Precision measurement of the ratio B(t -> Wb)/B(t -> Wq)
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Precision measurement of the ratio B ( t → W b ) / B ( t → W q ) V.M. Abazov, B. Abbott, B.S. Acharya, M. Adams, T. Adams, G.D. Alexeev, G. Alkhazov, A. Alton a , G. Alverson, G.A. Alves, M. Aoki, M. Arov, A. Askew, B. ˚Asman, O. Atramentov, C. Avila, J. BackusMayes, F. Badaud, L. Bagby, B. Baldin, D.V. Bandurin, S. Banerjee, E. Barberis, P. Baringer, J. Barreto, J.F. Bartlett, U. Bassler, V. Bazterra, S. Beale, A. Bean, M. Begalli, M. Begel, C. Belanger-Champagne, L. Bellantoni, S.B. Beri, G. Bernardi, R. Bernhard, I. Bertram, M. Besan¸con, R. Beuselinck, V.A. Bezzubov, P.C. Bhat, V. Bhatnagar, G. Blazey, S. Blessing, K. Bloom, A. Boehnlein, D. Boline, E.E. Boos, G. Borissov, T. Bose, A. Brandt, O. Brandt, R. Brock, G. Brooijmans, A. Bross, D. Brown, J. Brown, X.B. Bu, M. Buehler, V. Buescher, V. Bunichev, S. Burdin b , T.H. Burnett, C.P. Buszello, B. Calpas, E. Camacho-P´erez, M.A. Carrasco-Lizarraga, B.C.K. Casey, H. Castilla-Valdez, S. Chakrabarti, D. Chakraborty, K.M. Chan, A. Chandra, G. Chen, S. Chevalier-Th´ery, D.K. Cho, S.W. Cho, S. Choi, B. Choudhary, S. Cihangir, D. Claes, J. Clutter, M. Cooke, W.E. Cooper, M. Corcoran, F. Couderc, M.-C. Cousinou, A. Croc, D. Cutts, A. Das, G. Davies, K. De, S.J. de Jong, E. De La Cruz-Burelo, F. D´eliot, M. Demarteau, R. Demina, D. Denisov, S.P. Denisov, S. Desai, C. Deterre, K. DeVaughan, H.T. Diehl, M. Diesburg, P.F. Ding, A. Dominguez, T. Dorland, A. Dubey, L.V. Dudko, D. Duggan, A. Duperrin, S. Dutt, A. Dyshkant, M. Eads, D. Edmunds, J. Ellison, V.D. Elvira, Y. Enari, H. Evans, A. Evdokimov, V.N. Evdokimov, G. Facini, T. Ferbel, F. Fiedler, F. Filthaut, W. Fisher, H.E. Fisk, M. Fortner, H. Fox, S. Fuess, A. Garcia-Bellido, V. Gavrilov, P. Gay, W. Geng,
15, 62
D. Gerbaudo, C.E. Gerber, Y. Gershtein, G. Ginther,
48, 69
G. Golovanov, A. Goussiou, P.D. Grannis, S. Greder, H. Greenlee, Z.D. Greenwood, E.M. Gregores, G. Grenier, Ph. Gris, J.-F. Grivaz, A. Grohsjean, S. Gr¨unendahl, M.W. Gr¨unewald, T. Guillemin, F. Guo, G. Gutierrez, P. Gutierrez, A. Haas c , S. Hagopian, J. Haley, L. Han, K. Harder, A. Harel, J.M. Hauptman, J. Hays, T. Head, T. Hebbeker, D. Hedin, H. Hegab, A.P. Heinson, U. Heintz, C. Hensel, I. Heredia-De La Cruz, K. Herner, G. Hesketh d , M.D. Hildreth, R. Hirosky, T. Hoang, J.D. Hobbs, B. Hoeneisen, M. Hohlfeld, Z. Hubacek,
10, 18
N. Huske, V. Hynek, I. Iashvili, Y. Ilchenko, R. Illingworth, A.S. Ito, S. Jabeen, M. Jaffr´e, D. Jamin, A. Jayasinghe, R. Jesik, K. Johns, M. Johnson, D. Johnston, A. Jonckheere, P. Jonsson, J. Joshi, A.W. Jung, A. Juste, K. Kaadze, E. Kajfasz, D. Karmanov, P.A. Kasper, I. Katsanos, R. Kehoe, S. Kermiche, N. Khalatyan, A. Khanov, A. Kharchilava, Y.N. Kharzheev, M.H. Kirby, J.M. Kohli, A.V. Kozelov, J. Kraus, S. Kulikov, A. Kumar, A. Kupco, T. Kurˇca, V.A. Kuzmin, J. Kvita, S. Lammers, G. Landsberg, P. Lebrun, H.S. Lee, S.W. Lee, W.M. Lee, J. Lellouch, L. Li, Q.Z. Li, S.M. Lietti, J.K. Lim, D. Lincoln, J. Linnemann, V.V. Lipaev, R. Lipton, Y. Liu, Z. Liu, A. Lobodenko, M. Lokajicek, R. Lopes de Sa, H.J. Lubatti, R. Luna-Garcia e , A.L. Lyon, A.K.A. Maciel, D. Mackin, R. Madar, R. Maga˜na-Villalba, S. Malik, V.L. Malyshev, Y. Maravin, J. Mart´ınez-Ortega, R. McCarthy, C.L. McGivern, M.M. Meijer, A. Melnitchouk, D. Menezes, P.G. Mercadante, M. Merkin, A. Meyer, J. Meyer, F. Miconi, N.K. Mondal, G.S. Muanza, M. Mulhearn, E. Nagy, M. Naimuddin, M. Narain, R. Nayyar, H.A. Neal, J.P. Negret, P. Neustroev, S.F. Novaes, T. Nunnemann, G. Obrant ‡ , J. Orduna, N. Osman, J. Osta, G.J. Otero y Garz´on, M. Padilla, A. Pal, N. Parashar, V. Parihar, S.K. Park, J. Parsons, R. Partridge c , N. Parua, A. Patwa, B. Penning, M. Perfilov, K. Peters, Y. Peters, K. Petridis, G. Petrillo, P. P´etroff, R. Piegaia, M.-A. Pleier, P.L.M. Podesta-Lerma f , V.M. Podstavkov, P. Polozov, A.V. Popov, M. Prewitt, D. Price, N. Prokopenko, S. Protopopescu, J. Qian, A. Quadt, B. Quinn, M.S. Rangel, K. Ranjan, P.N. Ratoff, I. Razumov, P. Renkel, M. Rijssenbeek, I. Ripp-Baudot, F. Rizatdinova, M. Rominsky, A. Ross, C. Royon, P. Rubinov, R. Ruchti, G. Safronov, G. Sajot, P. Salcido, A. S´anchez-Hern´andez, M.P. Sanders, B. Sanghi, A.S. Santos, G. Savage, L. Sawyer, T. Scanlon, R.D. Schamberger, Y. Scheglov, H. Schellman, T. Schliephake, S. Schlobohm, C. Schwanenberger, R. Schwienhorst, J. Sekaric, H. Severini, E. Shabalina, V. Shary, A.A. Shchukin, R.K. Shivpuri, V. Simak, V. Sirotenko, P. Skubic, P. Slattery, D. Smirnov, K.J. Smith, G.R. Snow, J. Snow, S. Snyder, S. S¨oldner-Rembold, L. Sonnenschein, K. Soustruznik, J. Stark, V. Stolin, D.A. Stoyanova, M. Strauss, D. Strom, L. Stutte, L. Suter, P. Svoisky, M. Takahashi, A. Tanasijczuk, W. Taylor, M. Titov, V.V. Tokmenin, Y.-T. Tsai, D. Tsybychev, B. Tuchming, C. Tully, L. Uvarov, S. Uvarov, S. Uzunyan, R. Van Kooten, W.M. van Leeuwen, N. Varelas, E.W. Varnes, I.A. Vasilyev, P. Verdier, L.S. Vertogradov, M. Verzocchi, M. Vesterinen, D. Vilanova, P. Vokac, H.D. Wahl, M.H.L.S. Wang, J. Warchol, G. Watts, M. Wayne, M. Weber g , L. Welty-Rieger, A. White, D. Wicke, M.R.J. Williams, G.W. Wilson, M. Wobisch, D.R. Wood, T.R. Wyatt, Y. Xie, C. Xu, S. Yacoob, R. Yamada, W.-C. Yang, T. Yasuda, Y.A. Yatsunenko, Z. Ye, H. Yin, K. Yip, S.W. Youn, J. Yu, S. Zelitch, T. Zhao, B. Zhou, J. Zhu, M. Zielinski, D. Zieminska, and L. Zivkovic (The D0 Collaboration ∗ ) Universidad de Buenos Aires, Buenos Aires, Argentina LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil Universidade Federal do ABC, Santo Andr´e, Brazil Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada University of Science and Technology of China, Hefei, People’s Republic of China Universidad de los Andes, Bogot´a, Colombia Charles University, Faculty of Mathematics and Physics,Center for Particle Physics, Prague, Czech Republic Czech Technical University in Prague, Prague, Czech Republic Center for Particle Physics, Institute of Physics,Academy of Sciences of the Czech Republic, Prague, Czech Republic Universidad San Francisco de Quito, Quito, Ecuador LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, Grenoble, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, Paris, France CEA, Irfu, SPP, Saclay, France IPHC, Universit´e de Strasbourg, CNRS/IN2P3, Strasbourg, France IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, G¨ottingen, Germany Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany Fachbereich Physik, Bergische Universit¨at Wuppertal, Wuppertal, Germany Panjab University, Chandigarh, India Delhi University, Delhi, India Tata Institute of Fundamental Research, Mumbai, India University College Dublin, Dublin, Ireland Korea Detector Laboratory, Korea University, Seoul, Korea CINVESTAV, Mexico City, Mexico Nikhef, Science Park, Amsterdam, the Netherlands Radboud University Nijmegen, Nijmegen, the Netherlands and Nikhef, Science Park, Amsterdam, the Netherlands Joint Institute for Nuclear Research, Dubna, Russia Institute for Theoretical and Experimental Physics, Moscow, Russia Moscow State University, Moscow, Russia Institute for High Energy Physics, Protvino, Russia Petersburg Nuclear Physics Institute, St. Petersburg, Russia Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA) and Institut de F´ısica d’Altes Energies (IFAE), Barcelona, Spain Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden Lancaster University, Lancaster LA1 4YB, United Kingdom Imperial College London, London SW7 2AZ, United Kingdom The University of Manchester, Manchester M13 9PL, United Kingdom University of Arizona, Tucson, Arizona 85721, USA University of California Riverside, Riverside, California 92521, USA Florida State University, Tallahassee, Florida 32306, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Illinois at Chicago, Chicago, Illinois 60607, USA Northern Illinois University, DeKalb, Illinois 60115, USA Northwestern University, Evanston, Illinois 60208, USA Indiana University, Bloomington, Indiana 47405, USA Purdue University Calumet, Hammond, Indiana 46323, USA University of Notre Dame, Notre Dame, Indiana 46556, USA Iowa State University, Ames, Iowa 50011, USA University of Kansas, Lawrence, Kansas 66045, USA Kansas State University, Manhattan, Kansas 66506, USA Louisiana Tech University, Ruston, Louisiana 71272, USA Boston University, Boston, Massachusetts 02215, USA Northeastern University, Boston, Massachusetts 02115, USA University of Michigan, Ann Arbor, Michigan 48109, USA Michigan State University, East Lansing, Michigan 48824, USA University of Mississippi, University, Mississippi 38677, USA University of Nebraska, Lincoln, Nebraska 68588, USA Rutgers University, Piscataway, New Jersey 08855, USA Princeton University, Princeton, New Jersey 08544, USA State University of New York, Buffalo, New York 14260, USA Columbia University, New York, New York 10027, USA University of Rochester, Rochester, New York 14627, USA State University of New York, Stony Brook, New York 11794, USA Brookhaven National Laboratory, Upton, New York 11973, USA Langston University, Langston, Oklahoma 73050, USA University of Oklahoma, Norman, Oklahoma 73019, USA Oklahoma State University, Stillwater, Oklahoma 74078, USA Brown University, Providence, Rhode Island 02912, USA University of Texas, Arlington, Texas 76019, USA Southern Methodist University, Dallas, Texas 75275, USA Rice University, Houston, Texas 77005, USA University of Virginia, Charlottesville, Virginia 22901, USA University of Washington, Seattle, Washington 98195, USA (Dated: June 27, 2011)We present a measurement of the ratio of top quark branching fractions R = B ( t → W b ) / B ( t → W q ), where q can be a d , s or b quark, in the lepton+jets and dilepton t ¯ t final states. The measurement uses data from 5.4 fb − of p ¯ p collisions collected with the D0detector at the Fermilab Tevatron Collider. We measure R = 0 . ± .
04, and we extract the CKMmatrix element | V tb | as | V tb | = 0 . ± .
02, assuming unitarity of the 3 × PACS numbers: 12.15.Hh, 13.85.Qk, 14.65.Ha
The standard model (SM) of particle physics containsthree generations of quarks. The top quark belongs to thethird generation, and is of interest not only because of itslarge mass [1], but also because its decay has not beenexamined in great detail, and may prove to be inconsis-tent with the SM. The decay rate of the top quark intoa W boson and a down-type quark q ( q = d, s, b ) is pro-portional to | V tq | , the squared element of the CabibboKobayashi Maskawa (CKM) matrix [2]. Under the as-sumption of a unitary 3 × | V tb | is highlyconstrained to | V tb | = 0 . +0 . − . [3], and the top ∗ with visitors from a Augustana College, Sioux Falls, SD, USA, b The University of Liverpool, Liverpool, UK, c SLAC, Menlo Park,CA, USA, d University College London, London, UK, e Centrode Investigacion en Computacion - IPN, Mexico City, Mexico, f ECFM, Universidad Autonoma de Sinaloa, Culiac´an, Mexico, and g Universit¨at Bern, Bern, Switzerland. ‡ Deceased. quark decays almost exclusively to
W b . The existenceof a fourth generation of quarks would remove this con-straint and accomodate significantly smaller values of | V tb | . A smaller value of | V tb | could be observed directlythrough the electroweak production of single top quarks,for which the cross section is proportional to | V tb | , andcould also affect the decay rates in the t ¯ t productionchannel. The latter can be used to extract the ratio ofbranching fractions R : R = B ( t → W b ) B ( t → W q ) = | V tb | | V tb | + | V ts | + | V td | . (1)Given the constraints on the unitary 3 × R is expected to be 0 . +0 . − . . Along witha measurement of | V tb | using single top quark production,the measurement of R provides the possibility of a studyof | V tq | [4].This Letter presents a measurement of R using adata sample corresponding to an integrated luminosity of5.4 fb − of p ¯ p collisions, collected with the D0 detector atthe Fermilab Tevatron p ¯ p Collider at √ s = 1.96 TeV. Wepresent measurements in the lepton+jets ( ℓ +jets) chan-nel, in which one W boson from tt → W + qW − q produc-tion decays into a quark and an antiquark and the otherinto a charged lepton and a neutrino, and in dilepton ( ℓℓ )final states, in which both W bosons decay into ℓν . Wealso present the combination of these two measurements.We consider events in which the charged leptons are ei-ther electrons or muons, produced directly from the W decay or from the leptonic decay of a τ lepton. The re-sult from the ℓ +jets channel corresponds to an improve-ment of the measurement using 0 . − [5], in which weextracted R > .
79 at a 95% CL. This is the first D0measurement of R in the ℓℓ channel. The CDF Collabo-ration has measured R in the ℓ +jets and ℓℓ channels in160 pb − of integrated luminosity [6], and found a limitof R > .
61 at 95% CL.Our measurement is performed by distinguishing be-tween the standard decay mode of the top quark t ¯ t → W + bW − ¯ b (indicated by bb ), and decay modes that in-clude light quarks ( q l = d, s ): t ¯ t → W + bW − ¯ q l ( bq l ) and t ¯ t → W + q l W − ¯ q l ( q l q l ). The selection of an enriched t ¯ t sample and identification of jets from b quarks are crucialelements of the analysis.The D0 detector [7] has a central tracking system con-sisting of a silicon microstrip tracker and a fiber tracker,both located within a 1.9 T superconducting solenoidalmagnet, designed to optimize tracking at pseudorapidi-ties | η | < | η | upto ≈ .
1, and two end calorimeters that extend cover-age to | η | ≈ . | η | <
2, consists of a layer of tracking detectors and scin-tillation trigger counters in front of 1.8 T toroids, fol-lowed by two similar layers behind the toroids [9]. In the ℓ +jets channel, we rely on the event selections used forthe measurement of the t ¯ t production cross section [10].Details on object identification and selections are onlybriefly summarized as follows. We select t ¯ t events bytaking advantage of their distinct topology. We requireat least three jets within | η | < .
5, with transverse mo-mentum p T >
20 GeV, of which at least one has tohave p T >
40 GeV. We require one electron (muon)of p T >
20 GeV, | η | < . | η | < .
0) isolated fromjets. In addition, events with a second isolated elec-tron or muon of p T >
15 GeV are removed in order toensure that the ℓ +jets and ℓℓ samples are statisticallyindependent. The imbalance in transverse energy, E T ,must fulfill E T >
20 GeV ( E T >
25 GeV) in the e +jets( µ +jets) channel. The most important background inthe ℓ +jets channel is from W +jets events which can pro-duce a similar final state to t ¯ t events. There is also sig-nificant background contribution from multijet produc-tion, in which a jet is misidentified as an electron, or amuon from the semileptonic decay of a hadron appears isolated. Smaller background contributions arise fromelectroweak single top quark production, Drell-Yan and Z boson production (decaying to l + l − +jets) or dibosonproduction ( W W , W Z or ZZ ). The multijet backgroundis estimated from control samples in data [10], while the t ¯ t signal and electroweak backgrounds are simulated us-ing Monte Carlo (MC) event generators alpgen and pythia [11, 12], and a geant -based [13] simulation ofthe D0 detector. Drell-Yan and Z boson production isnormalized to the next-to-next-to-leading order (NNLO)QCD prediction [14]. All other electroweak backgroundsare normalized to their next-to-leading order (NLO) crosssections, while the W +jets background is normalized todata using an iterative procedure [10].For the ℓℓ channel, we use the same selections as usedfor the measurement of the t ¯ t cross section described inRef. [15]. In this final state, the t ¯ t signature consists oftwo energetic, oppositely charged isolated leptons, large E T and two high p T jets. We consider separately thethree final states ee , µµ and eµ . For the eµ final state, wealso consider events with only one reconstructed jet. Toselect t ¯ t events, we require two isolated leptons, electronsor muons, with p T >
15 GeV, | η | < . . < | η | < . | η | <
2) for the electron (muon), and at least two jetswith p T >
20 GeV and | η | < .
5. For µµ events werequire E T >
40 GeV. In the eµ channel, the sum of thetransverse momenta of the lepton and two jets of highest p T must be larger than 110 GeV. That sum must behigher than 105 GeV when only one jet is reconstructed.In the ee and µµ channels we use the E T significance todifferentiate events with true E T from escaping neutrinosand events with E T arising from mismeasurement. The E T significance for each event is defined in terms of alikelihood discriminant constructed from the ratio of E T to its uncertainty [16]. The significance is required tocorrespond to more than five. The main background inthe ℓℓ final states is composed of Drell-Yan, Z bosonproduction and diboson events, and is estimated usingMC simulation, normalized to the NNLO and NLO crosssections respectively. There is also a background frommultijet events that we estimate from data [15].We use a neural network (NN) b -tagging algorithm [17]to identify jets that contain b quarks, and thereby distin-guish the bb , bq l and q l q l t ¯ t final states. The inputs to theNN include impact parameters of tracks associated withthe jets, and the properties of secondary vertices withinthe jet. Only taggable jets, i.e., jets matched to a set oftracks, are considered by the NN. For each taggable jet,we obtain an output from the NN which ranges betweenzero and twelve, with larger values more likely to corre-spond to jets originating from b quarks. Non-taggablejets are assigned the NN output value − R in the ℓ +jets and ℓℓ channels. In the ℓ +jets channel, we countthe number of jets that pass our threshold on the b -tagging NN output; this requirement has an efficiencyfor b jets of 55 ± ± e or µ ), the number of jets in the event(3 and > − andthe rest [10]), and the number of identified b jets (0, 1 or > b -tagged jets, or one b -tagged jet in the sample with exactly three jets, and zero b -tagged jets in the sample with more than three jets.This discriminant is based on a multivariate technique(random forest of decision trees [18]) and uses severalvariables that exploit the kinematic differences between t ¯ t signal and background. In addition to t ¯ t MC sam-ples with SM decay t ¯ t → W bW b , samples for the decaymodes including light quarks are generated with pythia ( t ¯ t → W bW q l and t ¯ t → W q l W q l ), for a top quark massof m t = 172 . t ¯ t eventswith m b -tagged jets can be written as: µ m t ¯ t ( R, σ t ¯ t ) = [ R ǫ m ( bb ) + 2 R (1 − R ) ǫ m ( bq l )+ (1 − R ) ǫ m ( q l q l )] σt ¯ t B ( t → W q ) L , (2)where ǫ m is the product of the selection efficiency andthe probability of an event to have m b -tagged jets foreach of the three ( bb , bq l and q l q l ) decay modes, σ t ¯ t isthe t ¯ t production cross section and L is the integratedluminosity. A maximum likelihood fit is performed usingthe function: L ℓ +jets = N ch Y i =1 P [ n i , µ i ( R, σ t ¯ t , ν k )] P [ n iMJ , µ iMJ ] × Y k G ( ν k ; 0 , SD) (3)where i runs over the subsamples and bins of the multi-variate discriminant, and P [ n, µ ( R, σ t ¯ t , ν k )] is the Pois-son probability to observe n events for an expected num-ber of µ ( R, σ t ¯ t , ν k ) events. The expectation µ ( R, σ t ¯ t , ν k )is the sum of the expected number of t ¯ t → bb , bq l and q l q l events and the expected number of backgroundevents. The observed and expected numbers of multi-jet events are denoted n iMJ and µ iMJ , and the Poissonterms P [ n iMJ , µ iMJ ] take into account the fluctuation ofthe number of multijet events within the statistical un-certainties with which it is determined in dedicated datasamples. Figures 1 (a) and (b) show the number of b -tagged jets in ℓ +jets events for data and simulation for R = 0, R = 0 . R = 1. To reduce the dependenceof the measurement on the input t ¯ t cross section, we si-multaneously extract σ t ¯ t from data, taking into accountthe three channels t ¯ t → bb , bq l and q l q l . A parameter ν k that accounts for each independent source of systematicuncertainty k is modeled by a Gaussian function G with amean of zero and a width corresponding to one estimatedstandard deviation (SD) of that uncertainty. This proce-dure correlates systematic uncertainties among channels by using the same parameter for a common source ofsystematic uncertainty.In the dilepton channels ee , µµ , and eµ with at least2 jets, we apply the NN b -tagging algorithm to the twojets of highest- p T , and use the smaller of the two NNoutputs to calculate the likelihood. as it yields the bestexpected precision on R for values close to unity. The b -tagging algorithm is applied to the single reconstructedjet in the eµ channel with exactly 1 jet. We construct thetemplates for the decay modes bb , bq l , q l q l for t ¯ t as well asfor all background components, forming the likelihood byrunning the product of Eq. 4 over all fourteen bins of theNN discriminant in all four channels, yielding thereby aproduct with 56 factors: L ℓℓ = N ch Y i =1 P [ n i , µ i ( R, σ t ¯ t , ν k )] Y k G ( ν k ; 0 , SD) . (4)The expected number of events, µ mt ¯ t ( R, σ t ¯ t , ν k ), is givenby Eq. 2, where ǫ m describes now the efficiency for thediscriminant bin m , and ν k can affect the individual com-ponents of µ mt ¯ t ( R, σ t ¯ t ). Figure 1 (c) compares the distri-butions of the discriminant for predicted and observedevents in the combined ℓℓ final state.Several systematic uncertainties can impact the mea-surement of R . We consider the same sources of system-atic uncertainties as for the cross-section measurementsin the ℓ +jets and ℓℓ channels, and refer to Refs. [10, 15]for details. The main source of systematic uncertaintyon R is from the b -tagging probability. Other importantcontributions to the systematic uncertainty on R arisefrom the jet identification efficiency, jet energy scale andresolution, and uncertainties on the background normal-ization as well as on modeling of the signal. The latterincludes contributions from higher order effects, color re-connection, choice of parton distribution functions andinitial and final-state gluon radiation. For consistencywith Refs. [10, 15] we also quote separately the smallersystematic contributions from limited number of eventsin the templates and the uncertainties on the heavy-flavorfraction for the W +jets process, the trigger efficiency andlepton identification. We account for the fact that un-certainties from jet identification, jet energy scale andresolution, b -jet identification, and higher-order correc-tions can affect the distribution of the discriminants inthe ℓ +jets channel, and the NN discriminants in the ℓℓ channel. We verify that the measurement of R does notdepend on m t by generating MC samples at different m t values. In the ℓ +jets channel we obtain: R = 0 . ± .
07 (stat+syst) σ t ¯ t = 7 . +0 . − . (stat+syst) pb,and in the ℓℓ channel R = 0 . ± .
05 (stat+syst) σ t ¯ t = 8 . +1 . − . (stat+syst) pb.The results are in agreement with each other, and theextracted cross sections are consistent with those from tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N -1 DØ, L=5.3 fb tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N -1 DØ, L=5.3 fb tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N tag N ≥ eve n t N NN output eve n t N -1
10 Data R=1tt R=0.5tt R=0ttBackground -1 DØ, L=5.4 fb (a) (b) (c)
FIG. 1: (color online) (a) Number of b -tagged jets in ℓ +jets events with three jets and (b) at least four jets. (c) Distributionin the minimum b -tag NN output of the jets of highest- p T for dilepton final states. Refs. [10, 15]. In these σ t ¯ t measurements, we do not as-sume that B ( t → W b ) = 1 as was done for the resultsin Refs. [10, 15], but only require B ( t → W q ) = 1. Thecombined measurement is obtained by fitting simultane-ously all channels in the ℓℓ and ℓ +jets final states. Thisyields: R = 0 . ± .
04 (stat+syst) σ t ¯ t = 7 . +0 . − . (stat+syst) pb.Table I summarizes the systematic uncertainties for thethree results on R . While in the ℓℓ channel the statisti-cal uncertainty still dominates, the ℓ +jets and the com-bined result are dominated by systematic uncertainties.If we assume unitarity of the CKM matrix, we extract | V tb | = 0 . ± .
02. Constraining the t ¯ t cross section tothe SM value of 7 . +0 . − . pb [19] yields R = 0 . ± . R as well as on | V tb | from Eq. (1), assuming unitarity of the3 × R as 0.82–0.98 and V tb as 0.90–0.99 at 95% CL. The ex-pected limits are R > .
92 and V tb > .
96 at 95% CL.Figure 2 shows the bands for 68%, 95% and 99.7% confi-dence limits on R . Our result is compatible with the SMexpectation at the 1.6% level. At 99.7% CL, we obtain R > .
77 and | V tb | > . − R ) /R = ( | V ts | + | V td | ) / | V tb | , and set a limiton this ratio at 99.7% CL of: (1 − R ) /R < . R = B ( t → W b ) / B ( t → W q ) in both lep-ton+jets and dilepton channels. In the combined analy-sis, we find R = 0 . ± .
04, which agrees within approxi-mately 2.5 standard deviations with the SM prediction of meas
R0 0.5 1 R -1 DØ, 5.4 fb
FIG. 2: (color online) Limit bands at 68%, 95% and 99.7%CL on R , with the measured value (dotted line). R close to one. This is the most precise determination of R to date. Using the approach of Ref. [20] and assumingthe unitarity of the CKM matrix, we extract the intervalat 95% CL on the element V tb as 0.90–0.99.We thank the staffs at Fermilab and collaboratinginstitutions, and acknowledge support from the DOEand NSF (USA); CEA and CNRS/IN2P3 (France);FASI, Rosatom and RFBR (Russia); CNPq, FAPERJ,FAPESP and FUNDUNESP (Brazil); DAE and DST (In-dia); Colciencias (Colombia); CONACyT (Mexico); KRFand KOSEF (Korea); CONICET and UBACyT (Ar-gentina); FOM (The Netherlands); STFC and the RoyalSociety (United Kingdom); MSMT and GACR (CzechRepublic); CRC Program and NSERC (Canada); BMBFand DFG (Germany); SFI (Ireland); The Swedish Re-search Council (Sweden); and CAS and CNSF (China). TABLE I: Uncertainties on the measurements of R in the ℓℓ and ℓ +jets channels as well as for the combination of the two.We evaluate the impact of each class of systematic uncertainties by calculating R and σ t ¯ t using the corresponding parameters ν shifted by ± ℓℓ ℓ +jets CombinationSource +SD − SD +SD − SD +SD − SDStatistical 0.041 − .
042 0.030 − .
029 0.023 − . − .
002 0.000 − .
001 0.001 − . − .
004 0.000 − .
000 0.001 − . − .
006 0.009 − .
011 0.004 − . − .
003 0.001 − .
001 0.002 − . − .
008 0.017 − .
016 0.003 − . − .
009 0.018 − .
022 0.009 − . b -tagging 0.018 − .
019 0.065 − .
056 0.034 − . − .
020 0.004 − .
005 0.008 − . − .
001 0.001 − . − .
013 0.003 − .
004 0.005 − . − .
010 0.001 − .
001 0.004 − . − .
002 0.000 − .
000 0.001 − . − .
002 0.011 − .
011 0.010 − . − .
035 0.071 − .
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