+ < m_t− m_b which preferably decays via H+ _{→ c¯s as predicted in} some supersymmetric extensions of the SM [11]. In this case, the fusion process H+_{b → t can compete with} the SM single top quark production (W+

b → t), and the decay t → H+_{b can compete with the SM decay} (t → W+_{b). This would enhance the measured t-channel} cross section, and affect the measured branching fraction B(t → W b). A third example studied in more detail in this Letter is a new fourth generation b′ _quark.

To extract the partial width Γ(t → W b), we use the measurement of the inclusive t-channel cross section ob-tained from data corresponding to 2.3 fb−1 _{of integrated} luminosity [6]. Without assuming B(t → W b) = 1 as in that publication, the cross section measurement can be expressed as

σ(t−channel) B(t → W b) = 3.14+0.94

−0.80pb . (3) Given the linear dependence of the cross section on the partial width, we derive the partial width as

Γ(t → W b) = σ(t−channel) Γ(t → W b)SM σ(t−channel)SM

. (4)

For the predicted SM t-channel cross section, we use a calculation in NLO QCD that yields σ(t−channel)SM = 2.14 ± 0.18 pb [12] for mt = 170 GeV. For the partial width in the SM, we use the NLO result of Γ(t → W b)SM = 1.26 GeV from Eq. 1. Using Eqs. 2 and 4, the total width becomes:

Γt= σ(t−channel) Γ(t → W b)SM B(t → W b) σ(t−channel)SM

. (5)

The branching fraction B(t → W b) is determined from our previous studies of t¯t events with different identified b jet multiplicities [9]:

B(t → W b) = 0.962+0.068−0.066(stat) +0.064

−0.052(syst) . (6) The B(t → W b) measurement (Eq. 6) is used twice: to obtain the partial width in Eqs. 3 and 4, and to derive the total width in Eq. 5.

The analysis starts with the same Bayesian Neural Network (BNN) discriminants trained to measure the t-channel cross section [6] in 24 independent analysis chan-nels, separated according to data-taking period, lepton flavor (e or µ), jet multiplicity (2, 3 or 4), and number of b-tagged jets (1 or 2). We then form a Bayesian probabil-ity densprobabil-ity [13] for the partial width based on Eq. 4. This

is combined with the measurement of B(t → W b) which is performed selecting 3 and 4 jets, and 0, 1 or 2 b-tags for the e and µ channels. In combining the probability densities we assume that all the values of Γ(t → W b) are equiprobable, which corresponds to assuming a uniform probability density for the t-channel cross section and for Γt.

Systematic uncertainties are treated in the same way as for the combination [14] of the CDF [15] and D0 [16] single top quark cross section measurements. The terms included in the uncertainty calculation are:

• Uncertainty on the integrated luminosity of 6.1%. • Uncertainties on modeling the single top quark

sig-nal, which applies only to the t-channel cross sec-tion and includes uncertainties from initial- and final-state radiation, scale uncertainties and parton distribution functions (pdfs).

• Uncertainties in the modeling of the t¯t pair pro-duction signal for the B(t → W b) measurement, which include uncertainties from pdfs, different event generators and hadronization models. They are correlated with the t¯t background yield uncer-tainty in the t-channel measurement.

• Uncertainties on the background MC simulation, including the t¯t normalization uncertainty in the t-channel obtained from theoretical calculations tak-ing into account the uncertainty on mt, and for B(t → W b) the uncertainty on the W +jets and heavy-flavor samples normalization.

• Detector simulation uncertainty arising from the modeling of particle identification in MC.

• Uncertainties arising from the modeling of the dif-ferent background sources that are obtained using data-driven methods.

• Uncertainty on b-jet identification involving b, c and light-flavor jet tagging rates and the calorimeter response to b-jets.

• Jet energy scale (JES) uncertainty from the calorimeter response to light jets, uncertainties from JES corrections dependent on pseudorapidity and transverse momentum and other smaller con-tributions.

All systematic uncertainties of the t-channel cross sec-tion and the B(t → W b) measurement are assumed to be either fully correlated or uncorrelated. Table I shows the relative systematic uncertainties used in the t-channel and B(t → W b) measurements, and displays how the cor-relations are treated.

The expected and observed Bayesian probability densi-ties for the partial width Γ(t → W b) are shown in Fig. 2.

Wb) [GeV] → (t Γ 0 0.5 1 1.5 2 2.5 3 3.5 4 ] -1

Posterior density [GeV

0 0.2 0.4 0.6 0.8 1 1.2 Wb) [GeV] → (t Γ 0 0.5 1 1.5 2 2.5 3 3.5 4 ] -1

Posterior density [GeV

0 0.2 0.4 0.6 0.8 1 1.2 _GeV -0.44 +0.53 Wb) = 1.32 → (t Γ Expected GeV -0.51 +0.58 Wb) = 1.92 → (t Γ Observed -1 DØ 2.3 fb

FIG. 2: Probability density for the expected and measured partial width Γ(t → W b). The hatched areas represent one standard deviation around the most probable value.

The most probable value for the partial width is defined by the peak of the probability density function and cor-responds to

Γ(t → W b) = 1.92+0.58−0.51GeV. (7) The measurement of the partial width alone can be used to set a lower limit on the total width. From the observed partial width probability density in Fig. 2, we obtain that Γ(t → W b) > 1.21 GeV at 95% C.L. This is the lowest value of the partial width that bounds 95% of the area of the probability density. Since the total width must be larger than the partial width, it also must satisfy

Γt> 1.21 GeV at 95% C.L. (8)

Calculating the lifetime τt as the inverse of the total width, we determine an upper limit of τt< 5.4 × 10−25s. Models including an additional chiral-tensorial W tb cou-pling leading to non-SM helicity amplitudes of the top quark can be excluded by this result because they pre-dict a partial width Γ(t → W b) = 0.66 GeV [17].

Combining the partial width (Eq. 7) with B(t → W b) as in Eq. 2, we obtain the expected and observed prob-ability densities for the total width Γt shown in Fig. 3. The total top quark width is found to be

Γt= 1.99+0.69_−0.55GeV, (9)

which can be expressed as a top quark lifetime of

τt= (3.3+1.3_−0.9) × 10−25s. (10) The determination of the top quark width is used to set constraints on the coupling of a fourth generation b′

Sources σ(t-channel), % B(t → W b), % Correlations Components for normalization

Luminosity 6.1 0.0

Single top quark signal modeling 3.5–13.6 0.0

Top pair production signal modeling — 1.0 X

Other background from MC 15.1 0.6 X

Detector modeling 7.1 0.1 X

Components for normalization and shape

Background from data 13.7–54 1.7 X

b-jet identification 2–30 6.3 X

Jet energy scale 0.1–13.1 0.0

TABLE I: Sources of systematic uncertainties affecting the determination of Γt, including sources

that affect both the normalization and the shape of the final discriminant. For some uncertainties we quote the range across the different channels. In the t-channel cross section measurement the top pair production modeling uncertainty is included in the “Other background from MC” modeling category. It is taken as fully correlated to the “Top pair production signal modeling” uncertainty in the B(t → W b) measurement. The sources are 100% correlated between the two measurements for rows with an “X” in the correlations column, and uncorrelated otherwise.

[GeV] t Γ 0 0.5 1 1.5 2 2.5 3 3.5 4 ] -1

Posterior density [GeV

0 0.2 0.4 0.6 0.8 1 1.2 [GeV] t Γ 0 0.5 1 1.5 2 2.5 3 3.5 4 ] -1

Posterior density [GeV

0 0.2 0.4 0.6 0.8 1 1.2 GeV -0.44 +0.53 = 1.32 t Γ Expected GeV -0.55 +0.69 = 1.99 t Γ Observed -1 DØ 2.3 fb

FIG. 3: Probability density for the expected and measured total width Γt. The hatched areas represent one standard

deviation around the most probable value.

quark to the top quark. Assuming mb′ > mt− mW, a small probability density for the b′ _{quark in protons and} antiprotons, and unitarity of the quark-mixing matrix, including the fourth quark generation (|Vtb|2+|Vtb′|2= 1, and |Vtd|, |Vts| ≪ 1), the measurement of the total top quark width can be used to extract a limit on the mixing matrix element |Vtb′|. Using a flat prior for 0 ≤ |Vtb| ≤ 1 yields |Vtb′| < 0.63 at 95% C.L. This is the first limit on the W boson coupling to the top quark and a fourth-generation b′ _quark.

In summary, we have presented the most precise de-termination of the width of the top quark. It is based on the measurement of two quantities, the partial decay

width of the top quark into W b and the branching frac-tion B(t → W b). It is assumed that the coupling leading to t-channel single top quark production is identical to the coupling leading to top quark decay. The total top quark width is determined to be Γt= 1.99+0.69_−0.55GeV for mt= 170 GeV, which corresponds to a top quark lifetime of τt= (3.3+1.3_−0.9) × 10−25 s. In addition, we set the first limit on a fourth-generation b′ _{quark coupling to the top} quark of |Vtb′| < 0.63 at 95% C.L.

Acknowledgments

We wish to thank C.-P. Yuan for fruitful discussions regarding this analysis. 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); 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); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); CRC Program and NSERC (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China).

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