Measurement of the anomalous like-sign dimuon charge asymmetry with 9 fb\bm{{}^{-1}} of \bm{p\bar{p}} collisions

Measurement of the anomalous like-sign dimuon charge asymmetry with 9 fb of  collisions

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    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    G. Alverson Northeastern University, Boston, Massachusetts 02115, USA    G.A. Alves LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil    M. Aoki Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Arov Louisiana Tech University, Ruston, Louisiana 71272, USA    A. Askew Florida State University, Tallahassee, Florida 32306, USA    B. Åsman Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden    O. Atramentov Rutgers University, Piscataway, New Jersey 08855, USA    C. Avila Universidad de los Andes, Bogotá, Colombia    J. BackusMayes University of Washington, Seattle, Washington 98195, USA    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 Florida State University, Tallahassee, Florida 32306, 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. Barreto Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil    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    S. Beale Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada    A. Bean University of Kansas, Lawrence, Kansas 66045, USA    M. Begalli Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil    M. Begel Brookhaven National Laboratory, Upton, New York 11973, USA    C. Belanger-Champagne Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden    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    V.A. Bezzubov Institute for High Energy Physics, Protvino, Russia    P.C. Bhat Fermi National Accelerator Laboratory, Batavia, Illinois 60510, 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    T. Bose Boston University, Boston, Massachusetts 02215, USA    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    G. Brooijmans Columbia University, New York, New York 10027, USA    A. Bross Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Brown LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    J. Brown LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    X.B. Bu Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Buehler University of Virginia, Charlottesville, Virginia 22901, 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    T.H. Burnett University of Washington, Seattle, Washington 98195, USA    C.P. Buszello Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden    B. Calpas CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    E. Camacho-Pérez CINVESTAV, Mexico City, Mexico    M.A. Carrasco-Lizarraga University of Kansas, Lawrence, Kansas 66045, USA    B.C.K. Casey Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    H. Castilla-Valdez CINVESTAV, Mexico City, Mexico    S. Chakrabarti State University of New York, Stony Brook, New York 11794, USA    D. Chakraborty Northern Illinois University, DeKalb, Illinois 60115, USA    K.M. Chan University of Notre Dame, Notre Dame, Indiana 46556, USA    A. Chandra Rice University, Houston, Texas 77005, USA    G. Chen University of Kansas, Lawrence, Kansas 66045, USA    S. Chevalier-Théry CEA, Irfu, SPP, Saclay, France    D.K. Cho Brown University, Providence, Rhode Island 02912, 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    A. Croc CEA, Irfu, SPP, Saclay, France    D. Cutts Brown University, Providence, Rhode Island 02912, USA    A. Das University of Arizona, Tucson, Arizona 85721, USA    G. Davies Imperial College London, London SW7 2AZ, United Kingdom    K. De University of Texas, Arlington, Texas 76019, USA    S.J. de Jong Radboud University Nijmegen, Nijmegen, the Netherlands and Nikhef, Science Park, Amsterdam, the Netherlands    E. De La Cruz-Burelo CINVESTAV, Mexico City, Mexico    F. Déliot CEA, Irfu, SPP, Saclay, France    M. Demarteau Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    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 CEA, Irfu, SPP, Saclay, France    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    T. Dorland University of Washington, Seattle, Washington 98195, USA    A. Dubey Delhi University, Delhi, India    L.V. Dudko Moscow State University, Moscow, Russia    D. Duggan Rutgers University, Piscataway, New Jersey 08855, USA    A. Duperrin CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    S. Dutt Panjab University, Chandigarh, India    A. Dyshkant Northern Illinois University, DeKalb, Illinois 60115, USA    M. Eads University of Nebraska, Lincoln, Nebraska 68588, 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 Brookhaven National Laboratory, Upton, New York 11973, USA    V.N. Evdokimov Institute for High Energy Physics, Protvino, Russia    G. Facini Northeastern University, Boston, Massachusetts 02115, USA    T. Ferbel University of Rochester, Rochester, New York 14627, USA    F. Fiedler Institut für Physik, Universität Mainz, Mainz, Germany    F. Filthaut Radboud University Nijmegen, Nijmegen, the Netherlands and Nikhef, Science Park, Amsterdam, 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    A. Garcia-Bellido University of Rochester, Rochester, New York 14627, USA    V. Gavrilov Institute for Theoretical and Experimental Physics, Moscow, Russia    P. Gay LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France    W. Geng CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France Michigan State University, East Lansing, Michigan 48824, USA    D. Gerbaudo Princeton University, Princeton, New Jersey 08544, 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    G. Golovanov Joint Institute for Nuclear Research, Dubna, Russia    A. Goussiou University of Washington, Seattle, Washington 98195, USA    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    Z.D. Greenwood Louisiana Tech University, Ruston, Louisiana 71272, USA    E.M. Gregores Universidade Federal do ABC, Santo André, Brazil    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    F. Guo State University of New York, Stony Brook, New York 11794, USA    G. Gutierrez Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P. Gutierrez University of Oklahoma, Norman, Oklahoma 73019, USA    A. Haas Columbia University, New York, New York 10027, USA    S. Hagopian Florida State University, Tallahassee, Florida 32306, USA    J. Haley Northeastern University, Boston, Massachusetts 02115, 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 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany    I. Heredia-De La Cruz CINVESTAV, Mexico City, Mexico    K. Herner University of Michigan, Ann Arbor, Michigan 48109, 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 22901, 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    M. Hohlfeld Institut für Physik, Universität Mainz, Mainz, Germany    Z. Hubacek Czech Technical University in Prague, Prague, Czech Republic CEA, Irfu, SPP, Saclay, France    N. Huske LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, 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 Brown University, Providence, Rhode Island 02912, USA    M. Jaffré LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France    D. Jamin CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    A. Jayasinghe University of Oklahoma, Norman, Oklahoma 73019, USA    R. Jesik Imperial College London, London SW7 2AZ, United Kingdom    K. Johns University of Arizona, Tucson, Arizona 85721, USA    M. Johnson Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    D. Johnston University of Nebraska, Lincoln, Nebraska 68588, USA    A. Jonckheere Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P. Jonsson Imperial College London, London SW7 2AZ, United Kingdom    J. Joshi Panjab University, Chandigarh, India    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    K. Kaadze Kansas State University, Manhattan, Kansas 66506, USA    E. Kajfasz CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    D. Karmanov Moscow State University, Moscow, Russia    P.A. Kasper Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    I. Katsanos University of Nebraska, Lincoln, Nebraska 68588, USA    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    M.H. Kirby Northwestern University, Evanston, Illinois 60208, USA    J.M. Kohli Panjab University, Chandigarh, India    A.V. Kozelov Institute for High Energy Physics, Protvino, Russia    J. Kraus Michigan State University, East Lansing, Michigan 48824, USA    S. Kulikov Institute for High Energy Physics, Protvino, Russia    A. Kumar State University of New York, Buffalo, New York 14260, USA    A. Kupco Center for Particle Physics, 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    J. Kvita Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic    S. Lammers Indiana University, Bloomington, Indiana 47405, USA    G. Landsberg Brown University, Providence, Rhode Island 02912, 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    J. Lellouch LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France    L. Li University of California Riverside, Riverside, California 92521, USA    Q.Z. Li Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    S.M. Lietti Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil    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    Y. Liu University of Science and Technology of China, Hefei, People’s Republic of China    Z. Liu Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada    A. Lobodenko Petersburg Nuclear Physics Institute, St. Petersburg, Russia    M. Lokajicek Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic    R. Lopes de Sa State University of New York, Stony Brook, New York 11794, USA    H.J. Lubatti University of Washington, Seattle, Washington 98195, 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    D. Mackin Rice University, Houston, Texas 77005, USA    R. Madar CEA, Irfu, SPP, Saclay, France    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    Y. Maravin Kansas State University, Manhattan, Kansas 66506, USA    J. Martínez-Ortega CINVESTAV, Mexico City, Mexico    R. McCarthy State University of New York, Stony Brook, New York 11794, USA    C.L. McGivern University of Kansas, Lawrence, Kansas 66045, USA    M.M. Meijer Radboud University Nijmegen, Nijmegen, the Netherlands and Nikhef, Science Park, Amsterdam, the Netherlands    A. Melnitchouk University of Mississippi, University, Mississippi 38677, 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    G.S. Muanza CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    M. Mulhearn University of Virginia, Charlottesville, Virginia 22901, USA    E. Nagy CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France    M. Naimuddin Delhi University, Delhi, India    M. Narain Brown University, Providence, Rhode Island 02912, USA    R. Nayyar Delhi University, Delhi, India    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    S.F. Novaes Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil    T. Nunnemann Ludwig-Maximilians-Universität München, München, Germany    G. Obrant Petersburg Nuclear Physics Institute, St. Petersburg, Russia    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    G.J. Otero y Garzón Universidad de Buenos Aires, Buenos Aires, Argentina    M. Padilla University of California Riverside, Riverside, California 92521, 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    J. Parsons Columbia University, New York, New York 10027, USA    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 Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    M. Perfilov Moscow State University, Moscow, Russia    K. Peters The University of Manchester, Manchester M13 9PL, United Kingdom    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    R. Piegaia Universidad de Buenos Aires, Buenos Aires, Argentina    M.-A. Pleier Brookhaven National Laboratory, Upton, New York 11973, USA    P.L.M. Podesta-Lerma CINVESTAV, Mexico City, Mexico    V.M. Podstavkov Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    P. Polozov Institute for Theoretical and Experimental Physics, Moscow, Russia    A.V. Popov Institute for High Energy Physics, Protvino, Russia    M. Prewitt Rice University, Houston, Texas 77005, USA    D. Price Indiana University, Bloomington, Indiana 47405, USA    N. Prokopenko Institute for High Energy Physics, Protvino, Russia    S. Protopopescu Brookhaven National Laboratory, Upton, New York 11973, USA    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    M.S. Rangel LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil    K. Ranjan Delhi University, Delhi, India    P.N. Ratoff Lancaster University, Lancaster LA1 4YB, United Kingdom    I. Razumov Institute for High Energy Physics, Protvino, Russia    P. Renkel Southern Methodist University, Dallas, Texas 75275, USA    M. Rijssenbeek State University of New York, Stony Brook, New York 11794, USA    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. Safronov Institute for Theoretical and Experimental Physics, Moscow, Russia    G. Sajot LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France    P. Salcido Northern Illinois University, DeKalb, Illinois 60115, USA    A. Sánchez-Hernández CINVESTAV, Mexico City, Mexico    M.P. Sanders Ludwig-Maximilians-Universität München, München, Germany    B. Sanghi Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    A.S. Santos Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil    G. Savage Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    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    T. Schliephake Fachbereich Physik, Bergische Universität Wuppertal, Wuppertal, Germany    S. Schlobohm University of Washington, Seattle, Washington 98195, USA    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    A.A. Shchukin Institute for High Energy Physics, Protvino, Russia    R.K. Shivpuri Delhi University, Delhi, India    V. Simak Czech Technical University in Prague, Prague, Czech Republic    V. Sirotenko Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    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    K.J. Smith State University of New York, Buffalo, New York 14260, 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    V. Stolin Institute for Theoretical and Experimental Physics, Moscow, Russia    D.A. Stoyanova Institute for High Energy Physics, Protvino, Russia    M. Strauss University of Oklahoma, Norman, Oklahoma 73019, USA    D. Strom University of Illinois at Chicago, Chicago, Illinois 60607, USA    L. Stutte Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    L. Suter The University of Manchester, Manchester M13 9PL, United Kingdom    P. Svoisky University of Oklahoma, Norman, Oklahoma 73019, USA    M. Takahashi The University of Manchester, Manchester M13 9PL, United Kingdom    A. Tanasijczuk Universidad de Buenos Aires, Buenos Aires, Argentina    W. Taylor Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada    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    P. Verdier IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France    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    M. Weber Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    L. Welty-Rieger Northwestern University, Evanston, Illinois 60208, USA    A. White University of Texas, Arlington, Texas 76019, USA    D. Wicke Fachbereich Physik, Bergische Universität Wuppertal, Wuppertal, Germany    M.R.J. Williams Lancaster University, Lancaster LA1 4YB, United Kingdom    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    C. Xu University of Michigan, Ann Arbor, Michigan 48109, USA    S. Yacoob Northwestern University, Evanston, Illinois 60208, USA    R. Yamada Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    W.-C. Yang The University of Manchester, Manchester M13 9PL, United Kingdom    T. Yasuda Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    Y.A. Yatsunenko Joint Institute for Nuclear Research, Dubna, Russia    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. Yu University of Texas, Arlington, Texas 76019, USA    S. Zelitch University of Virginia, Charlottesville, Virginia 22901, USA    T. Zhao University of Washington, Seattle, Washington 98195, USA    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 Brown University, Providence, Rhode Island 02912, USA
June 30, 2011
Abstract

We present an updated measurement of the anomalous like-sign dimuon charge asymmetry for semi-leptonic -hadron decays in 9.0 fb of collisions recorded with the D0 detector at a center-of-mass energy of TeV at the Fermilab Tevatron collider. We obtain . This result differs by standard deviations from the prediction of the standard model and provides evidence for anomalously large violation in semi-leptonic neutral decay. The dependence of the asymmetry on the muon impact parameter is consistent with the hypothesis that it originates from semi-leptonic -hadron decays.

pacs:
13.25.Hw; 14.40.Nd; 11.30.Er

Fermilab-Pub-11/307-E

The D0 Collaboration111with visitors from Augustana College, Sioux Falls, SD, USA, The University of Liverpool, Liverpool, UK, SLAC, Menlo Park, CA, USA, University College London, London, UK, Centro de Investigacion en Computacion - IPN, Mexico City, Mexico, ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico, and Universität Bern, Bern, Switzerland. Deceased.

I Introduction

We measure the like-sign dimuon charge asymmetry of semi-leptonic decays of hadrons,

(1)

in 9.0 fb of collisions recorded with the D0 detector at a center-of-mass energy  TeV at the Fermilab Tevatron collider. Here and are the number of events containing two positively charged or two negatively charged muons, respectively, both of which are produced in prompt semi-leptonic -hadron decays. At the Fermilab Tevatron collider, quarks are produced mainly in pairs. Hence, to observe an event with two like-sign muons from semi-leptonic -hadron decay, one of the hadrons must be a or meson that oscillates and decays to a muon of charge opposite of that expected from the original quark charge (). The oscillation ( or ) is described by higher order loop diagrams that are sensitive to hypothetical particles that may not be directly accessible at the Tevatron.

The asymmetry has contributions from the semi-leptonic charge asymmetries and of and mesons Grossman (), respectively:

(2)
(3)

where is a CP-violating phase, and and are the mass and width differences between the eigenstates of the propagation matrices of the neutral mesons. The coefficients and depend on the mean mixing probability, , and the production rates of and mesons. We use the values of these quantities measured at LEP as averaged by the Heavy Flavor Averaging Group (HFAG) hfag () and obtain

(4)

The value of measured by the CDF Collaboration recently cdf-chi0 () is consistent with the LEP value, which supports this choice of parameters. Using the standard model (SM) prediction for and Nierste (), we find

(5)

which is negligible compared to present experimental sensitivity. Additional contributions to violation via loop diagrams appear in some extensions of the SM and can result in an asymmetry within experimental reach Randall (); Hewett (); Hou (); Soni (); buras ().

This Article is an update to Ref. PRD () that reported evidence for an anomalous like-sign dimuon charge asymmetry with 6.1 fb of data, at the 3.2 standard deviation level. All notations used here are given in Ref. PRD (). This new measurement is based on a larger dataset and further improvements in the measurement technique. In addition, the asymmetry’s dependence on the muon impact parameter (IP) impact () is studied. The D0 detector is described in Ref. d0-det (). We include a brief overview of the analysis in Sec. II. Improvements made to muon selections are presented in Sec. III; the measurement of all quantities required to determine the asymmetry is described in Secs. IVX, and the result is given in Sec. XI. Sections XIIXIII present consistency checks of the measurement; Sec. XIV describes the study of the asymmetry’s IP dependence. Conclusions are given in Sec. XV.

Ii Method

The elements of our analysis are described in detail in Ref. PRD (). Here, we summarize briefly the method, emphasizing the improvements to our previous procedure. We use two sets of data: (i) inclusive muon data collected with inclusive muon triggers that provide positively charged muons and negatively charged muons, and (ii) like-sign dimuon data, collected with dimuon triggers that provide events with two positively charged muons and events with two negatively charged muons. If an event contains more than one muon, each muon is included in the inclusive muon sample. Such events constitute about 0.5% of the total inclusive muon sample. If an event contains more than two muons, the two muons with the highest transverse momentum () are selected for inclusion in the dimuon sample. Such events comprise about 0.7% of the total like-sign dimuon sample.

From these data we obtain the inclusive muon charge asymmetry and the like-sign dimuon charge asymmetry , defined as

(6)

In addition to a possible signal asymmetry , these asymmetries have contributions from muons produced in kaon and pion decay, or from hadrons that punch through the calorimeter and iron toroids to penetrate the outer muon detector. The charge asymmetry related to muon detection and identification also contributes to and . These contributions are measured with data, with only minimal input from simulation. The largest contribution by far is from kaon decays. Positively charged kaons have smaller cross sections in the detector material than negatively charged kaons pdg (), giving them more time to decay. This difference produces a positive charge asymmetry.

We consider muon candidates with in the range 1.5 to  GeV. This range is divided into six bins as shown in Table 1. The inclusive muon charge asymmetry can be expressed PRD () as

(7)

where the fraction of reconstructed muons, , in a given interval in the inclusive muon sample is given in Table 1. The fractions of these muons produced by kaons, pions, and protons in a given interval are , , and , and their charge asymmetries are , , and , respectively. We refer to these muons as “long” or “” muons since they are produced by particles traveling long distances before decaying within the detector material. The track of a muon in the central tracker is dominantly produced by the parent hadron. The charge asymmetry of muons results from the difference in the interactions of positively and negatively charged particles with the detector material, and is not related to CP violation. The background fraction is defined as . The quantity is the fraction of muons from weak decays of and quarks and leptons, and from decays of short-lived mesons (). We refer to these muons as “short” or “” muons, since they arise from the decay of particles at small distances from the interaction point. These particles are not affected by interactions in the detector material, and once muon detection and identification imbalances are removed, the muon charge asymmetry must therefore be produced only through CP violation in the underlying physical processes. The quantity in Eq. (7) is the charge asymmetry related to muon detection and identification. The background charge asymmetries , , and are measured in the inclusive muon data, and include any detector asymmetry. The therefore accounts only for muons and is multiplied by the factor .

The like-sign dimuon charge asymmetry can be expressed PRD () as

(8)

The quantity is the charge asymmetry of the events with two like-sign muons. The quantity is the fraction of like-sign dimuon events with two muons, is the fraction of like-sign dimuon events with one and one muon. We also define the quantity as the fraction of like-sign dimuon events with two muons. The quantity is the fraction of muons in the interval in the like-sign dimuon data. The quantities () are defined as , where is the number of muons produced by kaons, pions, and protons, respectively, in a interval , with being the number of muons in this interval, with the factor of two taking into account the normalization of these quantities per like-sign dimuon event. The quantity is a sum over muons produced by hadrons:

(9)

We also define as

(11)

The estimated contribution from the neglected quadratic terms in Eq. (8) is approximately , which corresponds to about 5% of the statistical uncertainty on .

The asymmetries and in Eqs. (7) and (8) are the only asymmetries due to CP violation in the processes producing muons, and are proportional to the asymmetry :

(12)

The dilution coefficients and are discussed in Ref. PRD () and in Sec. X below.

Bin Muon range (GeV)
1 0.0077 0.0774
2 0.2300 0.3227
3 0.4390 0.3074
4 0.1702 0.1419
5 0.1047 0.1057
6 0.0484 0.0449
Table 1: Fractions of muon candidates in the inclusive muon sample () and in the like-sign dimuon sample (, with two entries per event).

Equations (7) – (12) are used to measure the asymmetry . The major contributions to the uncertainties on are from the statistical uncertainty on and the total uncertainty on , and . To reduce the latter contributions, we measure the asymmetry using the asymmetry , which is defined as

(13)

Since the same physical processes contribute to both and , their uncertainties are strongly correlated, and therefore partially cancel in Eq. (13) for an appropriate choice of the coefficient . The contribution from the asymmetry , however, does not cancel in Eq. (13) because PRD (). Full details of the measurements of different quantities entering in Eqs. (7) – (12) are given in Ref. PRD (). The main improvements in the present analysis are related to muon selection and the measurement of and . These modifications are described in Sections III, IV and V.

Iii Muon selection

The muon selection is similar to that described in Ref. PRD (). The inclusive muon and like-sign dimuon samples are obtained from data collected with single and dimuon triggers, respectively. Charged particles with transverse momentum in the range GeV and with pseudorapidity rapidity () are considered as muon candidates. The upper limit on is applied to suppress the contribution of muons from and boson decays. To ensure that the muon candidate passes through the detector, including all three layers of the muon system, we require either GeV or a longitudinal momentum component GeV. Muon candidates are selected by matching central tracks with a segment reconstructed in the muon system and by applying tight quality requirements aimed at reducing false matching and background from cosmic rays and beam halo. The transverse impact parameter of the muon track relative to the reconstructed interaction vertex must be smaller than 0.3 cm, with the longitudinal distance from the point of closest approach to this vertex smaller than 0.5 cm. Strict quality requirements are also applied to the tracks and to the reconstructed interaction vertex. The inclusive muon sample contains all muons passing the selection requirements. If an event contains more than one muon, each muon is included in the inclusive muon sample. The like-sign dimuon sample contains all events with at least two muon candidates with the same charge. These two muons are required to have an invariant mass greater than 2.8 GeV to minimize the number of events in which both muons originate from the same quark (e.g., , ). Compared to Ref. PRD (), the following modifications to the muon selection are applied:

  • To reduce background from a mismatch of tracks in the central detector with segments in the outer muon system, we require that the sign of the curvature of the track measured in the central tracker be the same as in the muon system. This selection was not applied in Ref. PRD (), and removes only about 1% of the dimuon events.

  • To ensure that the muon candidate can penetrate all three layers of the muon detector, we require either a transverse momentum GeV, or a longitudinal momentum component  GeV, instead of GeV or GeV in Ref. PRD (). With this change, the number of like-sign dimuon events increases by 25%, without impacting the condition that the muon must penetrate the calorimeter and toroids, as can be deduced from Fig. 1.

  • To reduce background from kaon and pion decays in flight, we require that the calculated from the difference between the track parameters measured in the central tracker and in the muon system be (for 4 d.o.f.) instead of 40 used in Ref. PRD (). With this tighter selection, the number of like-sign dimuon events is decreased by 12%.

Compared to the selections applied in Ref. PRD (), the total number of like-sign dimuon events after applying all these modifications is increased by 13% in addition to the increase due to the larger integrated luminosity of this analysis.

Figure 1: (color online). Smallest muon momentum required to penetrate the calorimeter and toroids at different pseudorapidities, (solid line), and the momentum selection used in this analysis (dashed line).

The muon charge is determined by the central tracker. The probability of charge mis-measurement is obtained by comparing the charge measured by the central tracker and by the muon system and is found to be less than 0.1%.

The polarities of the toroidal and solenoidal magnetic fields are reversed on average every two weeks so that the four solenoid-toroid polarity combinations are exposed to approximately the same integrated luminosity. This allows for a cancellation of first-order effects related to the instrumental asymmetry D01 (). To ensure such cancellation, the events are weighted according to the number of events for each data sample corresponding to a different configuration of the magnets’ polarities. These weights are given in Table 2. During the data taking of the last part of the sample, corresponding to approximately 2.9 fb of collisions, the magnet polarities were specially chosen to equalize the number of dimuon events with different polarities in the entire sample. The weights in Table 2 are therefore closer to unity compared to those used in Ref. PRD ().

Solenoid Toroid Weight Weight
polarity polarity inclusive muon like-sign dimuon
0.994 0.964
+1 1.000 1.000
+1 0.985 0.958
+1 +1 0.989 0.978
Table 2: Weights assigned to the events recorded with different solenoid and toroid polarities in the inclusive muon and like-sign dimuon samples.

Iv Measurement of , ,

The fraction in the inclusive muon sample is measured using decays, with the kaon identified as a muon (see Ref. PRD () for details). The transverse momentum of the meson is required to be in the interval . Since the momentum of a particle is measured by the central tracking detector, a muon produced by a kaon is assigned the momentum of this kaon (a small correction for kaons decaying within the tracker volume is introduced later). The fraction of these decays is converted to the fraction using the relation

(14)

where and are the number of reconstructed and decays, respectively. The transverse momentum of the meson is required to be in the interval . We require in addition that one of the pions from the decay be identified as a muon. In the previous analysis PRD () the production of mesons was studied in a sample of events with an additional reconstructed muon, but we did not require that this muon be associated with a pion from decay. The fraction of events containing and/or quarks was therefore enhanced in the sample, which could result in a bias of the measured fraction . This bias does not exceed the systematic uncertainty of and its impact on the value is less than 0.03%. The application of the new requirement ensures that the flavor composition in the selected and samples is the same and this bias is eliminated.

The selection criteria and fitting procedures used to select and determine the number of , and events are given in Ref. PRD (). As an example, Fig. 2 displays the invariant mass distribution and the fitted candidates in the inclusive muon sample, with at least one pion identified as a muon, for GeV. Figure 3 shows the mass distribution and fit to candidates for all candidates with GeV and MeV. Figure 4 shows the mass distribution and the fit result for candidates for all kaons with GeV. The mass distribution contains contributions from light meson resonances decaying to . The most important contribution comes from the decay with . It produces a broad peak in the mass region close to the mass. The distortions in the background distribution due to other light resonances, which are not identified explicitly, can also be seen in Fig. 4. Our background model therefore includes the contribution of and two additional Gaussian terms to take into account the distortions around 1.1 GeV. More details of the background description are given in Ref. PRD ().

Figure 2: (color online). The invariant mass distribution for candidates in the inclusive muon sample with at least one pion identified as a muon with GeV. The solid line represents the result of the fit to the content, and the dashed line represents the fitted background contribution.
Figure 3: (color online). (a) The invariant mass distribution for candidates in the inclusive muon sample. The candidate is required to have MeV and GeV. The solid line represents the result of the fit to the content, and the dashed line shows the background contribution. (b) Difference between data and the result of the fit.
Figure 4: (color online). (a) The invariant mass distribution for candidates in the inclusive muon sample for all kaons with GeV. The solid line corresponds to the result of the fit to the content, and the dashed line shows the contribution from combinatorial background. The shaded histogram is the contribution from events. (b) Difference between data and the result of the fit.

The measurement of the fractions and is also performed using the method of Ref. PRD (). The values of and are divided by the factors and , respectively, which take into account the fraction of kaons and pions reconstructed by the tracking system before they decay. These factors are discussed in Ref. PRD (), and are determined through simulation. Contrary to Ref. PRD (), this analysis determines these factors separately for kaons and pions. We find the values:

(15)

The uncertainties include contributions from the number of simulated events and from the uncertainties in the momentum spectrum of the generated particles.

The values of , and in different muon bins are shown in Fig. 5 and in Table 3. The changes in the muon candidates selection adopted here is the main source of differences relative to the corresponding values in Ref. PRD (). The fractions and are poorly measured in bins 1 and 2, and bins 5 and 6 due to the small number of events, and their contents are therefore combined through their weighted average.

Bin
1
2
3
4
5
6
All
Table 3: Fractions , , and for different bins. The bottom row shows the weighted average of these quantities obtained with weights given by the fraction of muons in a given interval, , in the inclusive muon sample, see Table 1. Only statistical uncertainties are given.
Figure 5: (color online). The fraction of (a) tracks, (b) tracks and (c) tracks in the inclusive muon sample as a function of the kaon, pion and proton , respectively. The horizontal dashed lines show the mean values.

V Measurement of , ,

The quantity is expressed as

(16)

where is the ratio of the fractions of muons produced by kaons in like-sign dimuon and in inclusive muon data. For the interval , is defined as

(17)

where and are the number of reconstructed mesons identified as muons in the like-sign dimuon and in the inclusive muon samples, respectively. The transverse momentum of the meson is required to be in the interval . The quantities and are the number of muons in the interval . A multiplicative factor of two is included in Eq. (17) because there are two muons in a like-sign dimuon event, and is normalized to the number of like-sign dimuon events.

In the previous analysis PRD (), the quantity was obtained from a measurement of the production rate. Presenting it in the form of Eq. (16) also allows the determination of through an independent measurement of the fraction of mesons in dimuon and in inclusive muon data where one of the pions from decay is identified as a muon. This measurement is discussed below. In addition, Eq. (16) offers an explicit separation of systematic uncertainties associated with . The systematic uncertainty on the fraction affects the two determinations of based on Eqs. (7) and (8) in a fully correlated way; therefore, its impact on the measurement obtained using Eq. (13) is significantly reduced. The systematic uncertainty on the ratio does not cancel in Eq. (13). It is estimated directly from a comparison of the values of obtained in two independent channels.

One way to measure is from the fraction of events in the inclusive muon and like-sign dimuon data,

(18)

where and are the number of reconstructed decays, with the kaon identified as a muon in the like-sign dimuon and in the inclusive muon samples, respectively. The transverse momentum of the meson is required to be in the interval . The measurement using Eq. (18) is based on the assumption

(19)

which was validated through simulations in Ref. PRD (). The corresponding systematic uncertainty is discussed below.

In Ref. PRD (), the fractions and were obtained independently from a fit of the invariant mass distribution in the like-sign dimuon and inclusive muon sample, respectively. Figure 6 shows the same mass studies as in Fig. 4, but for the like-sign dimuon sample. The fit in both cases is complicated by the contribution from light meson resonances that decay to , producing a reflection in the invariant mass distribution. In addition, the detector resolution is not known a priori and has to be included in the fit. All these complications are reduced significantly or eliminated in the “null-fit” method introduced in Ref. PRD (), which is used in this analysis to measure the ratio .

Figure 6: (color online). (a) The invariant mass distribution of candidates in the like-sign dimuon sample for all kaons with GeV. The solid line corresponds to the result of the fit to the content, and the dashed line shows the contribution from combinatorial background. The shaded histogram is the contribution from events. (b) Difference between data and the result of the fit.

In this method, for each interval , we define a set of distributions that depend on a parameter :

(20)

where and are the number of entries in the bin of the invariant mass distributions in the like-sign dimuon and inclusive muon samples, respectively. For each value of the number of decays, , and its uncertainty, , are measured from the distribution. The value of for which defines . The uncertainty is determined from the condition that corresponding to .

The advantage of this method is that the influence of the detector resolution becomes minimal for close to zero, and the contribution from the peaking background is reduced in to the same extent as the contribution of mesons, and becomes negligible when is close to zero. As an example, Fig. 7 shows the mass distribution for , for all kaons with GeV. This distribution is obtained from the distributions shown in Figs. 4 and 6, using Eq. (20). The contributions of both and , as well as any other resonance in the background, disappear. As a result, the fitting procedure becomes more robust, the fitting range can be extended, and the resulting value of becomes stable under a variation of the fitting parameters over a wider range.

Figure 7: (color online). (a) The invariant mass distribution obtained using Eq. (20) for for all kaons with GeV. The dashed line shows the contribution from the combinatorial background. (b) Difference between data and the result of the fit.

The value of is also obtained from the production rate of mesons in the inclusive muon and dimuon samples. We compute for a given interval , as

(21)

where and are the number of reconstructed decays with one pion identified as a muon in the dimuon and the inclusive muon data, respectively. The correction factor is discussed later in this section. The measurement of using Eq. (21) assumes isospin invariance and consequent equality of the ratio of production rates in the dimuon and in the inclusive muon samples of and mesons, i.e.,

(22)

Since the charged kaon in Eq. (22) is required to be within the interval , the transverse momentum of the meson in Eq. (21) is also required to be within the interval . We expect approximately the same number of positive and negative pions from decays to be identified as a muon. Therefore, we use both like-sign and opposite-sign dimuon events to measure and we do not use the multiplicative factor of two in Eq. (21). The requirement of having one pion identified as a muon makes the flavor composition in the samples of charged events and events similar.

The charges of the kaon and the additional muon in a dimuon event can be correlated, i.e., in general . However, the number of events is not correlated with the charge of the additional muon, i.e., . Since the ratio is determined for the sample of like-sign dimuon events, we apply in Eq. (21) the correction factor , defined as

(23)

to take into account the correlation between the charges of the kaon and muon. The abbreviation “c.c.” in Eq. (23) denotes “charge conjugate states”. The coefficients are measured in data using the events with a reconstructed decay and an additional muon. To reproduce the selection for the dimuon sample PRD (), the invariant mass of the system, with the kaon assigned the mass of a muon, is required to be greater than 2.8 GeV. The fitting procedure and selection criteria to measure the number of events are described in Ref. PRD (). The values of for different intervals are given in Fig. 8 and in Table 4.

bin
1
2
3
4
5
6
Mean
Table 4: Values of in different bins. The bottom row shows their average. Only statistical uncertainties are given.
Figure 8: (color online). The correction coefficient as a function of the kaon transverse momentum. The horizontal dashed line shows the mean value.

The average muon detection efficiency is different for the inclusive muon and like-sign dimuon samples because of different thresholds used in their triggers. The difference in muon detection efficiency is large for muons with small , but it is insignificant for muons above the inclusive-muon trigger threshold. The ratio in Eq. (21) is measured as a function of the transverse momenta of mesons, , while the ratio is measured in bins of muon . Each bin contains with different values. The muon detection efficiency therefore does not cancel in Eq. (21), and can affect the measurement of . Figure 9 shows the ratio of detection efficiencies in the inclusive muon and dimuon data. To compute this ratio, we select the mesons in a given interval. The distribution of pions produced in the decay with a given is the same in the dimuon and inclusive muon data. Therefore, any difference in this distribution between dimuon and inclusive muon data is due to the detection. We compute the ratio of these distributions, and normalize it such that it equals unity for GeV. The value of this threshold corresponds to the threshold for single muon triggers. Figure 9 presents the average of the ratios for different intervals. The ratio is suppressed for GeV, and is consistent with a constant for GeV. To remove the bias due to the trigger threshold, we measure for events with GeV. As a result, the ratio is not defined for the first two bins in the channel.

Figure 9: (color online). The ratio of detection efficiencies for the inclusive muon and dimuon data as a function of the muon transverse momentum. The horizontal dashed line shows the mean value for GeV.

The values of obtained through the null-fit method, for different muon bins, are shown in Fig. 10(a) and in Table 5. The values of are contained in Fig. 10(b) and in Table 5. The difference between the values of measured with mesons and with mesons is shown in Fig. 11. The mean value of this difference is

(24)

and the /d.o.f. is 1.7/4. We use two independent methods, each relying on different assumptions, to measure the ratio and obtain results that are consistent with each other. The methods are subject to different systematic uncertainties, and therefore provide an important cross-check. As an independent cross-check, the value of obtained in simulation is consistent with that measured in data, see Sec. XIII for details. We take the average of the two channels weighted by their uncertainties as our final values of for  GeV and use the values measured in the channel for  GeV. These values are given in Table 5 and in Fig. 10(c). As we do not observe any difference between the two measurements, we take half of the uncertainty of as the systematic uncertainty of . This corresponds to a relative uncertainty of 3.0% on the value of . In our previous measurement PRD (), this uncertainty was 3.6%, and was based on simulation of the events.

Using the extracted values of , we derive the values of , and . The computation of is done using Eq. (16), and we follow the procedure described in Ref. PRD () to determine and . The results are shown in Fig. 12 and in Table 6. The fractions and are poorly determined for the lowest and highest because of the small number of events. The content of bins 1 and 2, and bins 5 and 6 are therefore combined.

bin from from average
1
2
3
4
5
6
Mean
Table 5: Values of obtained using and meson production in different bins. The bottom row shows their average. Only statistical uncertainties are given. The ratio in the channel is not measured in the first two bins, see Sec. V.
Figure 10: (color online). The ratio obtained using (a) production, (b) production, and (c) combination of these two channels as a function of the kaon transverse momentum. The horizontal dashed lines show the mean values.
Figure 11: (color online). The difference as a function of kaon transverse momentum. The horizontal dashed line shows the mean value.
Bin
1
2
3
4
5
6
All
Table 6: Values of , , and for different bins. The last line shows the weighted average of these quantities obtained with weights given by the fraction of muons in a given interval in the dimuon sample, see Table 1. Only statistical uncertainties are given.
Figure 12: (color online). The values of (a) , (b) and (c) in the like-sign dimuon sample as a function of the kaon, pion and proton , respectively. The horizontal dashed lines show the mean values.

Vi Systematic uncertainties for background fractions

The systematic uncertainties for the background fractions are discussed in Ref. PRD (), and we only summarize the values used in this analysis. The systematic uncertainty on the fraction is set to 9% PRD (). The systematic uncertainty on the ratio , as indicated in Sec. V, is set to half of the uncertainty on given in Eq. (24). The systematic uncertainties on the ratios of multiplicities and in interactions are set to 4% notation (). These multiplicities are required to compute the quantities , . The ratios and , required to compute the quantities and PRD () are assigned an additional 4% systematic uncertainty. The values of these uncertainties are discussed in Ref. PRD ().

Vii Measurement of ,

We determine the fraction of muons in the inclusive muon sample and the fraction of events with two muons in the like-sign dimuon sample following the procedure described in Ref. PRD (). We use the following value from simulation

(25)

and obtain