Measurement of higher cumulants of net-charge multiplicity distributions in Au+Au collisions at \sqrt{s_{{}_{NN}}}=7.7–200 GeV

Measurement of higher cumulants of net-charge multiplicity distributions in AuAu collisions at –200 GeV

A. Adare University of Colorado, Boulder, Colorado 80309, USA    S. Afanasiev Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    C. Aidala Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA    N.N. Ajitanand Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    Y. Akiba RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R. Akimoto Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    H. Al-Bataineh New Mexico State University, Las Cruces, New Mexico 88003, USA    J. Alexander Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    H. Al-Ta’ani New Mexico State University, Las Cruces, New Mexico 88003, USA    A. Angerami Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    K. Aoki KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    N. Apadula Iowa State University, Ames, Iowa 50011, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    Y. Aramaki Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    H. Asano Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    E.C. Aschenauer Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    E.T. Atomssa Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    R. Averbeck Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    T.C. Awes Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    B. Azmoun Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    V. Babintsev IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    M. Bai Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    G. Baksay Florida Institute of Technology, Melbourne, Florida 32901, USA    L. Baksay Florida Institute of Technology, Melbourne, Florida 32901, USA    B. Bannier Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    K.N. Barish University of California-Riverside, Riverside, California 92521, USA    B. Bassalleck University of New Mexico, Albuquerque, New Mexico 87131, USA    A.T. Basye Abilene Christian University, Abilene, Texas 79699, USA    S. Bathe Baruch College, City University of New York, New York, New York, 10010 USA University of California-Riverside, Riverside, California 92521, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    V. Baublis PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    C. Baumann Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany    S. Baumgart RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    A. Bazilevsky Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S. Belikov Deceased Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R. Belmont University of Colorado, Boulder, Colorado 80309, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA Vanderbilt University, Nashville, Tennessee 37235, USA    R. Bennett Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Berdnikov Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia    Y. Berdnikov Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia    A.A. Bickley University of Colorado, Boulder, Colorado 80309, USA    D. Black University of California-Riverside, Riverside, California 92521, USA    D.S. Blau National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    J.S. Bok University of New Mexico, Albuquerque, New Mexico 87131, USA New Mexico State University, Las Cruces, New Mexico 88003, USA Yonsei University, IPAP, Seoul 120-749, Korea    K. Boyle RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    M.L. Brooks Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    J. Bryslawskyj Baruch College, City University of New York, New York, New York, 10010 USA    H. Buesching Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    V. Bumazhnov IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    G. Bunce Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S. Butsyk Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA University of New Mexico, Albuquerque, New Mexico 87131, USA    C.M. Camacho Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    S. Campbell Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    P. Castera Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    C.-H. Chen RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    C.Y. Chi Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    M. Chiu Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    I.J. Choi University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Yonsei University, IPAP, Seoul 120-749, Korea    J.B. Choi Chonbuk National University, Jeonju, 561-756, Korea    S. Choi Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    R.K. Choudhury Bhabha Atomic Research Centre, Bombay 400 085, India    P. Christiansen Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    T. Chujo Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    P. Chung Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    O. Chvala University of California-Riverside, Riverside, California 92521, USA    V. Cianciolo Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    Z. Citron Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA Weizmann Institute, Rehovot 76100, Israel    B.A. Cole Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    M. Connors Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    P. Constantin Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    N. Cronin Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    N. Crossette Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    M. Csanád ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary    T. Csörgő Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary    T. Dahms Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    S. Dairaku Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    I. Danchev Vanderbilt University, Nashville, Tennessee 37235, USA    K. Das Florida State University, Tallahassee, Florida 32306, USA    A. Datta Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA University of New Mexico, Albuquerque, New Mexico 87131, USA    M.S. Daugherity Abilene Christian University, Abilene, Texas 79699, USA    G. David Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    K. Dehmelt Florida Institute of Technology, Melbourne, Florida 32901, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Denisov IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    A. Deshpande RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    E.J. Desmond Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    K.V. Dharmawardane New Mexico State University, Las Cruces, New Mexico 88003, USA    O. Dietzsch Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    L. Ding Iowa State University, Ames, Iowa 50011, USA    A. Dion Iowa State University, Ames, Iowa 50011, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    J.H. Do Yonsei University, IPAP, Seoul 120-749, Korea    M. Donadelli Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    L. D’Orazio University of Maryland, College Park, Maryland 20742, USA    O. Drapier Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France    A. Drees Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    K.A. Drees Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    J.M. Durham Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Durum IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    D. Dutta Bhabha Atomic Research Centre, Bombay 400 085, India    S. Edwards Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Florida State University, Tallahassee, Florida 32306, USA    Y.V. Efremenko Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    F. Ellinghaus University of Colorado, Boulder, Colorado 80309, USA    T. Engelmore Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    A. Enokizono Lawrence Livermore National Laboratory, Livermore, California 94550, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    H. En’yo RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S. Esumi Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    K.O. Eyser Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA University of California-Riverside, Riverside, California 92521, USA    B. Fadem Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    D.E. Fields University of New Mexico, Albuquerque, New Mexico 87131, USA    M. Finger Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic    M. Finger, Jr. Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic    F. Fleuret Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France    S.L. Fokin National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    Z. Fraenkel Deceased Weizmann Institute, Rehovot 76100, Israel    J.E. Frantz Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Franz Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    A.D. Frawley Florida State University, Tallahassee, Florida 32306, USA    K. Fujiwara RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    Y. Fukao RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    T. Fusayasu Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan    K. Gainey Abilene Christian University, Abilene, Texas 79699, USA    C. Gal Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    P. Garg Department of Physics, Banaras Hindu University, Varanasi 221005, India    A. Garishvili University of Tennessee, Knoxville, Tennessee 37996, USA    I. Garishvili Lawrence Livermore National Laboratory, Livermore, California 94550, USA University of Tennessee, Knoxville, Tennessee 37996, USA    F. Giordano University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    A. Glenn University of Colorado, Boulder, Colorado 80309, USA Lawrence Livermore National Laboratory, Livermore, California 94550, USA    H. Gong Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    X. Gong Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    M. Gonin Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France    Y. Goto RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R. Granier de Cassagnac Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France    N. Grau Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    S.V. Greene Vanderbilt University, Nashville, Tennessee 37235, USA    M. Grosse Perdekamp University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y. Gu Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    T. Gunji Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    L. Guo Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    H.-Å. Gustafsson Deceased Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    T. Hachiya Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    J.S. Haggerty Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    K.I. Hahn Ewha Womans University, Seoul 120-750, Korea    H. Hamagaki Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    J. Hamblen University of Tennessee, Knoxville, Tennessee 37996, USA    R. Han Peking University, Beijing 100871, People’s Republic of China    J. Hanks Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    E.P. Hartouni Lawrence Livermore National Laboratory, Livermore, California 94550, USA    K. Hashimoto RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    E. Haslum Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    R. Hayano Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    S. Hayashi Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    X. He Georgia State University, Atlanta, Georgia 30303, USA    M. Heffner Lawrence Livermore National Laboratory, Livermore, California 94550, USA    T.K. Hemmick Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    T. Hester University of California-Riverside, Riverside, California 92521, USA    J.C. Hill Iowa State University, Ames, Iowa 50011, USA    M. Hohlmann Florida Institute of Technology, Melbourne, Florida 32901, USA    R.S. Hollis University of California-Riverside, Riverside, California 92521, USA    W. Holzmann Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    K. Homma Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    B. Hong Korea University, Seoul, 136-701, Korea    T. Horaguchi Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    Y. Hori Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    D. Hornback University of Tennessee, Knoxville, Tennessee 37996, USA    S. Huang Vanderbilt University, Nashville, Tennessee 37235, USA    T. Ichihara RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R. Ichimiya RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    J. Ide Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    H. Iinuma KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    Y. Ikeda RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    K. Imai Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    Y. Imazu RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    J. Imrek Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary    M. Inaba Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    A. Iordanova University of California-Riverside, Riverside, California 92521, USA    D. Isenhower Abilene Christian University, Abilene, Texas 79699, USA    M. Ishihara RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    A. Isinhue Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    T. Isobe Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    M. Issah Vanderbilt University, Nashville, Tennessee 37235, USA    A. Isupov Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    D. Ivanishchev PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    B.V. Jacak Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    M. Javani Georgia State University, Atlanta, Georgia 30303, USA    J. Jia Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    X. Jiang Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    J. Jin Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    B.M. Johnson Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    K.S. Joo Myongji University, Yongin, Kyonggido 449-728, Korea    D. Jouan IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406, Orsay, France    D.S. Jumper Abilene Christian University, Abilene, Texas 79699, USA University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    F. Kajihara Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    S. Kametani RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    N. Kamihara RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    J. Kamin Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    S. Kaneti Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    B.H. Kang Hanyang University, Seoul 133-792, Korea    J.H. Kang Yonsei University, IPAP, Seoul 120-749, Korea    J.S. Kang Hanyang University, Seoul 133-792, Korea    J. Kapustinsky Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    K. Karatsu Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    M. Kasai RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    D. Kawall Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    M. Kawashima RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    A.V. Kazantsev National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    T. Kempel Iowa State University, Ames, Iowa 50011, USA    J.A. Key University of New Mexico, Albuquerque, New Mexico 87131, USA    P.K. Khandai Department of Physics, Banaras Hindu University, Varanasi 221005, India    A. Khanzadeev PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    K.M. Kijima Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    B.I. Kim Korea University, Seoul, 136-701, Korea    C. Kim Korea University, Seoul, 136-701, Korea    D.H. Kim Myongji University, Yongin, Kyonggido 449-728, Korea    D.J. Kim Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland    E. Kim Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    E.-J. Kim Chonbuk National University, Jeonju, 561-756, Korea    H.J. Kim Yonsei University, IPAP, Seoul 120-749, Korea    K.-B. Kim Chonbuk National University, Jeonju, 561-756, Korea    S.H. Kim Yonsei University, IPAP, Seoul 120-749, Korea    Y.-J. Kim University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    Y.K. Kim Hanyang University, Seoul 133-792, Korea    E. Kinney University of Colorado, Boulder, Colorado 80309, USA    K. Kiriluk University of Colorado, Boulder, Colorado 80309, USA    Á. Kiss ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary    E. Kistenev Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    J. Klatsky Florida State University, Tallahassee, Florida 32306, USA    D. Kleinjan University of California-Riverside, Riverside, California 92521, USA    P. Kline Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    L. Kochenda PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    Y. Komatsu Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    B. Komkov PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    M. Konno Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    J. Koster University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    D. Kotchetkov University of New Mexico, Albuquerque, New Mexico 87131, USA Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA    D. Kotov PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia    A. Kozlov Weizmann Institute, Rehovot 76100, Israel    A. Král Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic    A. Kravitz Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    F. Krizek Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland    G.J. Kunde Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    K. Kurita RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    M. Kurosawa RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y. Kwon Yonsei University, IPAP, Seoul 120-749, Korea    G.S. Kyle New Mexico State University, Las Cruces, New Mexico 88003, USA    R. Lacey Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    Y.S. Lai Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    J.G. Lajoie Iowa State University, Ames, Iowa 50011, USA    A. Lebedev Iowa State University, Ames, Iowa 50011, USA    B. Lee Hanyang University, Seoul 133-792, Korea    D.M. Lee Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    J. Lee Ewha Womans University, Seoul 120-750, Korea    K. Lee Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    K.B. Lee Korea University, Seoul, 136-701, Korea Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    K.S. Lee Korea University, Seoul, 136-701, Korea    S.H. Lee Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    S.R. Lee Chonbuk National University, Jeonju, 561-756, Korea    M.J. Leitch Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    M.A.L. Leite Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    M. Leitgab University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    E. Leitner Vanderbilt University, Nashville, Tennessee 37235, USA    B. Lenzi Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    B. Lewis Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    X. Li Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, People’s Republic of China    P. Liebing RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S.H. Lim Yonsei University, IPAP, Seoul 120-749, Korea    L.A. Linden Levy University of Colorado, Boulder, Colorado 80309, USA Lawrence Livermore National Laboratory, Livermore, California 94550, USA    T. Liška Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic    A. Litvinenko Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    H. Liu Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA New Mexico State University, Las Cruces, New Mexico 88003, USA    M.X. Liu Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    B. Love Vanderbilt University, Nashville, Tennessee 37235, USA    R. Luechtenborg Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany    D. Lynch Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    C.F. Maguire Vanderbilt University, Nashville, Tennessee 37235, USA    Y.I. Makdisi Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    M. Makek Weizmann Institute, Rehovot 76100, Israel University of Zagreb, Faculty of Science, Department of Physics, Bijenička 32, HR-10002 Zagreb, Croatia    A. Malakhov Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    M.D. Malik University of New Mexico, Albuquerque, New Mexico 87131, USA    A. Manion Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    V.I. Manko National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    E. Mannel Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    Y. Mao Peking University, Beijing 100871, People’s Republic of China RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    T. Maruyama Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan    H. Masui Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    S. Masumoto Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    F. Matathias Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    M. McCumber University of Colorado, Boulder, Colorado 80309, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    P.L. McGaughey Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    D. McGlinchey University of Colorado, Boulder, Colorado 80309, USA Florida State University, Tallahassee, Florida 32306, USA    C. McKinney University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    N. Means Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Meles New Mexico State University, Las Cruces, New Mexico 88003, USA    M. Mendoza University of California-Riverside, Riverside, California 92521, USA    B. Meredith University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    Y. Miake Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    T. Mibe KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    J. Midori Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    A.C. Mignerey University of Maryland, College Park, Maryland 20742, USA    P. Mikeš Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic    K. Miki RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    A. Milov Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Weizmann Institute, Rehovot 76100, Israel    D.K. Mishra Bhabha Atomic Research Centre, Bombay 400 085, India    M. Mishra Department of Physics, Banaras Hindu University, Varanasi 221005, India    J.T. Mitchell Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y. Miyachi RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan    S. Miyasaka RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan    A.K. Mohanty Bhabha Atomic Research Centre, Bombay 400 085, India    S. Mohapatra Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    H.J. Moon Myongji University, Yongin, Kyonggido 449-728, Korea    Y. Morino Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    A. Morreale University of California-Riverside, Riverside, California 92521, USA    D.P. Morrison morrison@bnl.gov Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    M. Moskowitz Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    S. Motschwiller Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    T.V. Moukhanova National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    T. Murakami Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    J. Murata RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan    A. Mwai Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    T. Nagae Kyoto University, Kyoto 606-8502, Japan    S. Nagamiya KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    J.L. Nagle jamie.nagle@colorado.edu University of Colorado, Boulder, Colorado 80309, USA    M. Naglis Weizmann Institute, Rehovot 76100, Israel    M.I. Nagy ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary    I. Nakagawa RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y. Nakamiya Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    K.R. Nakamura Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    T. Nakamura KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    K. Nakano RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan    C. Nattrass University of Tennessee, Knoxville, Tennessee 37996, USA    A. Nederlof Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    P.K. Netrakanti Bhabha Atomic Research Centre, Bombay 400 085, India    J. Newby Lawrence Livermore National Laboratory, Livermore, California 94550, USA    M. Nguyen Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    M. Nihashi Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    T. Niida Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    R. Nouicer Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    N. Novitzky Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    A. Nukariya Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    A.S. Nyanin National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    H. Obayashi Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    E. O’Brien Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S.X. Oda Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    C.A. Ogilvie Iowa State University, Ames, Iowa 50011, USA    M. Oka Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    K. Okada RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y. Onuki RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    A. Oskarsson Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    M. Ouchida Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    K. Ozawa Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    R. Pak Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    V. Pantuev Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    V. Papavassiliou New Mexico State University, Las Cruces, New Mexico 88003, USA    B.H. Park Hanyang University, Seoul 133-792, Korea    I.H. Park Ewha Womans University, Seoul 120-750, Korea    J. Park Chonbuk National University, Jeonju, 561-756, Korea Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    S. Park Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    S.K. Park Korea University, Seoul, 136-701, Korea    W.J. Park Korea University, Seoul, 136-701, Korea    S.F. Pate New Mexico State University, Las Cruces, New Mexico 88003, USA    L. Patel Georgia State University, Atlanta, Georgia 30303, USA    H. Pei Iowa State University, Ames, Iowa 50011, USA    J.-C. Peng University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    H. Pereira Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France    D.V. Perepelitsa Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    V. Peresedov Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    D.Yu. Peressounko National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    R. Petti Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    C. Pinkenburg Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R.P. Pisani Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    M. Proissl Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    M.L. Purschke Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    A.K. Purwar Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    H. Qu Abilene Christian University, Abilene, Texas 79699, USA Georgia State University, Atlanta, Georgia 30303, USA    J. Rak Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland    A. Rakotozafindrabe Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France    I. Ravinovich Weizmann Institute, Rehovot 76100, Israel    K.F. Read Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA University of Tennessee, Knoxville, Tennessee 37996, USA    K. Reygers Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany    D. Reynolds Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    V. Riabov National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    Y. Riabov PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia    E. Richardson University of Maryland, College Park, Maryland 20742, USA    N. Riveli Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA    D. Roach Vanderbilt University, Nashville, Tennessee 37235, USA    G. Roche Deceased LPC, Université Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France    S.D. Rolnick University of California-Riverside, Riverside, California 92521, USA    M. Rosati Iowa State University, Ames, Iowa 50011, USA    C.A. Rosen University of Colorado, Boulder, Colorado 80309, USA    S.S.E. Rosendahl Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    P. Rosnet LPC, Université Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France    P. Rukoyatkin Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia    P. Ružička Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic    M.S. Ryu Hanyang University, Seoul 133-792, Korea    B. Sahlmueller Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    N. Saito KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    T. Sakaguchi Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    K. Sakashita RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan    H. Sako Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan    V. Samsonov National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    M. Sano Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    S. Sano Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan    M. Sarsour Georgia State University, Atlanta, Georgia 30303, USA    S. Sato Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    T. Sato Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    S. Sawada KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    K. Sedgwick University of California-Riverside, Riverside, California 92521, USA    J. Seele University of Colorado, Boulder, Colorado 80309, USA    R. Seidl University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    A.Yu. Semenov Iowa State University, Ames, Iowa 50011, USA    A. Sen Georgia State University, Atlanta, Georgia 30303, USA University of Tennessee, Knoxville, Tennessee 37996, USA    R. Seto University of California-Riverside, Riverside, California 92521, USA    P. Sett Bhabha Atomic Research Centre, Bombay 400 085, India    D. Sharma Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA Weizmann Institute, Rehovot 76100, Israel    I. Shein IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    T.-A. Shibata RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan    K. Shigaki Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    M. Shimomura Iowa State University, Ames, Iowa 50011, USA Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    K. Shoji Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    P. Shukla Bhabha Atomic Research Centre, Bombay 400 085, India    A. Sickles Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    C.L. Silva Iowa State University, Ames, Iowa 50011, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    D. Silvermyr Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    C. Silvestre Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France    K.S. Sim Korea University, Seoul, 136-701, Korea    B.K. Singh Department of Physics, Banaras Hindu University, Varanasi 221005, India    C.P. Singh Department of Physics, Banaras Hindu University, Varanasi 221005, India    V. Singh Department of Physics, Banaras Hindu University, Varanasi 221005, India    M. Skolnik Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    M. Slunečka Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic    S. Solano Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA    R.A. Soltz Lawrence Livermore National Laboratory, Livermore, California 94550, USA    W.E. Sondheim Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    S.P. Sorensen University of Tennessee, Knoxville, Tennessee 37996, USA    I.V. Sourikova Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    N.A. Sparks Abilene Christian University, Abilene, Texas 79699, USA    P.W. Stankus Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    P. Steinberg Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    E. Stenlund Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden    M. Stepanov Deceased Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA New Mexico State University, Las Cruces, New Mexico 88003, USA    A. Ster Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary    S.P. Stoll Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    T. Sugitate Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    A. Sukhanov Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    J. Sun Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    J. Sziklai Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary    E.M. Takagui Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil    A. Takahara Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    A. Taketani RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R. Tanabe Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    Y. Tanaka Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan    S. Taneja Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    K. Tanida Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea    M.J. Tannenbaum Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    S. Tarafdar Department of Physics, Banaras Hindu University, Varanasi 221005, India Weizmann Institute, Rehovot 76100, Israel    A. Taranenko National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    P. Tarján Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary    E. Tennant New Mexico State University, Las Cruces, New Mexico 88003, USA    H. Themann Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    T.L. Thomas University of New Mexico, Albuquerque, New Mexico 87131, USA    T. Todoroki RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    M. Togawa Kyoto University, Kyoto 606-8502, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan    A. Toia Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    L. Tomášek Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic    M. Tomášek Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic    H. Torii Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    R.S. Towell Abilene Christian University, Abilene, Texas 79699, USA    I. Tserruya Weizmann Institute, Rehovot 76100, Israel    Y. Tsuchimoto Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    T. Tsuji Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    C. Vale Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Iowa State University, Ames, Iowa 50011, USA    H. Valle Vanderbilt University, Nashville, Tennessee 37235, USA    H.W. van Hecke Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA    M. Vargyas ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary    E. Vazquez-Zambrano Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    A. Veicht Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    J. Velkovska Vanderbilt University, Nashville, Tennessee 37235, USA    R. Vértesi Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary    A.A. Vinogradov National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    M. Virius Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic    B. Voas Iowa State University, Ames, Iowa 50011, USA    A. Vossen University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    V. Vrba Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic    E. Vznuzdaev PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia    X.R. Wang New Mexico State University, Las Cruces, New Mexico 88003, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    D. Watanabe Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    K. Watanabe RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan    Y. Watanabe RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y.S. Watanabe Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan    F. Wei Iowa State University, Ames, Iowa 50011, USA New Mexico State University, Las Cruces, New Mexico 88003, USA    R. Wei Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA    J. Wessels Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany    S. Whitaker Iowa State University, Ames, Iowa 50011, USA    S.N. White Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    D. Winter Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    S. Wolin University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    J.P. Wood Abilene Christian University, Abilene, Texas 79699, USA    C.L. Woody Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    R.M. Wright Abilene Christian University, Abilene, Texas 79699, USA    M. Wysocki University of Colorado, Boulder, Colorado 80309, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    B. Xia Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA    W. Xie RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Y.L. Yamaguchi Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA    K. Yamaura Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan    R. Yang University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA    A. Yanovich IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia    J. Ying Georgia State University, Atlanta, Georgia 30303, USA    S. Yokkaichi RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    Z. You Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Peking University, Beijing 100871, People’s Republic of China    G.R. Young Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    I. Younus Physics Department, Lahore University of Management Sciences, Lahore 54792, Pakistan University of New Mexico, Albuquerque, New Mexico 87131, USA    I.E. Yushmanov National Research Center “Kurchatov Institute”, Moscow, 123098 Russia    W.A. Zajc Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA    A. Zelenski Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    C. Zhang Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    S. Zhou Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, People’s Republic of China    L. Zolin Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
July 13, 2019
Abstract

We report the measurement of cumulants () of the net-charge distributions measured within pseudorapidity ( 0.35) in AuAu collisions at =7.7–200 GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g. , ) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of and can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy. The extracted baryon chemical potentials are in excellent agreement with a thermal-statistical analysis model.

pacs:
25.75.Dw

PHENIX Collaboration

One of the main goals in the study of relativistic heavy ion collisions is to map the quantum chromodynamics (QCD) phase diagram at finite temperature () and baryon chemical potential (Stephanov et al. (1998). Although the exact nature of the phase transition at finite baryon density is still not well established, several models suggest that, at large and low , the phase transition between the hadronic phase and the quark-gluon-plasma (QGP) phase is of first order Alford et al. (1998); Stephanov (1996) and that at high and low there is a simple cross over from the QGP to hadronic phase Aoki et al. (2006); Pisarski and Wilczek (1984); Stephanov (2004); Fodor and Katz (2004); Ejiri (2008). The point at which the first-order phase transition ends in the plane is called the QCD critical end point (CEP), which is one of the central targets of the Relativistic Heavy Ion Collider (RHIC) beam-energy-scan program. Several calculations also reported the possible existence of the CEP in the phase diagram Fodor and Katz (2004); Stephanov (2004); Stephanov et al. (1999).

RHIC at Brookhaven National Laboratory has provided a large amount of data from AuAu collisions at different colliding energies, which gives us a unique opportunity to scan the plane and investigate the possible existence and location of the CEP. In the thermodynamic limit, the correlation length () diverges at the CEP Stephanov et al. (1998). Event-by-event fluctuations of various conserved quantities, such as net-baryon number, net-charge, and net-strangeness are proposed as possible signatures of the existence of the CEP Koch et al. (2005); Asakawa et al. (2000, 2009). It has been shown in lattice QCD that with a next-to-leading-order Taylor series expansion around vanishing chemical potentials, the cumulants of charge-fluctuations are sensitive indicators for the occurrence of a transition from the hadronic to QGP phase Ejiri et al. (2006); Bazavov et al. (2012). Typically, the variances of net-baryon, net-charge, and net-strangeness distributions are proportional to as (=)= Stephanov et al. (1999), where is the multiplicity, and (=) is the mean of the distribution.

Recent calculations reveal that higher cumulants of the fluctuations are much more sensitive to the proximity of the CEP than earlier measurements using second cumulants (Stephanov (2009); Asakawa et al. (2009). The skewness () and kurtosis () are related to the third and fourth moments (= and (=. The ratio of the various order () of cumulants () and conventional values (, , and ) can be related as follows: = , = , = , and = . Because diverges at the CEP, the ratios of cumulants and should rise rapidly when approaching the CEP Gavai and Gupta (2011); Cheng et al. (2009). The cumulants of conserved quantities of net-baryon, net-charge, and net-strangeness obtained from lattice QCD calculations Ejiri et al. (2006); Bazavov et al. (2012); Cheng et al. (2009) and a hadron resonance gas (HRG) model Karsch and Redlich (2011) are related to the generalized susceptibilities of -th order () associated with the conserved quantum numbers as , , , and . One advantage of measuring , , , and is that the volume dependence of , , , and cancel out in the ratios, hence theoretical calculations can be directly compared with the experimental measurements. These cumulant ratios can also be used to extract the freeze-out parameters and the location of the CEP Bazavov et al. (2012). Net-electric charge fluctuations are more straightforward to measure experimentally than net-baryon number fluctuations, which are partially accessible via net-proton measurement Aggarwal et al. (2010). While net-charge fluctuations are not as sensitive as net-baryon fluctuations to the theoretical parameters, both measurements are desirable for a full understanding of the theory.

We report here precise measurements of the energy and centrality dependence of higher cumulants of net-charge multiplicity ( = ) distributions measured by the PHENIX experiment at RHIC in AuAu collisions at  = 7.7, 19.6, 27, 39, 62.4, and 200 GeV. These measurements cover a broad range of in the QCD phase diagram.

The PHENIX detector is composed of two central spectrometer arms, two forward muon arms, and global detectors Adcox et al. (2003). In this analysis, we use the central arm spectrometers, which cover a pseudorapidity range of 0.35. Each of the two arms subtends /2 radians in azimuth and is designed to detect charged hadrons, electrons, and photons. For data taken at  = 62.4 and 200 GeV in 2010 and 2007, respectively, the event centrality is determined using total charge deposited in the beam-beam counters (BBC), which are also used for triggering and vertex determination. For lower energies ( = 39 GeV and below) the acceptance of the BBCs (3.0 3.9) are within the fragmentation region, so alternate detectors must be employed. For data taken at  = 39 and 7.7 GeV in 2010, centrality is determined using the total charge deposited in the outer ring of the reaction plane detector (RXNP), which covers  Richardson et al. (2011). For data taken at  = 19.6 and 27 GeV in 2011, the RXNP was absent, so centrality is determined using the total energy of electromagnetic calorimeter (EMCal) clusters to minimize the correlation with the charge of the tracks measured in the same acceptance. More details on the procedure are given in Adler et al. (2005). The analyzed events for the above mentioned energies are within a collision vertex of 30 cm. The number of analyzed events are 2M, 6M, 21M, 154M, 474M, and 1681M for = 7.7, 19.6, 27, 39, 62.4, and 200 GeV AuAu collisions, respectively.

The number of positively charged () and negatively charged () particles measured on an event-by-event basis are used to calculate the net-charge () distributions for each collision centrality and energy. The charged-particle trajectories are reconstructed using information from the drift chamber and pad chambers (PC1 and PC3). A combination of reconstructed drift-chamber tracks and matching hits in PC1 are used to determine the momentum and charge of the particle. Tracks having a transverse momentum () between 0.3 and 2.0 GeV/ are selected for this analysis. The ring imaging Čerenkov detector is used to reduce the electron background resulting from conversion photons. To further reduce the background, selected tracks are required to lie within a 2.5 matching window between track projections and PC3 hits, and a 3 matching window for the EMCal.

Figure 1: (Color online). Uncorrected net-charge () distributions, within 0.35 for different energies, from AuAu collisions for (a) central (0%–5%) and (b) peripheral (55%–60%) centrality. (c)–(f) are the efficiency corrected cumulants of net-charge distributions as a function of from AuAu collisions at different collision energies. Systematic uncertainties on moments are shown for central (0%–5%) collisions.

Figure 1(a) and (b) show distributions in AuAu collisions for central (0%–5%) and peripheral (55%–60%) collisions at different collision energies. These distributions are not corrected for reconstruction efficiency. The centrality classes associated with the average number of participants () are defined for each 5% centrality bin. These classes are determined using a Monte-Carlo simulation based on Glauber model calculations with the BBC, RXNP, and EMCal detector response taken into account Adler et al. (2005); Miller et al. (2007).

The distributions are characterized by cumulants and related quantities such as , , , and , which are calculated from the distributions. The statistical uncertainties for the cumulants are calculated using the bootstrap method Efron and Tibshirani (1994). Corrections are then made for the reconstruction efficiency, which is estimated for each centrality and energy using the hijing1.37 event generator Wang and Gyulassy (1991) and then processed through a geant simulation with the PHENIX detector setup. For all collision energies, the average efficiency for detecting the particles within the acceptance varies between 65%–72% and 76%–85% for central (0%–5%) and peripheral (55%–60%) events, respectively with 4%–5% variation as a function of energy. The efficiency correction applied to the cumulants is based on a binomial probability distribution for the reconstruction efficiency Bzdak et al. (2013). The efficiency corrected , , , and as a function of are shown in panels (c-f) of Fig. 1.

The and for net-charge distributions increase with increasing , while and decrease with increasing for all collision energies. At a given value, , , and of net-charge distributions decrease with increasing collision energy. However, the width () of net-charge distributions increases with increasing collision energy indicating the increase of fluctuations in the system at higher .

Figure 2: (Color online). dependence of efficiency corrected (a) , (b) , (c) , and (d) of net-charge distributions for AuAu collisions at different collision energies. Statistical errors are shown along with the data points while systematic uncertainties are shown for (0%–5%) collisions.

The systematic uncertainties are estimated by: (1) varying the cut to less than 10 cm; (2) varying the matching parameters of PC3 hits and EMCal clusters with the projected tracks to study the effect of background tracks originating from secondary interactions or from ghost tracks; (3) varying the centrality bin width to study nondynamical contributions to the net-charge fluctuations due to the finite width of the centrality bins Adare et al. (2008); Adler et al. (2007); Konchakovski et al. (2006); and (4) varying the lower cut. The total systematic uncertainties estimated for various cumulants for all energies are: 10%–24% for , 5%–10% for , 25%–30% for , and 12%–19% for . The systematic uncertainties are similar for all centralities at a given energy and are treated as uncorrelated as a function of . For clarity of presentation, the systematic uncertainties are only shown for central (0%–5%) collisions.

Figure 3: (Color online). The energy dependence of efficiency corrected (a) , (b) , (c) , and (d) of net-charge distributions for central (0%–5%) AuAu collisions. The error bars are statistical and caps are systematic uncertainties. The triangle symbol shows the corresponding efficiency corrected cumulant ratios for net-charge, from NBD fits to the individual and distributions.

Figure 2 shows the dependence of , , , and extracted from the net-charge distributions in AuAu collisions at different . The results are corrected for the reconstruction efficiencies. Statistical uncertainties are shown along with the data points. The systematic uncertainties are constant fractional errors for all centralities at a particular energy, hence they are presented for the central (0%–5%) collision data point only. The systematic uncertainties on these ratios across different energies varies as follows: 20%–30% for , 15%–34% for , 12%–22% for , and 17%–32% for . It is observed in Fig. 2 that the ratios of the cumulants are weakly dependent on for each collision energy; the values of and decrease from lower to higher collision energies, while the and values are constant as a function of within systematic uncertainties.

The collision energy dependence of , , and of the net-charge distributions for central (0%–5%) AuAu collisions are shown in Fig. 3. The statistical and systematic uncertainties are shown along with the data points. The experimental data are compared with negative-binomial-distribution (NBD) expectations, which are calculated by computing the efficiency corrected cumulants for the measured and distributions fit with NBD’s respectively, which also describe total charge () distributions very well Adare et al. (2008); Adler et al. (2007). The various order ( = 1, 2, 3 and 4) of net-charge cumulants from NBD are given as = , where and are cumulants of and distributions, respectively Barndorff-Nielsen et al. (2012); Tarnowsky and Westfall (2013).

The and values in Fig. 3(a) and Fig. 3(b), respectively both decrease with increasing . The NBD expectation agrees well with the data. The values in Fig. 3(c) remain constant and positive, between at all the collision energies within the statistical and systematic uncertainties. However, there is 25% increase of values at lower energies compared to higher energies above = 39 GeV, which is within the systematic uncertainties. These data are in agreement with a previous measurement Adamczyk et al. (2014a), but provide a more precise determination of the higher cumulant ratios, verified by the NBD method of correcting for efficiency, which is simple and analytical for all cumulant ratios with the standard binomial correction Bzdak et al. (2013). The values in Fig. 3(d) remain constant at all collision energies within the uncertainties and are well described by the NBD expectation. From the energy dependence of , , , and , no obvious nonmonotonic behavior is observed. Although both previous measurements by STAR Adamczyk et al. (2014a, b) use the pseudorapidity range , compared to the present measurement spanning , these measurements are all within the central rapidity region and are expected to be valid for comparison to lattice QCD calculations. The efficiency corrected results for the cumulant ratios , , and remain the same within statistics whether each single arm of the PHENIX central spectrometer (azimuthal aperture ) or both arms () are used. This is a clear verification of the insensitivity of measured cumulant ratios to volume effects.

Figure 4: (Color online). The energy dependence of the chemical freeze-out parameter . The dashed line is the parametrization given in Ref. Cleymans et al. (2006) and the other experimental data are from Ref. Cleymans et al. (2006) and references therein.
PHENIX + Ref. Bazavov et al. (2012); Mukherjee (2014) PHENIX + Ref. Borsanyi et al. (2013) STAR + Ref. Borsanyi et al. (2014)
(GeV) (MeV) (MeV) (MeV) (MeV) (MeV)
27
39
62.4
200
Table 1: Freeze-out and vs. in the range GeV from this work compared to values from Ref. Borsanyi et al. (2014), which used STAR net-charge cumulant measurements from Ref. Adamczyk et al. (2014a) for ; with MeV MeV obtained from STAR net-proton measurement in Ref. Adamczyk et al. (2014b) by averaging over = 27, 39, 62.4 and 200 GeV.

The precise measurement of both and in the present study allow both and to be determined, unlike a previous calculation in Ref. Borsanyi et al. (2014, 2013), which was only able to use the measurement from Ref. Adamczyk et al. (2014a). The comparison of for different with the lattice calculations (Fig. 3(b) in Ref. Bazavov et al. (2012); Mukherjee (2014)) enables us to extract the chemical freeze-out temperature (). Furthermore, can be extracted by comparing the measured ratios with the lattice calculations of (Fig.3(a) in Ref. Bazavov et al. (2012); Mukherjee (2014)). The extracted and values are listed in Table 1. The and extracted using the lattice calculations in the continuum limit from Ref. Borsanyi et al. (2013) are also depicted in Table 1. The extracted freeze-out parameters using different lattice results agree very well. However, the extracted are 2-4 MeV lower using Ref. Borsanyi et al. (2013) than with Ref. Bazavov et al. (2012); Mukherjee (2014), which is well within the stated uncertainties. The detailed freeze-out parameter extraction procedure is given in Ref. Bazavov et al. (2012); Borsanyi et al. (2013, 2014). This is a direct combination of experimental data and lattice calculations to extract physical quantities. The dependence of shown in Fig. 4 is in agreement with the thermal-statistical analysis model of identified particle yields Cleymans et al. (2006). The extracted in the present net-charge measurement and the values reported in Borsanyi et al. (2014) are in agreement within stated uncertainties, with some tension at = 27 GeV. Available lattice results allow extraction of and from  = 27 GeV and higher using the present net-charge experimental data. Other recent calculations Alba et al. (2014); Bazavov et al. () have used both net-proton and net-charge measurements to estimate the freeze-out parameters.

In summary, fluctuations of net-charge distributions have been studied using higher cumulants (, , , and ) for 0.35 with the PHENIX experiment in AuAu collisions ranging from = 7.7 to 200 GeV. The ratios of cumulants (, , , and ) have been derived from the individual cumulants of the distributions studied as a function of and . The and values decrease with increasing collision energy and are weakly dependent on centrality, whereas and values remain constant over all collision energies within uncertainties. The efficiency corrected values from the NBD expectation reproduce the experimental data. These data are in agreement with a previous measurement Adamczyk et al. (2014a), but provide more precise determination of the higher cumulant ratios and . In the present study we do not observe any significant nonmonotonic behavior of , , , and as a function of collision energies. Comparison of the present measurements together with the lattice calculations enables us to extract the freeze-out temperature and baryon chemical potential () over a range of collision energies. The extracted values are in excellent agreement with the thermal-statistical analysis model Cleymans et al. (2006).

We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We thank F. Karsch and S. Mukherjee for providing us with tables of their calculations and for helpful discussions. We acknowledge support from the Office of Nuclear Physics in the Office of Science of the Department of Energy, the National Science Foundation, Abilene Christian University Research Council, Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan), Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China), Ministry of Science, Education, and Sports (Croatia), Ministry of Education, Youth and Sports (Czech Republic), Centre National de la Recherche Scientifique, Commissariat à l’Énergie Atomique, and Institut National de Physique Nucléaire et de Physique des Particules (France), Bundesministerium für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), National Science Fund, OTKA, Károly Róbert University College, and the Ch. Simonyi Fund (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Basic Science Research Program through NRF of the Ministry of Education (Korea), Physics Department, Lahore University of Management Sciences (Pakistan), Ministry of Education and Science, Russian Academy of Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg Foundation (Sweden), the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, the Hungarian American Enterprise Scholarship Fund, and the US-Israel Binational Science Foundation.

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