Simultaneous measurement of forward-backward asymmetry and top polarization in dilepton final states from t\bar{t} production at the Tevatron

Simultaneous measurement of forward-backward asymmetry and top polarization in dilepton final states from  production at the Tevatron

V.M. Abazov Joint Institute for Nuclear Research, Dubna, Russia    B. Abbott University of Oklahoma, Norman, Oklahoma 73019, USA    B.S. Acharya Tata Institute of Fundamental Research, Mumbai, India    M. Adams University of Illinois at Chicago, Chicago, Illinois 60607, USA    T. Adams Florida State University, Tallahassee, Florida 32306, USA    J.P. Agnew The University of Manchester, Manchester M13 9PL, United Kingdom    G.D. Alexeev Joint Institute for Nuclear Research, Dubna, Russia    G. Alkhazov Petersburg Nuclear Physics Institute, St. Petersburg, Russia    A. Alton University of Michigan, Ann Arbor, Michigan 48109, USA    A. Askew Florida State University, Tallahassee, Florida 32306, USA    S. Atkins Louisiana Tech University, Ruston, Louisiana 71272, USA    K. Augsten Czech Technical University in Prague, Prague, Czech Republic    C. Avila Universidad de los Andes, Bogotá, Colombia    F. Badaud LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France    L. Bagby Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    B. Baldin Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D.V. Bandurin University of Virginia, Charlottesville, Virginia 22904, USA    S. Banerjee Tata Institute of Fundamental Research, Mumbai, India    E. Barberis Northeastern University, Boston, Massachusetts 02115, USA    P. Baringer University of Kansas, Lawrence, Kansas 66045, USA    J.F. Bartlett Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    U. Bassler CEA, Irfu, SPP, Saclay, France    V. Bazterra University of Illinois at Chicago, Chicago, Illinois 60607, USA    A. Bean University of Kansas, Lawrence, Kansas 66045, USA    M. Begalli Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil    L. Bellantoni Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S.B. Beri Panjab University, Chandigarh, India    G. Bernardi LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    R. Bernhard Physikalisches Institut, Universität Freiburg, Freiburg, Germany    I. Bertram Lancaster University, Lancaster LA1 4YB, United Kingdom    M. Besançon CEA, Irfu, SPP, Saclay, France    R. Beuselinck Imperial College London, London SW7 2AZ, United Kingdom    P.C. Bhat Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S. Bhatia University of Mississippi, University, Mississippi 38677, USA    V. Bhatnagar Panjab University, Chandigarh, India    G. Blazey Northern Illinois University, DeKalb, Illinois 60115, USA    S. Blessing Florida State University, Tallahassee, Florida 32306, USA    K. Bloom University of Nebraska, Lincoln, Nebraska 68588, USA    A. Boehnlein Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Boline State University of New York, Stony Brook, New York 11794, USA    E.E. Boos Moscow State University, Moscow, Russia    G. Borissov Lancaster University, Lancaster LA1 4YB, United Kingdom    M. Borysova Taras Shevchenko National University of Kyiv, Kiev, Ukraine    A. Brandt University of Texas, Arlington, Texas 76019, USA    O. Brandt II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    R. Brock Michigan State University, East Lansing, Michigan 48824, USA    A. Bross Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Brown LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    X.B. Bu Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Buehler Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    V. Buescher Institut für Physik, Universität Mainz, Mainz, Germany    V. Bunichev Moscow State University, Moscow, Russia    S. Burdin Lancaster University, Lancaster LA1 4YB, United Kingdom    C.P. Buszello Uppsala University, Uppsala, Sweden    E. Camacho-Pérez CINVESTAV, Mexico City, Mexico    B.C.K. Casey Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    H. Castilla-Valdez CINVESTAV, Mexico City, Mexico    S. Caughron Michigan State University, East Lansing, Michigan 48824, USA    S. Chakrabarti State University of New York, Stony Brook, New York 11794, USA    K.M. Chan University of Notre Dame, Notre Dame, Indiana 46556, USA    A. Chandra Rice University, Houston, Texas 77005, USA    E. Chapon CEA, Irfu, SPP, Saclay, France    G. Chen University of Kansas, Lawrence, Kansas 66045, USA    S.W. Cho Korea Detector Laboratory, Korea University, Seoul, Korea    S. Choi Korea Detector Laboratory, Korea University, Seoul, Korea    B. Choudhary Delhi University, Delhi, India    S. Cihangir Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Claes University of Nebraska, Lincoln, Nebraska 68588, USA    J. Clutter University of Kansas, Lawrence, Kansas 66045, USA    M. Cooke Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    W.E. Cooper Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Corcoran Rice University, Houston, Texas 77005, USA    F. Couderc CEA, Irfu, SPP, Saclay, France    M.-C. Cousinou CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    J. Cuth Institut für Physik, Universität Mainz, Mainz, Germany    D. Cutts Brown University, Providence, Rhode Island 02912, USA    A. Das Southern Methodist University, Dallas, Texas 75275, USA    G. Davies Imperial College London, London SW7 2AZ, United Kingdom    S.J. de Jong Nikhef, Science Park, Amsterdam, the Netherlands Radboud University Nijmegen, Nijmegen, the Netherlands    E. De La Cruz-Burelo CINVESTAV, Mexico City, Mexico    F. Déliot CEA, Irfu, SPP, Saclay, France    R. Demina University of Rochester, Rochester, New York 14627, USA    D. Denisov Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S.P. Denisov Institute for High Energy Physics, Protvino, Russia    S. Desai Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    C. Deterre The University of Manchester, Manchester M13 9PL, United Kingdom    K. DeVaughan University of Nebraska, Lincoln, Nebraska 68588, USA    H.T. Diehl Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Diesburg Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P.F. Ding The University of Manchester, Manchester M13 9PL, United Kingdom    A. Dominguez University of Nebraska, Lincoln, Nebraska 68588, USA    A. Dubey Delhi University, Delhi, India    L.V. Dudko Moscow State University, Moscow, Russia    A. Duperrin CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    S. Dutt Panjab University, Chandigarh, India    M. Eads Northern Illinois University, DeKalb, Illinois 60115, USA    D. Edmunds Michigan State University, East Lansing, Michigan 48824, USA    J. Ellison University of California Riverside, Riverside, California 92521, USA    V.D. Elvira Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    Y. Enari LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    H. Evans Indiana University, Bloomington, Indiana 47405, USA    A. Evdokimov University of Illinois at Chicago, Chicago, Illinois 60607, USA    V.N. Evdokimov Institute for High Energy Physics, Protvino, Russia    A. Fauré CEA, Irfu, SPP, Saclay, France    L. Feng Northern Illinois University, DeKalb, Illinois 60115, USA    T. Ferbel University of Rochester, Rochester, New York 14627, USA    F. Fiedler Institut für Physik, Universität Mainz, Mainz, Germany    F. Filthaut Nikhef, Science Park, Amsterdam, the Netherlands Radboud University Nijmegen, Nijmegen, the Netherlands    W. Fisher Michigan State University, East Lansing, Michigan 48824, USA    H.E. Fisk Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Fortner Northern Illinois University, DeKalb, Illinois 60115, USA    H. Fox Lancaster University, Lancaster LA1 4YB, United Kingdom    S. Fuess Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P.H. Garbincius Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A. Garcia-Bellido University of Rochester, Rochester, New York 14627, USA    J.A. García-González CINVESTAV, Mexico City, Mexico    V. Gavrilov Institute for Theoretical and Experimental Physics, Moscow, Russia    W. Geng CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France Michigan State University, East Lansing, Michigan 48824, USA    C.E. Gerber University of Illinois at Chicago, Chicago, Illinois 60607, USA    Y. Gershtein Rutgers University, Piscataway, New Jersey 08855, USA    G. Ginther Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Rochester, Rochester, New York 14627, USA    O. Gogota Taras Shevchenko National University of Kyiv, Kiev, Ukraine    G. Golovanov Joint Institute for Nuclear Research, Dubna, Russia    P.D. Grannis State University of New York, Stony Brook, New York 11794, USA    S. Greder IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France    H. Greenlee Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    G. Grenier IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France    Ph. Gris LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France    J.-F. Grivaz LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France    A. Grohsjean CEA, Irfu, SPP, Saclay, France    S. Grünendahl Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M.W. Grünewald University College Dublin, Dublin, Ireland    T. Guillemin LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France    G. Gutierrez Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P. Gutierrez University of Oklahoma, Norman, Oklahoma 73019, USA    J. Haley Oklahoma State University, Stillwater, Oklahoma 74078, USA    L. Han University of Science and Technology of China, Hefei, People’s Republic of China    K. Harder The University of Manchester, Manchester M13 9PL, United Kingdom    A. Harel University of Rochester, Rochester, New York 14627, USA    J.M. Hauptman Iowa State University, Ames, Iowa 50011, USA    J. Hays Imperial College London, London SW7 2AZ, United Kingdom    T. Head The University of Manchester, Manchester M13 9PL, United Kingdom    T. Hebbeker III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany    D. Hedin Northern Illinois University, DeKalb, Illinois 60115, USA    H. Hegab Oklahoma State University, Stillwater, Oklahoma 74078, USA    A.P. Heinson University of California Riverside, Riverside, California 92521, USA    U. Heintz Brown University, Providence, Rhode Island 02912, USA    C. Hensel LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil    I. Heredia-De La Cruz CINVESTAV, Mexico City, Mexico    K. Herner Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    G. Hesketh The University of Manchester, Manchester M13 9PL, United Kingdom    M.D. Hildreth University of Notre Dame, Notre Dame, Indiana 46556, USA    R. Hirosky University of Virginia, Charlottesville, Virginia 22904, USA    T. Hoang Florida State University, Tallahassee, Florida 32306, USA    J.D. Hobbs State University of New York, Stony Brook, New York 11794, USA    B. Hoeneisen Universidad San Francisco de Quito, Quito, Ecuador    J. Hogan Rice University, Houston, Texas 77005, USA    M. Hohlfeld Institut für Physik, Universität Mainz, Mainz, Germany    J.L. Holzbauer University of Mississippi, University, Mississippi 38677, USA    I. Howley University of Texas, Arlington, Texas 76019, USA    Z. Hubacek Czech Technical University in Prague, Prague, Czech Republic CEA, Irfu, SPP, Saclay, France    V. Hynek Czech Technical University in Prague, Prague, Czech Republic    I. Iashvili State University of New York, Buffalo, New York 14260, USA    Y. Ilchenko Southern Methodist University, Dallas, Texas 75275, USA    R. Illingworth Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A.S. Ito Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S. Jabeen Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Jaffré LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France    A. Jayasinghe University of Oklahoma, Norman, Oklahoma 73019, USA    M.S. Jeong Korea Detector Laboratory, Korea University, Seoul, Korea    R. Jesik Imperial College London, London SW7 2AZ, United Kingdom    P. Jiang University of Science and Technology of China, Hefei, People’s Republic of China    K. Johns University of Arizona, Tucson, Arizona 85721, USA    E. Johnson Michigan State University, East Lansing, Michigan 48824, USA    M. Johnson Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A. Jonckheere Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P. Jonsson Imperial College London, London SW7 2AZ, United Kingdom    J. Joshi University of California Riverside, Riverside, California 92521, USA    A.W. Jung Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A. Juste Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Física d’Altes Energies (IFAE), Barcelona, Spain    E. Kajfasz CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    D. Karmanov Moscow State University, Moscow, Russia    I. Katsanos University of Nebraska, Lincoln, Nebraska 68588, USA    M. Kaur Panjab University, Chandigarh, India    R. Kehoe Southern Methodist University, Dallas, Texas 75275, USA    S. Kermiche CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    N. Khalatyan Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A. Khanov Oklahoma State University, Stillwater, Oklahoma 74078, USA    A. Kharchilava State University of New York, Buffalo, New York 14260, USA    Y.N. Kharzheev Joint Institute for Nuclear Research, Dubna, Russia    I. Kiselevich Institute for Theoretical and Experimental Physics, Moscow, Russia    J.M. Kohli Panjab University, Chandigarh, India    A.V. Kozelov Institute for High Energy Physics, Protvino, Russia    J. Kraus University of Mississippi, University, Mississippi 38677, USA    A. Kumar State University of New York, Buffalo, New York 14260, USA    A. Kupco Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic    T. Kurča IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France    V.A. Kuzmin Moscow State University, Moscow, Russia    S. Lammers Indiana University, Bloomington, Indiana 47405, USA    P. Lebrun IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France    H.S. Lee Korea Detector Laboratory, Korea University, Seoul, Korea    S.W. Lee Iowa State University, Ames, Iowa 50011, USA    W.M. Lee Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    X. Lei University of Arizona, Tucson, Arizona 85721, USA    J. Lellouch LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    D. Li LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    H. Li University of Virginia, Charlottesville, Virginia 22904, USA    L. Li University of California Riverside, Riverside, California 92521, USA    Q.Z. Li Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    J.K. Lim Korea Detector Laboratory, Korea University, Seoul, Korea    D. Lincoln Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    J. Linnemann Michigan State University, East Lansing, Michigan 48824, USA    V.V. Lipaev Institute for High Energy Physics, Protvino, Russia    R. Lipton Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    H. Liu Southern Methodist University, Dallas, Texas 75275, USA    Y. Liu University of Science and Technology of China, Hefei, People’s Republic of China    A. Lobodenko Petersburg Nuclear Physics Institute, St. Petersburg, Russia    M. Lokajicek Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic    R. Lopes de Sa Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    R. Luna-Garcia CINVESTAV, Mexico City, Mexico    A.L. Lyon Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A.K.A. Maciel LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil    R. Madar Physikalisches Institut, Universität Freiburg, Freiburg, Germany    R. Magaña-Villalba CINVESTAV, Mexico City, Mexico    S. Malik University of Nebraska, Lincoln, Nebraska 68588, USA    V.L. Malyshev Joint Institute for Nuclear Research, Dubna, Russia    J. Mansour II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    J. Martínez-Ortega CINVESTAV, Mexico City, Mexico    R. McCarthy State University of New York, Stony Brook, New York 11794, USA    C.L. McGivern The University of Manchester, Manchester M13 9PL, United Kingdom    M.M. Meijer Nikhef, Science Park, Amsterdam, the Netherlands Radboud University Nijmegen, Nijmegen, the Netherlands    A. Melnitchouk Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Menezes Northern Illinois University, DeKalb, Illinois 60115, USA    P.G. Mercadante Universidade Federal do ABC, Santo André, Brazil    M. Merkin Moscow State University, Moscow, Russia    A. Meyer III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany    J. Meyer II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    F. Miconi IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France    N.K. Mondal Tata Institute of Fundamental Research, Mumbai, India    M. Mulhearn University of Virginia, Charlottesville, Virginia 22904, USA    E. Nagy CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    M. Narain Brown University, Providence, Rhode Island 02912, USA    R. Nayyar University of Arizona, Tucson, Arizona 85721, USA    H.A. Neal University of Michigan, Ann Arbor, Michigan 48109, USA    J.P. Negret Universidad de los Andes, Bogotá, Colombia    P. Neustroev Petersburg Nuclear Physics Institute, St. Petersburg, Russia    H.T. Nguyen University of Virginia, Charlottesville, Virginia 22904, USA    T. Nunnemann Ludwig-Maximilians-Universität München, München, Germany    J. Orduna Rice University, Houston, Texas 77005, USA    N. Osman CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    J. Osta University of Notre Dame, Notre Dame, Indiana 46556, USA    A. Pal University of Texas, Arlington, Texas 76019, USA    N. Parashar Purdue University Calumet, Hammond, Indiana 46323, USA    V. Parihar Brown University, Providence, Rhode Island 02912, USA    S.K. Park Korea Detector Laboratory, Korea University, Seoul, Korea    R. Partridge Brown University, Providence, Rhode Island 02912, USA    N. Parua Indiana University, Bloomington, Indiana 47405, USA    A. Patwa Brookhaven National Laboratory, Upton, New York 11973, USA    B. Penning Imperial College London, London SW7 2AZ, United Kingdom    M. Perfilov Moscow State University, Moscow, Russia    Y. Peters The University of Manchester, Manchester M13 9PL, United Kingdom    K. Petridis The University of Manchester, Manchester M13 9PL, United Kingdom    G. Petrillo University of Rochester, Rochester, New York 14627, USA    P. Pétroff LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France    M.-A. Pleier Brookhaven National Laboratory, Upton, New York 11973, USA    V.M. Podstavkov Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A.V. Popov Institute for High Energy Physics, Protvino, Russia    M. Prewitt Rice University, Houston, Texas 77005, USA    D. Price The University of Manchester, Manchester M13 9PL, United Kingdom    N. Prokopenko Institute for High Energy Physics, Protvino, Russia    J. Qian University of Michigan, Ann Arbor, Michigan 48109, USA    A. Quadt II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    B. Quinn University of Mississippi, University, Mississippi 38677, USA    P.N. Ratoff Lancaster University, Lancaster LA1 4YB, United Kingdom    I. Razumov Institute for High Energy Physics, Protvino, Russia    I. Ripp-Baudot IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France    F. Rizatdinova Oklahoma State University, Stillwater, Oklahoma 74078, USA    M. Rominsky Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A. Ross Lancaster University, Lancaster LA1 4YB, United Kingdom    C. Royon CEA, Irfu, SPP, Saclay, France    P. Rubinov Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    R. Ruchti University of Notre Dame, Notre Dame, Indiana 46556, USA    G. Sajot LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France    A. Sánchez-Hernández CINVESTAV, Mexico City, Mexico    M.P. Sanders Ludwig-Maximilians-Universität München, München, Germany    A.S. Santos LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil    G. Savage Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Savitskyi Taras Shevchenko National University of Kyiv, Kiev, Ukraine    L. Sawyer Louisiana Tech University, Ruston, Louisiana 71272, USA    T. Scanlon Imperial College London, London SW7 2AZ, United Kingdom    R.D. Schamberger State University of New York, Stony Brook, New York 11794, USA    Y. Scheglov Petersburg Nuclear Physics Institute, St. Petersburg, Russia    H. Schellman Northwestern University, Evanston, Illinois 60208, USA    M. Schott Institut für Physik, Universität Mainz, Mainz, Germany    C. Schwanenberger The University of Manchester, Manchester M13 9PL, United Kingdom    R. Schwienhorst Michigan State University, East Lansing, Michigan 48824, USA    J. Sekaric University of Kansas, Lawrence, Kansas 66045, USA    H. Severini University of Oklahoma, Norman, Oklahoma 73019, USA    E. Shabalina II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    V. Shary CEA, Irfu, SPP, Saclay, France    S. Shaw The University of Manchester, Manchester M13 9PL, United Kingdom    A.A. Shchukin Institute for High Energy Physics, Protvino, Russia    V. Simak Czech Technical University in Prague, Prague, Czech Republic    P. Skubic University of Oklahoma, Norman, Oklahoma 73019, USA    P. Slattery University of Rochester, Rochester, New York 14627, USA    D. Smirnov University of Notre Dame, Notre Dame, Indiana 46556, USA    G.R. Snow University of Nebraska, Lincoln, Nebraska 68588, USA    J. Snow Langston University, Langston, Oklahoma 73050, USA    S. Snyder Brookhaven National Laboratory, Upton, New York 11973, USA    S. Söldner-Rembold The University of Manchester, Manchester M13 9PL, United Kingdom    L. Sonnenschein III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany    K. Soustruznik Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic    J. Stark LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France    D.A. Stoyanova Institute for High Energy Physics, Protvino, Russia    M. Strauss University of Oklahoma, Norman, Oklahoma 73019, USA    L. Suter The University of Manchester, Manchester M13 9PL, United Kingdom    P. Svoisky University of Oklahoma, Norman, Oklahoma 73019, USA    M. Titov CEA, Irfu, SPP, Saclay, France    V.V. Tokmenin Joint Institute for Nuclear Research, Dubna, Russia    Y.-T. Tsai University of Rochester, Rochester, New York 14627, USA    D. Tsybychev State University of New York, Stony Brook, New York 11794, USA    B. Tuchming CEA, Irfu, SPP, Saclay, France    C. Tully Princeton University, Princeton, New Jersey 08544, USA    L. Uvarov Petersburg Nuclear Physics Institute, St. Petersburg, Russia    S. Uvarov Petersburg Nuclear Physics Institute, St. Petersburg, Russia    S. Uzunyan Northern Illinois University, DeKalb, Illinois 60115, USA    R. Van Kooten Indiana University, Bloomington, Indiana 47405, USA    W.M. van Leeuwen Nikhef, Science Park, Amsterdam, the Netherlands    N. Varelas University of Illinois at Chicago, Chicago, Illinois 60607, USA    E.W. Varnes University of Arizona, Tucson, Arizona 85721, USA    I.A. Vasilyev Institute for High Energy Physics, Protvino, Russia    A.Y. Verkheev Joint Institute for Nuclear Research, Dubna, Russia    L.S. Vertogradov Joint Institute for Nuclear Research, Dubna, Russia    M. Verzocchi Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Vesterinen The University of Manchester, Manchester M13 9PL, United Kingdom    D. Vilanova CEA, Irfu, SPP, Saclay, France    P. Vokac Czech Technical University in Prague, Prague, Czech Republic    H.D. Wahl Florida State University, Tallahassee, Florida 32306, USA    M.H.L.S. Wang Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    J. Warchol University of Notre Dame, Notre Dame, Indiana 46556, USA    G. Watts University of Washington, Seattle, Washington 98195, USA    M. Wayne University of Notre Dame, Notre Dame, Indiana 46556, USA    J. Weichert Institut für Physik, Universität Mainz, Mainz, Germany    L. Welty-Rieger Northwestern University, Evanston, Illinois 60208, USA    M.R.J. Williams Indiana University, Bloomington, Indiana 47405, USA    G.W. Wilson University of Kansas, Lawrence, Kansas 66045, USA    M. Wobisch Louisiana Tech University, Ruston, Louisiana 71272, USA    D.R. Wood Northeastern University, Boston, Massachusetts 02115, USA    T.R. Wyatt The University of Manchester, Manchester M13 9PL, United Kingdom    Y. Xie Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    R. Yamada Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S. Yang University of Science and Technology of China, Hefei, People’s Republic of China    T. Yasuda Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    Y.A. Yatsunenko Joint Institute for Nuclear Research, Dubna, Russia    W. Ye State University of New York, Stony Brook, New York 11794, USA    Z. Ye Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    H. Yin Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    K. Yip Brookhaven National Laboratory, Upton, New York 11973, USA    S.W. Youn Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    J.M. Yu University of Michigan, Ann Arbor, Michigan 48109, USA    J. Zennamo State University of New York, Buffalo, New York 14260, USA    T.G. Zhao The University of Manchester, Manchester M13 9PL, United Kingdom    B. Zhou University of Michigan, Ann Arbor, Michigan 48109, USA    J. Zhu University of Michigan, Ann Arbor, Michigan 48109, USA    M. Zielinski University of Rochester, Rochester, New York 14627, USA    D. Zieminska Indiana University, Bloomington, Indiana 47405, USA    L. Zivkovic LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France
July 21, 2015
Abstract

We present a simultaneous measurement of the forward-backward asymmetry and the top-quark polarization in  production in dilepton final states using  of proton-antiproton collisions at  TeV with the D0 detector. To reconstruct the distributions of kinematic observables we employ a matrix element technique that calculates the likelihood of the possible kinematic configurations. After accounting for the presence of background events and for calibration effects, we obtain a forward-backward asymmetry of and a top-quark polarization times spin analyzing power in the beam basis of , with a correlation of between the measurements. If we constrain the forward-backward asymmetry to its expected standard model value, we obtain a measurement of the top polarization of If we constrain the top polarization to its expected standard model value, we measure a forward-backward asymmetry of A combination with the D0  measurement in the lepton+jets final state yields an asymmetry of Within their respective uncertainties, all these results are consistent with the standard model expectations.

pacs:
14.65.Ha, 12.38.Qk, 13.85.Qk, 11.30.Er

FERMILAB-PUB-15-312-E

The D0 Collaboration111with visitors from Augustana College, Sioux Falls, SD, USA, The University of Liverpool, Liverpool, UK, DESY, Hamburg, Germany, CONACyT, Mexico City, Mexico, SLAC, Menlo Park, CA, USA, University College London, London, UK, Centro de Investigacion en Computacion - IPN, Mexico City, Mexico, Universidade Estadual Paulista, São Paulo, Brazil, Karlsruher Institut für Technologie (KIT) - Steinbuch Centre for Computing (SCC), D-76128 Karlsruhe, Germany, Office of Science, U.S. Department of Energy, Washington, D.C. 20585, USA, American Association for the Advancement of Science, Washington, D.C. 20005, USA, Kiev Institute for Nuclear Research, Kiev, Ukraine, University of Maryland, College Park, Maryland 20742, USA and European Orgnaization for Nuclear Research (CERN), Geneva, Switzerland

I Introduction

In proton-antiproton collisions at =1.96 TeV, top quark pairs are predominantly produced in valence quark-antiquark annihilations. The standard model (SM) predicts this process to be slightly forward-backward asymmetric: the top quark (antiquark) tends to be emitted in the same direction as the incoming quark (antiquark), and thus, in the same direction as the incoming proton (antiproton). The forward-backward asymmetry in the production is mainly due to positive contributions from the interference between tree-level and next-to-leading-order (NLO) box diagrams. It receives smaller negative contributions from the interference between initial and final state radiation. The interferences with electroweak processes increase the asymmetry. In the SM, the asymmetry is predicted to be  Bernreuther and Si (2012); Czakon et al. (2015); Kidonakis (2015). Within the SM, the longitudinal polarizations of the top quark and antiquark are due to parity violating electroweak contributions to the production process. The polarization is expected to be for all choices of the spin quantization axis Bernreuther et al. (2006); Bernreuther (2008).

Physics beyond the SM could affect the  production mechanism and thus both the forward-backward asymmetry and the top quark and antiquark polarizations. In particular, models with a new parity violating interaction such as models with axigluons Frampton and Glashow (1987); Hall and Nelson (1985); Antunano et al. (2008); Frampton et al. (2010), can induce a large positive or negative asymmetry together with a sizable polarization.

The  production asymmetry, , is defined in terms of the difference between the rapidities of the top and antitop quarks, :

(1)

where is the number of events in configuration . By definition, is independent of effects from the top quark decay such as top quark polarization. However, it requires the reconstruction of the initial state from the decay products, which is challenging especially in dilepton channels.

Measurements of have been performed in the lepton+jets channels by the CDF Aaltonen et al. (2013a) and D0 Abazov et al. (2014a) Collaborations. Other asymmetry measurements have been performed using observables based on the pseudo-rapidity of the leptons from decays Aaltonen et al. (2013b, 2014); Abazov et al. (2014b, 2013a). All these measurements agree with the SM predictions. A comprehensive review of asymmetry measurements performed at the Tevatron can be found in Ref. Aguilar-Saavedra et al. (2015).

As top quarks decay before they hadronize, their spin properties are transferred to the decay products. The top (antitop) polarization () along a given quantization axis impacts the angular distribution of the positively (negatively) charged lepton Bernreuther (2008)

(2)

where () is the angle between the positively (negatively) charged lepton in the top (antitop) rest frame and the quantization axis , and () is the spin analyzing power of the positively (negatively) charged lepton, which is close to 1 () at the 0.1% level within the SM Bernreuther (2008). The polarization terms () can be obtained as two times the asymmetry of the () distribution

(3)

In the following we use the beam basis, where is the direction of the proton beam in the  zero momentum frame. Since we only use the beam basis, we omit the subscript in the following and define the polarization observable as:

(4)

Polarization effects have been studied at the Tevatron in the context of the measurements of the leptonic asymmetries in Ref. Abazov et al. (2013b), but no actual measurement of the polarization has been performed. Measurements of the polarization have been conducted for top pair production in collisions at the Large Hadron Collider at  TeV. These measurements, performed in different basis choices, are all consistent with the SM expectations Chatrchyan et al. (2014); Aad et al. (2013).

This article presents a simultaneous measurement of  and with the D0 detector in the dilepton decay channel. It is based on the full Tevatron integrated luminosity of  using  final states with two leptons, , , or . We first reconstruct the  and distributions employing a matrix element integration technique similar to that used for the top-quark mass measurement in the dilepton channel Abazov et al. (2011). These distributions are used to extract raw measurements of asymmetry and polarization,  and , in data. The experimental observables  and  are correlated because of acceptance and resolution effects. Using a mc@nlo Frixione and Webber (2002, 2008) simulation, we compute the relation between the raw measurements  and , and the true parton-level asymmetry and polarization to determine calibration corrections. We then extract the final measured values of  and . This is the first measurement of the  forward-backward asymmetry obtained from the reconstructed  distribution in the dilepton channel and the first measurement of the top quark polarization at the Fermilab Tevatron collider.

Ii Detector and object reconstruction

The D0 detector used for the Run II of the Fermilab Tevatron collider is described in detail in Refs. Abachi et al. (1994); Abazov et al. (2006); Abolins et al. (2008); Angstadt et al. (2010). The innermost part of the detector is composed of a central tracking system with a silicon microstrip tracker (SMT) and a central fiber tracker embedded within a 2 T solenoidal magnet. The tracking system is surrounded by a central preshower detector and a liquid-argon/uranium calorimeter with electromagnetic, fine hadronic, and coarse hadronic sections. The central calorimeter (CC) covers pseudorapidities Not (a) of . Two end calorimeters (EC) extend the coverage to , while the coverage of the pseudorapidity region , where the EC and CC overlap, is augmented with scintillating tiles. A muon spectrometer, with pseudorapidity coverage of , is located outside the calorimetry and comprises drift tubes and scintillation counters, before and after iron toroidal magnets. Trigger decisions are based on information from the tracking detectors, calorimeters, and muon spectrometer.

Electrons are reconstructed as isolated clusters in the electromagnetic calorimeter and required to spatially match a track in the central tracking system. They have to pass a boosted decision tree Abazov et al. (2014c) criterion based on calorimeter shower shape observables, calorimeter isolation, a spatial track match probability estimate, and the ratio of the electron cluster energy to track momentum (). Electrons are required to be in the acceptance of the electromagnetic calorimeter ( or ).

Muons are identified by the presence of at least one track segment reconstructed in the acceptance () of the muon spectrometer that is spatially consistent with a track in the central tracking detector Abazov et al. (2014d). The transverse momentum and charge are measured by the curvature in the central tracking system. The angular distance to the nearest jet, the momenta of charged particles in a cone around the muon track, and the energy deposited around the muon trajectory in the calorimeter, are used to select isolated muons.

Jets are reconstructed from energy deposits in the calorimeter using an iterative midpoint cone algorithm Blazey et al. (2000) with a cone radius of  Not (b). The jet energies are calibrated using transverse momentum balance in jet events Abazov et al. (2014e).

Iii Dataset and Event Selection

The signature of  production in dilepton final states consists of two high- leptons (electrons or muons), two high- jets arising from the showering of two quarks, and missing transverse energy () due to the undetected neutrinos. The main backgrounds in this final state arise from , with , , or , and diboson production (, , ). These backgrounds are evaluated from Monte Carlo (MC) simulated samples as described in section IV.3. Another source of background comes from +jets and multijet events, if one or two jets are misreconstructed as electrons or if a muon from a jet passes the isolation criteria. The contribution from these backgrounds, denoted as “instrumental background events”, are estimated directly from data as described in section IV.5. Each of the dilepton channels is subject to a different mixture and level of background contamination, in particular for the background arising from the  process. We therefore apply slightly different selection requirements. The main selection criteria to obtain the final samples of candidate events are:

  1. We select two high  ( ) isolated leptons of opposite charge.

  2. We require that at least one electron passes a single electron trigger condition in the  channel ( efficient), and that at least one muon passes a single muon trigger condition in the  channel ( efficient). In the channel, we do not require any specific trigger condition, i.e., we use all D0 trigger terms ( efficient).

  3. We require two or more jets of and .

  4. We further improve the purity of the selection by exploiting the significant imbalance of transverse energy due to undetected neutrinos and by exploiting several topological variables:

    1. The missing transverse energy  is the magnitude of the missing transverse momentum, obtained from the vector sum of the transverse components of energy deposits in the calorimeter, corrected for the differences in detector response of the reconstructed muons, electrons, and jets.

    2. The missing transverse energy significance, , is the logarithm of the probability to measure  under the hypothesis that the true missing transverse momentum is zero, accounting for the energy resolution of individual reconstructed objects and underlying event Schwartzman (2004).

    3. is the scalar sum of transverse momenta of the leading lepton and the two leading jets.

    In the  channel we require , in the  channel  , and in the  channel and .

  5. We require that at least one of the two leading jets be -tagged, using a cut on the multivariate discriminant described in Ref. Abazov et al. (2014f). The requirement is optimized separately for each channel. The  selection efficiencies for these requirements are , , and for the , , and  channels, respectively.

  6. The integration of the matrix elements by vegas, described in section V.1, may return a tiny probability if the event is not consistent with the  event hypothesis due to numerical instabilities in the integration process. After removing low probability events, we retain signal events in the MC simulation with an efficiency of 99.97%. For background MC, the efficiency is . We remove no data events with this requirement.

Iv Signal and background samples

iv.1 Signal

To simulate the signal, we employ MC events generated with the CTEQ6M1 parton distribution functions (PDFs) Nadolsky et al. (2008) and mc@nlo 3.4 Frixione and Webber (2002, 2008) interfaced to herwig 6.510 Corcella et al. (2001) for showering and hadronization. Alternate signal MC samples are generated to study systematic uncertainties and the shape of the  distribution. We use a sample generated with alpgen Mangano et al. (2003) interfaced to pythia 6.4 Sjostrand et al. (2006) for showering and hadronization and a sample generated with alpgen interfaced to herwig 6.510. For both samples we use cteq6l1 PDFs Nadolsky et al. (2008).

The mc@nlo generator is used for the nominal signal sample as it simulates NLO effects yielding non-zero . The value of  at parton level without applying any selection requirement is , which is smaller than a SM prediction Czakon et al. (2015) that includes higher order effects.

The MC events are generated with a top-quark mass of . They are normalized to a  production cross section of 7.45 pb, which corresponds to the calculation of Ref. Moch and Uwer (2008) for . The generated top mass of 172.5  differs from the Tevatron average mass of  Aaltonen et al. (2012). We correct for this small difference in section VI.2.

iv.2 Beyond standard model benchmarks

We also study the five benchmark axigluons models proposed in Ref. Carmona et al. (2014) that modify production. For each of the proposed beyond standard model (BSM) benchmarks, we produce a  MC sample using the madgraph Alwall et al. (2014) generator interfaced to pythia 6.4 for showering and hadronization, and the cteq6l1 PDFs. The boson model proposed in Ref. Carmona et al. (2014) is not considered here since it is excluded by our  differential cross-section measurement Abazov et al. (2014g).

iv.3 Background estimated with simulated events

The background samples are generated using the CTEQ6L1 PDFs. The  events are generated using alpgen interfaced to pythia 6.4. We normalize the sample to the NNLO cross section Gavin et al. (2011). The distribution of bosons is weighted to match the distribution observed in data Abazov et al. (2008), taking into account its dependence on the number of reconstructed jets. The diboson backgrounds are simulated using pythia and are normalized to the NLO cross section calculation performed by MCFM Campbell and Ellis (1999, 2010).

iv.4 D0 simulation

The signal and background processes except instrumental background are simulated with a detailed geant3-based Brun and Carminati (unpublished) MC simulation of the D0 detector. They are processed with the same reconstruction software as used for data. In order to model the effects of multiple interactions, the MC events are overlaid with events from random collisions with the same luminosity distribution as data. The jet energy calibration is adjusted in simulated events to match the one measured in data. Corrections for residual differences between data and simulation are applied to electrons, muons, and jets for both identification efficiencies and energy resolutions.

iv.5 Instrumental background estimated with data

The normalization of events with jets misidentified as electrons is estimated using the “matrix method” Abazov et al. (2007) separately for the  and  channels. The contribution from jets producing identified muons in the  channel is obtained using the same selection criteria as for the sample of candidate events, but demanding that the leptons have the same charge. In the channel, it is obtained in the same way but after subtracting the contribution from events with jets misidentified as electrons.

Once the absolute contribution of instrumental background events has been determined, we also need “template samples” that model their kinematic properties. In the  channel, the template for instrumental background events is obtained with the same selection criteria as for the samples of candidate events, but without applying the complete set of electron selection criteria. For the  and  channels, the contributions from instrumental background events is negligible and the result is not sensitive to the choice of template. For simplicity, we re-employ the  template for both the  and  channels.

Figure 1: [color online] Comparison of distributions between data and MC simulations at the final selection for (a) the transverse momentum of the leading lepton, (b) the transverse momentum of the secondary lepton, (c) the pseudorapidity of the leading lepton, (d) the pseudorapidity of the secondary lepton, (e) the transverse momentum of the leading jet, (f) the transverse momentum of the secondary jet, (g) the , and (h) the difference between the two lepton pseudorapidities. The overflow bin content has been added to the last bin.

iv.6 Comparison of MC simulation to selected data

A comparison between the expected and observed numbers of events at the final selection levels is reported in Table 1. The selected sample is relatively pure with a background fraction varying between 10% and 16% depending on the channel.

Channel Dibosons Instrumental Total expected Data
192
104
Table 1: Comparison between expected and observed numbers of events at the final selection level for the different channels. The values are reported with their statistical uncertainties.

A comparison of kinematic distributions between data and expectations at the final selection level is shown in Fig. 1.

V Matrix element method

To reconstruct distributions of kinematic observables describing the  events, we use a novel modification of the matrix element (ME) integration developed for the measurements Abazov et al. (2011, 2015) by the D0 Collaboration. In particular, this method is employed to reconstruct the , , and distributions, from which an estimate of the forward-backward asymmetry and top polarization are extracted.

v.1 Matrix element integration

The ME integration used in Refs. Abazov et al. (2011, 2015) consists in computing the likelihood to observe a given event with the vector of measured quantities ,

(5)

In this expression, is a vector describing the kinematic quantities of the six particles of the final state, is the matrix element describing the dynamics of the process, is the 6-body phase space term, the functions are the PDFs of the incoming partons of momenta and and of different possible flavors, , referred to as the transfer function, describes the probability density of a parton state to be reconstructed as , is a function describing the distribution of the system tranverse momentum, , while the azimuthal angle of this system, , is assumed to have a uniform distribution over , and is the product of the experimental acceptance and the production cross-section. The matrix element, , is computed at leading order (LO) for annihilation only, as it represents the main subprocess () of the total production. The functions are given by the CTEQ6L1 leading order PDF set. The function is derived from parton-level simulated events generated with alpgen interfaced to pythia. More details on this function can be found in Ref. Grohsjean (2008). Ambiguities between partons and reconstructed particle assignments are properly treated by defining an effective transfer function that sums over all the different assignments As we consider only the two leading jets in the integration process, there are only two possibilities to assign a given jet to either the or partons.

The number of variables to integrate is given by the six three-vectors of final state partons (of known mass), the transverse momentum and transverse direction, and the longitudinal momenta of the two incoming partons. These 22 integration variables are reduced by the following constraints: the lepton and -quark directions are assumed to be perfectly measured (8 constraints), the energy-momentum between the initial state and the final state is conserved (4 constraints), the and system have a mass of   Olive et al. (2014) (2 constraints), and the and system have a mass of   (2 constraints). Transfer functions account for muon and jet energies. The transfer functions are the same as used in Ref. Abazov et al. (2015). The electron momentum measurement has a precision of , which is much better than the muon momentum resolution of typically 10% and the jet momentum resolution of typically 20%. We thus consider that the electron momenta are perfectly measured. This gives one additional constraint in the channel and two additional constraints in the  channel. Thus, we integrate over 4, 5, and 6 variables in the , , and  channels, respectively. The integration variables are , , energy of leading jet, energy of sub-leading jet, and energy of the muon(s) (if applicable).

The integration is performed using the MC-based numerical integration program vegas Lepage (1978, 1980). The interface to the vegas integration algorithm is provided by the GNU Scientific Library (GSL) Galassi et al. (2009). The MC integration consists of randomly sampling the space of integration variables, computing a weight for each of the random points that accounts for both the integrand and the elementary volume of the sampling space, and finally summing all of the weights. The random sampling is based on a grid in the space of integration that is iteratively optimized to ensure fine sampling in regions with large variations of the integrand. For each of the random points, equations are solved to transform these integration variables into the parton-level variables of Eq. (5), accounting for the measured quantities . The Jacobian of the transformation is also computed to ensure proper weighting of the sampling space elementary volume.

v.2 Likelihood of a parton-level observable

For any kinematic quantity reconstructed from the parton momenta , for example , we can build a probability density that measures the likelihood of at the partonic level to give the reconstructed value . This likelihood is obtained by inserting a term in the integrand of Eq. (5), and normalizing the function so that . The probability density is obtained by modifying the vegas integration algorithm. For each reconstructed  event and each point in the integration space tested by vegas, the integrand of Eq. (5) and the quantity are computed. After the full space of integration has been sampled, we obtain a weighted distribution of the variable that represents the function up to an overall normalization factor.

For each reconstructed event with observed kinematics , where is an event index, we obtain a likelihood function . By accumulating these likelihood functions over the sample of events, we obtain a distribution that estimates the true distribution of the variable . The performance of this method of reconstruction for parton-level distributions is estimated by comparing the accumulation of likelihood functions to the true parton-level quantities for MC events, as shown in Fig. 2.

Figure 2: [color online] Accumulation of likelihood functions (, with along the vertical axis) versus the corresponding true parton level quantity ( along the horizontal axis) in  MC events after applying the selection criteria for (a) , (b) , and (c) . Each single MC event contributes in these plots with a complete distribution, , along the vertical axis for a given value on the horizontal axis, . The shades of color indicate the bin contents in arbitrary units.

v.3 Raw estimate of

We could choose to use the maximum of the likelihood function to estimate the true value of on an event-by-event basis. However, to maximize the use of available information, we keep the full shape of the functions and accumulate these functions over the sample of  events to obtain an estimate of the parton level distributions, which is then used to determine . This method has been verified to perform better than the maximum likelihood method. The distribution is shown in Fig. 3(a), after subtracting the background contributions from the data. The raw asymmetry , extracted from this distribution, is reported in Table 2. Since this distribution is an approximate estimation of the true distribution of , the raw asymmetry is an approximation of the true . The measurement therefore needs to be calibrated. The calibration is discussed below.

Channel            
Dilepton
Table 2: Raw forward-backward asymmetry in data before background subtraction, , asymmetry of the background, , and measurement once the background contribution has been subtracted, . Asymmetries are reported in percent, together with their statistical uncertainties.

The use of an event-by-event likelihood function allows us to define an asymmetry observable for each event

(6)

where the observable averaged over the sample of candidate events is equal to the raw asymmetry . By construction, lies in the interval . For a perfectly reconstructed event without resolution effects, would be either equal to for or to for . The use of allows us to determine the statistical uncertainty on as the uncertainty on the average of a distribution.

v.4 Raw estimate of

In the same way as in the previous section, we use the accumulation of the likelihoods and to estimate the distributions of and . The distributions and are shown in Figs. 3(b) and 3(c), after subtracting the background contributions from the data. The raw asymmetries, and , and the raw polarization extracted from the data are reported in Table 3. As for , the measurement of  needs to be calibrated to retrieve the parton-level values of the polarization.

Channel
Dilepton
Table 3: Asymmetry estimates for the distributions. The raw asymmetry measurement in the data before background subtraction, , the asymmetry of the background, , and the measurement once the background contribution has been subtracted, , are reported. The polarization estimates defined as are also given. All values are reported in percent, together with their statistical uncertainties.
Figure 3: [color online] Estimated distribution of the (a) , (b) , and (c) observables in dilepton events after subtracting the expected background contribution. Deviations beweeen the background-subtracted data and MC can be attributed to statistical fluctuations. The background-subtracted data asymmetries and the MC asymmetries extracted from these distributions are also reported. These raw asymmetries need to be corrected for calibration effects to retrieve the parton-level asymmetries.

v.5 Statistical correlation between  and

We measure the statistical correlation between and in the data, which is needed to determine the statistical correlation between the measurements of  and . In the same way as is the average of an event-by-event asymmetry , the raw asymmetries and are the averages of event-by-event asymmetries denoted by and . The correlation between  and  is identical to the correlation between the observables and . This correlation is determined from the background subtracted data by computing the RMS and mean values of the distributions of , , and :

(7)

We report the values measured in data in Table 4.

Channel Data Background DataBackground
Dilepton
Table 4: Measurement of the statistical correlation between the asymmetry and the polarization for the data, background, and background subtracted data. Values are reported in percent, together with their statistical uncertainties.

Vi Results corrected for calibration

The calibration procedure finds a relation between the raw asymmetry and polarization, , obtained after subtracting the background contributions, and the true asymmetry and polarization of  events. The calibration procedure corrects for dilution effects that arise from the limited acceptance for  events, the finite resolution of the kinematic reconstruction, and the simplified assumptions used in the matrix element integration (e.g., leading order ME, no ME, only two jets considered). The relation is inverted to extract a measurement of  and  from the values of  and  observed in data.

The nominal calibration is determined using a sample of simulated  mc@nlo dilepton events. The procedure is repeated with the samples from the other generators (see section IV.1 and IV.2) to determine different systematic uncertainties. We normalize the individual , , and  contributions to have the same proportions as observed in the data samples after subtracting the expected backgrounds.

vi.1 Samples for calibration

We produce test samples from a nominal MC sample by reweighting the events according to the true value of the parton-level , , and . The reweighting factors are computed as follows.

vi.1.1 Reweighting of lepton angular distributions

The general expression for the double differential lepton angle distribution is Bernreuther (2008)

(8)

where is the spin correlation coefficient, which is in the SM. In the beam basis one has . We use this relation to reweight a given MC sample to simulate a target polarization of .

vi.1.2 Reweighting of  distribution

To determine a method of reweighting the  distribution, denoted , we study its shape using the different MC samples of section IV at the generated level, i.e., before event selection and reconstruction. Inspired by the studies performed for the distribution of rapidity of the charged leptons in Ref. Hong et al. (2014), we rewrite as

(9)

where is the ratio between the odd and even part of the distribution, also called differential asymmetry as a function of ; we then fit with an empirical odd function

(10)

where and are shape parameters, while is a magnitude parameter. The term was not needed in the study of Ref. Hong et al. (2014), but improves the modeling significantly for the case of . The results of the fit for different  MC samples are shown in Fig. 4. If we reweight a MC sample so that the even part of the  distribution, the term , and the term are preserved, then the forward-backward asymmetry is proportional to .

Figure 4: [color online] Differential asymmetry at parton level for different MC samples. See Ref. Carmona et al. (2014) for the details on axigluon models. The observed is fitted with the functional form of Eq. (10).

These considerations yield the following procedure to produce a sample of test asymmetry starting from a MC sample of generated asymmetry . We first fit the differential asymmetry at the generated level with the function of Eq. (10) and determine the parameters , , and . Then we apply weights to the events processed through the D0 simulation

(11)

This procedure preserves the even part of the distribution of . It also preserves the original shape of the differential asymmetry, but changes its magnitude to the desired value.

vi.1.3 Calibration

Starting from the nominal mc@nlo  sample, we produce test samples using the product of the weights defined in sections VI.1.1 and VI.1.2. We use a grid of values for polarizations of and asymmetries of to obtain 30 samples in addition to the unweighted nominal sample. We apply the method of ME reconstruction to each of the 31 fully simulated samples and extract a raw measurement associated with a given parton-level . A fit to the obtained set of points in the space determines two affine functions that relate the reconstructed quantities to the true quantities: and . The affine functions fit the 31 points well, with residuals . We rewrite the affine relations using a matrix equation:

(12)

where is a calibration matrix and is a vector of offset terms. The values of the matrix and are reported in Table 5 for the the different dilepton channels. To determine the statistical uncertainties on the calibration parameters, we use an ensemble method. We split the mc@nlo samples into 100 independent ensembles and then repeat the calibration procedure for each of them.

Channel Calibration matrix Offset
Dilepton
Table 5: Calibration parameters and their statistical uncertainties for the different channels.

vi.2 Measurement of  and  after calibration

The calibration relation of Eq. (12) is inverted to retrieve the true partonic asymmetry and the true polarization  from the reconstructed and . We obtain a measurement of reported in Table 6 for each dileptonic channel using the calibration coefficients from Table 5 and the raw measurements from Tables 2 and 3.

Two alpgen+pythia  samples generated at different are used to estimate the dependence of the measurement on . Considering a top mass of  Aaltonen et al. (2012) as reference, the dilepton results reported in Table 6 have to be corrected by and for  and , respectively. The corrected combined dilepton results are

(13)
(14)
Channel

(%)

(%)

statistical(%)

correlation (%)

Dilepton
Table 6: Measurements of and  for each dileptonic channel corrected for the calibration (for ). The statistical correlation between the two measurements arises both from the statistical correlation of the experimental observables and the correction for the calibration.

Vii Systematic uncertainties

We consider three categories of uncertainties. Uncertainties affecting the signal are obtained by deriving calibration coefficients from alternate signal models and propagating them to the final results. Uncertainties affecting the background have an impact on the raw measurements,  and , as these observables are obtained after subtracting the background. They are propagated to the final measurement by applying the nominal calibration correction to the modified  and . The third category consists of the uncertainties on the calibration method. Since the measurement is performed after background subtraction, the calibration is independent of the normalization of the  simulation, and there is no systematic uncertainty due to signal normalization. The uncertainties on and  due to the different sources are summarized in Table 7, together with the correlations.

vii.1 Uncertainties on signal

Several sources of systematic uncertainties due to the detector and reconstruction model affect the jets and thus the signal kinematics. We consider uncertainties on the jet energy scale, flavor-dependent jet response, and jet energy resolution Abazov et al. (2014e). We also take into account uncertainties associated with tagging and vertexing Abazov et al. (2014f).

To estimate the impact of higher order correction, we compare the calibration obtained with mc@nlo+herwig to the calibration obtained with alpgen+herwig. To propagate uncertainty on the simulation of initial state and final state radiations (ISR/FSR), the amount of radiation is varied by scaling the ktfac parameter either by a factor of or in an alpgen+pythia simulation of  events Abazov et al. (2015). The hadronization and parton-shower model uncertainty is derived from the difference between the pythia and herwig generators, estimated by comparing alpgen+herwig to alpgen+pythia  samples. The different models for parton showers used by various MC generators yield different amounts of ISR between forward and backward events Skands et al. (2012); Winter et al. (2013). The uncertainty on the ISR model is defined as 50% of the difference between the nominal results and the results derived from a mc@nlo simulation in which the dependence of the forward-backward asymmetry on the of the system is removed. The uncertainty of 0.94 GeV on  Aaltonen et al. (2012) is propagated to the final result using two alpgen+pythia samples generated with different values. We determine PDF uncertainties by varying the 20 parameters describing the CTEQ6M1 PDF Nadolsky et al. (2008) within their uncertainties.

vii.2 Uncertainties on background

The uncertainty on the background level is obtained by varying the instrumental background normalization by 50% and the overall background normalization by 20%. The model of the instrumental background kinematics is varied, using the same method as in Ref. Abazov et al. (2013a). We reweight the reconstructed , , and distributions by a factor of , where is the statistical uncertainty band of the distribution and is chosen to be positive for , , , and negative for , , and <