PHENIX Collaboration

# Low-momentum direct photon measurement in Cu$+$Cu collisions at
$\sqrt{s_{{}_{NN}}}=200$ GeV

A. Adare  University of Colorado, Boulder, Colorado 80309, USA  S. Afanasiev
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia  C.
Aidala  Columbia University, New York, New York 10027 and Nevis Laboratories,
Irvington, New York 10533, USA  Department of Physics, University of Michigan,
Ann Arbor, Michigan 48109-1040, USA  N.N. Ajitanand  Deceased  Chemistry
Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400,
USA  Y. Akiba<EMAIL_ADDRESS>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  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  M. Alfred  Department of Physics and Astronomy,
Howard University, Washington, DC 20059, 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  L. Aphecetche  SUBATECH (Ecole des
Mines de Nantes, CNRS-IN2P3, Université de Nantes) BP 20722-44307, Nantes,
France  R. Armendariz  New Mexico State University, Las Cruces, New Mexico
88003, USA  S.H. Aronson  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  J. Asai  RIKEN BNL Research Center,
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  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  A.
Bagoly  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A,
Hungary  G. Baksay  Florida Institute of Technology, Melbourne, Florida 32901,
USA  L. Baksay  Florida Institute of Technology, Melbourne, Florida 32901, USA
A. Baldisseri  Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France  K.N.
Barish  University of California-Riverside, Riverside, California 92521, USA
P.D. Barnes  Deceased  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  B. Bassalleck  University of New Mexico, Albuquerque, New Mexico
87131, 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  S. Batsouli  Oak Ridge National Laboratory, Oak
Ridge, Tennessee 37831, USA  V. Baublis  PNPI, Petersburg Nuclear Physics
Institute, Gatchina, Leningrad region, 188300, Russia  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  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  M. Boer  Los Alamos National Laboratory, Los Alamos, New Mexico 87545,
USA  J.G. Boissevain  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  J.S. Bok  New Mexico State University, Las Cruces, New Mexico
88003, USA  H. Borel  Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France  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
University of California-Riverside, Riverside, California 92521, 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  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, 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  V. Canoa Roman
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  B.S. Chang  Yonsei University, IPAP, Seoul
120-749, Korea  J.-L. Charvet  Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette,
France  S. Chernichenko  IHEP Protvino, State Research Center of Russian
Federation, Institute for High Energy Physics, Protvino, 142281, Russia  C.Y.
Chi  Columbia University, New York, New York 10027 and Nevis Laboratories,
Irvington, New York 10533, USA  J. Chiba  KEK, High Energy Accelerator
Research Organization, Tsukuba, Ibaraki 305-0801, Japan  M. Chiu  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  I.J.
Choi  University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
Yonsei University, IPAP, Seoul 120-749, Korea  T. Chujo  Tomonaga Center for
the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305,
Japan  Vanderbilt University, Nashville, Tennessee 37235, USA  P. Chung
Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York
11794-3400, USA  A. Churyn  IHEP Protvino, State Research Center of Russian
Federation, Institute for High Energy Physics, Protvino, 142281, Russia  V.
Cianciolo  Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
C.R. Cleven  Georgia State University, Atlanta, Georgia 30303, USA  B.A. Cole
Columbia University, New York, New York 10027 and Nevis Laboratories,
Irvington, New York 10533, USA  M.P. Comets  IPN-Orsay, Univ. Paris-Sud,
CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406, Orsay, France  M. Connors
Georgia State University, Atlanta, Georgia 30303, USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  P.
Constantin  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
M. Csanád  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A,
Hungary  T. Csörgő  Eszterházy Károly University, Károly Róbert Campus, H-3200
Gyöngyös, Mátrai út 36, 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  T. Dahms  Department
of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  T.W. Danley  Department of Physics and Astronomy, Ohio
University, Athens, Ohio 45701, USA  K. Das  Florida State University,
Tallahassee, Florida 32306, USA  G. David  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  M.B. Deaton  Abilene Christian University, Abilene, Texas 79699, 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  H. Delagrange  Deceased  SUBATECH (Ecole des
Mines de Nantes, CNRS-IN2P3, Université de Nantes) BP 20722-44307, Nantes,
France  A. Denisov  IHEP Protvino, State Research Center of Russian
Federation, Institute for High Energy Physics, Protvino, 142281, Russia  D.
d’Enterria  Columbia University, New York, New York 10027 and Nevis
Laboratories, Irvington, New York 10533, USA  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  O. Dietzsch
Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo
CEP05315-970, Brazil  A. Dion  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
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  A.K. Dubey  Weizmann Institute, Rehovot 76100, Israel  J.M. Durham  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  A. Durum  IHEP
Protvino, State Research Center of Russian Federation, Institute for High
Energy Physics, Protvino, 142281, Russia  V. Dzhordzhadze  University of
California-Riverside, Riverside, California 92521, USA  Y.V. Efremenko  Oak
Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA  J. Egdemir
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  F. Ellinghaus  University of Colorado,
Boulder, Colorado 80309, USA  W.S. Emam  University of California-Riverside,
Riverside, California 92521, USA  A. Enokizono  Lawrence Livermore National
Laboratory, Livermore, California 94550, 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  Tomonaga Center for the History of
the Universe, 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  W. Fan  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  N. Feege  Department
of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  D.E. Fields  University of New Mexico, Albuquerque, New
Mexico 87131, USA  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  M. Finger  Charles University, Ovocný trh 5,
Praha 1, 116 36, Prague, Czech Republic  Joint Institute for Nuclear Research,
141980 Dubna, Moscow Region, Russia  M. Finger, Jr  Charles University, Ovocný
trh 5, Praha 1, 116 36, Prague, Czech Republic  Joint Institute for Nuclear
Research, 141980 Dubna, Moscow Region, Russia  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  Kyoto University, Kyoto 606-8502,
Japan  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  S. Gadrat  LPC, Université Blaise Pascal, CNRS-
IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France  P. Gallus  Czech Technical
University, Zikova 4, 166 36 Prague 6, Czech Republic  P. Garg  Department of
Physics, Banaras Hindu University, Varanasi 221005, India  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  I. Garishvili  Lawrence Livermore National Laboratory,
Livermore, California 94550, USA  University of Tennessee, Knoxville,
Tennessee 37996, USA  H. Ge  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, 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  M. Gonin  Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3,
Route de Saclay, F-91128, Palaiseau, France  J. Gosset  Dapnia, CEA Saclay,
F-91191, Gif-sur-Yvette, 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  Iowa
State University, Ames, Iowa 50011, 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  T. Gunji
Center for Nuclear Study, Graduate School of Science, University of Tokyo,
7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  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
Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan  RIKEN BNL
Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000,
USA  A. Hadj Henni  SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3,
Université de Nantes) BP 20722-44307, Nantes, France  C. Haegemann  University
of New Mexico, Albuquerque, New Mexico 87131, USA  J.S. Haggerty  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
H. Hamagaki  Center for Nuclear Study, Graduate School of Science, University
of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  R. Han  Peking
University, Beijing 100871, People’s Republic of China  H. Harada  Hiroshima
University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  E.P. Hartouni
Lawrence Livermore National Laboratory, Livermore, California 94550, USA  K.
Haruna  Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
S. Hasegawa  Advanced Science Research Center, Japan Atomic Energy Agency, 2-4
Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan  T.O.S.
Haseler  Georgia State University, Atlanta, Georgia 30303, USA  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  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  H. Hiejima  University of
Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  J.C. Hill  Iowa
State University, Ames, Iowa 50011, USA  K. Hill  University of Colorado,
Boulder, Colorado 80309, USA  R. Hobbs  University of New Mexico, Albuquerque,
New Mexico 87131, USA  A. Hodges  Georgia State University, Atlanta, Georgia
30303, USA  M. Hohlmann  Florida Institute of Technology, Melbourne, Florida
32901, USA  W. Holzmann  Chemistry Department, Stony Brook University, SUNY,
Stony Brook, New York 11794-3400, USA  K. Homma  Hiroshima University,
Kagamiyama, Higashi-Hiroshima 739-8526, Japan  B. Hong  Korea University,
Seoul, 136-701, Korea  T. Horaguchi  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  D.
Hornback  University of Tennessee, Knoxville, Tennessee 37996, USA  T. Hoshino
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  N.
Hotvedt  Iowa State University, Ames, Iowa 50011, USA  J. Huang  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, 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  H. Iinuma  Kyoto University, Kyoto 606-8502,
Japan  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, 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  M. Inaba
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  Y. Inoue  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.
Isenhower  Abilene Christian University, Abilene, Texas 79699, USA  L.
Isenhower  Abilene Christian University, Abilene, Texas 79699, USA  M.
Ishihara  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, Japan  T. Isobe  Center for Nuclear Study, Graduate School of
Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  M.
Issah  Chemistry Department, Stony Brook University, SUNY, Stony Brook, New
York 11794-3400, 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  Z. Ji  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  J. Jia  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  Chemistry Department, Stony Brook University,
SUNY, Stony Brook, New York 11794-3400, USA  J. Jin  Columbia University, New
York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA
O. Jinnouchi  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  B.M. Johnson  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  Georgia State
University, Atlanta, Georgia 30303, 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  F. Kajihara  Center for
Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo,
Bunkyo, Tokyo 113-0033, Japan  S. Kametani  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  N. Kamihara
RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198,
Japan  J. Kamin  Department of Physics and Astronomy, Stony Brook University,
SUNY, Stony Brook, New York 11794-3800, USA  M. Kaneta  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  J.H.
Kang  Yonsei University, IPAP, Seoul 120-749, Korea  H. Kanou  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  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  A.V.
Kazantsev  National Research Center “Kurchatov Institute”, Moscow, 123098
Russia  V. Khachatryan  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  A. Khanzadeev  PNPI,
Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300,
Russia  J. Kikuchi  Waseda University, Advanced Research Institute for Science
and Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan  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  Yonsei University, IPAP, Seoul 120-749, Korea  E. Kim
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  E.-J. Kim  Chonbuk National University, Jeonju, 561-756, Korea  M. Kim
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  D. Kincses  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P.
s. 1/A, Hungary  E. Kinney  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  A. Kiyomichi  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  J. Klay  Lawrence
Livermore National Laboratory, Livermore, California 94550, USA  C. Klein-
Boesing  Institut für Kernphysik, University of Münster, D-48149 Münster,
Germany  L. Kochenda  PNPI, Petersburg Nuclear Physics Institute, Gatchina,
Leningrad region, 188300, Russia  V. Kochetkov  IHEP Protvino, State Research
Center of Russian Federation, Institute for High Energy Physics, Protvino,
142281, Russia  B. Komkov  PNPI, Petersburg Nuclear Physics Institute,
Gatchina, Leningrad region, 188300, Russia  M. Konno  Tomonaga Center for the
History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
D. Kotchetkov  University of California-Riverside, Riverside, California
92521, 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  J. Kubart
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  G.J. Kunde  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  B. Kurgyis  ELTE, Eötvös Loránd
University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  N. Kurihara  Center
for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1
Hongo, Bunkyo, Tokyo 113-0033, Japan  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.J. Kweon  Korea University, Seoul, 136-701, Korea  Y. Kwon  University of
Tennessee, Knoxville, Tennessee 37996, USA  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  D.M. Lee  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  M.K. Lee  Yonsei University,
IPAP, Seoul 120-749, Korea  S.H. Lee  Iowa State University, Ames, Iowa 50011,
USA  T. Lee  Department of Physics and Astronomy, Seoul National University,
Seoul 151-742, 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  B. Lenzi
Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo
CEP05315-970, Brazil  Y.H. Leung  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  N.A. Lewis
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040,
USA  X. Li  Science and Technology on Nuclear Data Laboratory, China Institute
of Atomic Energy, Beijing 102413, People’s Republic of China  X. Li  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  S.H. Lim  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Yonsei
University, IPAP, Seoul 120-749, Korea  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  M.X. Liu  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  S. Lökös  ELTE, Eötvös
Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  B. Love
Vanderbilt University, Nashville, Tennessee 37235, USA  D. Lynch  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
C.F. Maguire  Vanderbilt University, Nashville, Tennessee 37235, USA  T.
Majoros  Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  Y.I.
Makdisi  Collider-Accelerator Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  A. Malakhov  Joint Institute for Nuclear
Research, 141980 Dubna, Moscow Region, Russia  M.D. Malik  University of New
Mexico, Albuquerque, New Mexico 87131, USA  V.I. Manko  National Research
Center “Kurchatov Institute”, Moscow, 123098 Russia  Y. Mao  Peking
University, Beijing 100871, People’s Republic of China  RIKEN Nishina Center
for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  L. Mašek
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  H. Masui  Tomonaga Center for the History
of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  F.
Matathias  Columbia University, New York, New York 10027 and Nevis
Laboratories, Irvington, New York 10533, USA  M. McCumber  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  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Y. Miake
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  A.C. Mignerey  University of Maryland, College
Park, Maryland 20742, USA  D.E. Mihalik  Department of Physics and Astronomy,
Stony Brook University, SUNY, Stony Brook, New York 11794-3800, 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  Tomonaga Center for the History
of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  T.E.
Miller  Vanderbilt University, Nashville, Tennessee 37235, USA  A. Milov
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  Weizmann Institute, Rehovot 76100, Israel  S.
Mioduszewski  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  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  M. Mitrovski
Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York
11794-3400, USA  G. Mitsuka  KEK, High Energy Accelerator Research
Organization, Tsukuba, Ibaraki 305-0801, Japan  RIKEN BNL Research Center,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  T. Moon
Yonsei University, IPAP, Seoul 120-749, Korea  A. Morreale  University of
California-Riverside, Riverside, California 92521, USA  D.P. Morrison  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
S.I. Morrow  Vanderbilt University, Nashville, Tennessee 37235, USA  T.V.
Moukhanova  National Research Center “Kurchatov Institute”, Moscow, 123098
Russia  D. Mukhopadhyay  Vanderbilt University, Nashville, Tennessee 37235,
USA  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  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
K. Nagashima  Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526,
Japan  Y. Nagata  Tomonaga Center for the History of the Universe, University
of Tsukuba, Tsukuba, Ibaraki 305, Japan  J.L. Nagle  University of Colorado,
Boulder, Colorado 80309, USA  M. Naglis  Weizmann Institute, Rehovot 76100,
Israel  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  T. Nakamura
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, 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  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  B.E. Norman  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  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  T. Novák  Eszterházy
Károly University, Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36,
Hungary  N. Novitzky  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  A.S. Nyanin  National
Research Center “Kurchatov Institute”, Moscow, 123098 Russia  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  H. Ohnishi  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
M. Oka  Tomonaga Center for the History of the Universe, University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  K. Okada  RIKEN BNL Research Center,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  O.O. Omiwade
Abilene Christian University, Abilene, Texas 79699, USA  J.D. Orjuela Koop
University of Colorado, Boulder, Colorado 80309, USA  J.D. Osborn  Department
of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA  A.
Oskarsson  Department of Physics, Lund University, Box 118, SE-221 00 Lund,
Sweden  M. Ouchida  Hiroshima University, Kagamiyama, Higashi-Hiroshima
739-8526, 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  Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  R. Pak  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  D. Pal  Vanderbilt University,
Nashville, Tennessee 37235, USA  A.P.T. Palounek  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, 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
J. Park  Department of Physics and Astronomy, Seoul National University, Seoul
151-742, Korea  S. Park  RIKEN Nishina Center for Accelerator-Based Science,
Wako, Saitama 351-0198, Japan  Department of Physics and Astronomy, Seoul
National University, Seoul 151-742, Korea  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
W.J. Park  Korea University, Seoul, 136-701, Korea  S.F. Pate  New Mexico
State University, Las Cruces, New Mexico 88003, USA  M. Patel  Iowa State
University, Ames, Iowa 50011, USA  H. Pei  Iowa State University, Ames, Iowa
50011, USA  J.-C. Peng  University of Illinois at Urbana-Champaign, Urbana,
Illinois 61801, USA  W. Peng  Vanderbilt University, Nashville, Tennessee
37235, USA  H. Pereira  Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France
D.V. Perepelitsa  University of Colorado, Boulder, Colorado 80309, USA  V.
Peresedov  Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region,
Russia  D.Yu. Peressounko  National Research Center “Kurchatov Institute”,
Moscow, 123098 Russia  C.E. PerezLara  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  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  Georgia State
University, Atlanta, Georgia 30303, USA  P.V. Radzevich  Saint Petersburg
State Polytechnic University, St. Petersburg, 195251 Russia  J. Rak  Helsinki
Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014
Jyväskylä, Finland  University of New Mexico, Albuquerque, New Mexico 87131,
USA  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  S. Rembeczki  Florida Institute of
Technology, Melbourne, Florida 32901, USA  M. Reuter  Department of Physics
and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800,
USA  K. Reygers  Institut für Kernphysik, University of Münster, D-48149
Münster, Germany  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  D. Richford  Baruch College, City University of New
York, New York, New York, 10010 USA  T. Rinn  Iowa State University, Ames,
Iowa 50011, USA  G. Roche  Deceased  LPC, Université Blaise Pascal, CNRS-
IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France  A. Romana  Deceased
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de
Saclay, F-91128, Palaiseau, France  M. Rosati  Iowa State University, Ames,
Iowa 50011, 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  Z. Rowan  Baruch College,
City University of New York, New York, New York, 10010 USA  P. Rukoyatkin
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia  J.
Runchey  Iowa State University, Ames, Iowa 50011, USA  V.L. Rykov  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
B. Sahlmueller  Institut für Kernphysik, University of Münster, D-48149
Münster, 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  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  T. Sakaguchi  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
S. Sakai  Tomonaga Center for the History of the Universe, University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  H. Sakata  Hiroshima University,
Kagamiyama, Higashi-Hiroshima 739-8526, 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. 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  S. Sawada  KEK, High Energy Accelerator Research
Organization, Tsukuba, Ibaraki 305-0801, Japan  B.K. Schmoll  University of
Tennessee, Knoxville, Tennessee 37996, 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  V. Semenov
IHEP Protvino, State Research Center of Russian Federation, Institute for High
Energy Physics, Protvino, 142281, Russia  R. Seto  University of California-
Riverside, Riverside, California 92521, USA  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  A. Shevel  PNPI, Petersburg Nuclear Physics
Institute, Gatchina, Leningrad region, 188300, Russia  Chemistry Department,
Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA  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  Tomonaga Center for the History of the Universe,
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  A. Sickles  University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
C.L. Silva  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  C.P. Singh
Department of Physics, Banaras Hindu University, Varanasi 221005, India  V.
Singh  Department of Physics, Banaras Hindu University, Varanasi 221005, India
M.J. Skoby  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  S. Skutnik  Iowa State University, Ames, Iowa 50011, USA  M.
Slunečka  Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech
Republic  Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region,
Russia  A. Soldatov  IHEP Protvino, State Research Center of Russian
Federation, Institute for High Energy Physics, Protvino, 142281, Russia  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  F. Staley  Dapnia, CEA Saclay,
F-91191, Gif-sur-Yvette, France  P.W. Stankus  Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37831, USA  E. Stenlund  Department of Physics, Lund
University, Box 118, SE-221 00 Lund, Sweden  M. Stepanov  Deceased  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  C. Suire  IPN-
Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406,
Orsay, France  Z. Sun  Debrecen University, H-4010 Debrecen, Egyetem tér 1,
Hungary  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  T. Tabaru  RIKEN BNL
Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000,
USA  S. Takagi  Tomonaga Center for the History of the Universe, University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  E.M. Takagui  Universidade de São Paulo,
Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil  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  Y. Tanaka  Nagasaki Institute of Applied
Science, Nagasaki-shi, Nagasaki 851-0193, Japan  K. Tanida  Advanced Science
Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-
mura, Naka-gun, Ibaraki-ken 319-1195, 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  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  T.L. Thomas  University of New Mexico, Albuquerque, New Mexico
87131, USA  R. Tieulent  IPNL, CNRS/IN2P3, Univ Lyon, Université Lyon 1,
F-69622, Villeurbanne, France  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  J. Tojo  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
L. Tomášek  Institute of Physics, Academy of Sciences of the Czech Republic,
Na Slovance 2, 182 21 Prague 8, Czech Republic  H. Torii  RIKEN Nishina Center
for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  R.S. Towell
Abilene Christian University, Abilene, Texas 79699, USA  V-N. Tram
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de
Saclay, F-91128, Palaiseau, France  I. Tserruya  Weizmann Institute, Rehovot
76100, Israel  Y. Tsuchimoto  Hiroshima University, Kagamiyama, Higashi-
Hiroshima 739-8526, Japan  Y. Ueda  Hiroshima University, Kagamiyama, Higashi-
Hiroshima 739-8526, Japan  B. Ujvari  Debrecen University, H-4010 Debrecen,
Egyetem tér 1, Hungary  C. Vale  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  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  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  M. Wagner  Kyoto University, Kyoto
606-8502, Japan  RIKEN Nishina Center for Accelerator-Based Science, Wako,
Saitama 351-0198, Japan  D. Walker  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  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
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  F. Wei  Iowa State University, Ames, Iowa
50011, USA  New Mexico State University, Las Cruces, New Mexico 88003, USA  J.
Wessels  Institut für Kernphysik, University of Münster, D-48149 Münster,
Germany  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  C.P. Wong
Georgia State University, Atlanta, Georgia 30303, USA  C.L. Woody  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
M. Wysocki  University of Colorado, Boulder, Colorado 80309, USA  Oak Ridge
National Laboratory, Oak Ridge, Tennessee 37831, USA  W. Xie  RIKEN BNL
Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000,
USA  C. Xu  New Mexico State University, Las Cruces, New Mexico 88003, USA  Q.
Xu  Vanderbilt University, Nashville, Tennessee 37235, USA  Y.L. Yamaguchi
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  Waseda University, Advanced
Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku,
Tokyo 162-0044, Japan  A. Yanovich  IHEP Protvino, State Research Center of
Russian Federation, Institute for High Energy Physics, Protvino, 142281,
Russia  Z. Yasin  University of California-Riverside, Riverside, California
92521, USA  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  J.H. Yoo  Korea University, Seoul, 136-701,
Korea  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  H. Yu  New Mexico State University, Las Cruces, New Mexico 88003,
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  O. Zaudtke  Institut für
Kernphysik, University of Münster, D-48149 Münster, Germany  C. Zhang  Oak
Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA  S. Zharko  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  S.
Zhou  Science and Technology on Nuclear Data Laboratory, China Institute of
Atomic Energy, Beijing 102413, People’s Republic of China  J. Zimamyi
Deceased  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  L. Zolin  Joint Institute for Nuclear
Research, 141980 Dubna, Moscow Region, Russia  L. Zou  University of
California-Riverside, Riverside, California 92521, USA

###### Abstract

We have measured direct photons for $p_{T}<5~{}$GeV/$c$ in minimum bias and
0%–40% most central events at midrapidity for Cu$+$Cu collisions at
$\sqrt{s_{{}_{NN}}}=200$ GeV. The $e^{+}e^{-}$ contribution from quasi-real
direct virtual photons has been determined as an excess over the known
hadronic contributions in the $e^{+}e^{-}$ mass distribution. A clear
enhancement of photons over the binary scaled $p$$+$$p$ fit is observed for
$p_{T}<4$ GeV/$c$ in Cu$+$Cu data. The $p_{T}$ spectra are consistent with the
Au$+$Au data covering a similar number of participants. The inverse slopes of
the exponential fits to the excess after subtraction of the $p$$+$$p$ baseline
are 285$\pm$53(stat)$\pm$57(syst) MeV/$c$ and 333$\pm$72(stat)$\pm$45(syst)
MeV/$c$ for minimum bias and 0%–40% most central events, respectively. The
rapidity density, $dN/dy$, of photons demonstrates the same power law as a
function of $dN_{\rm ch}/d\eta$ observed in Au$+$Au at the same collision
energy.

##  I Introduction

Direct photons are excellent probes for understanding the time evolution of
the hot and dense matter created in ultrarelativistic heavy ion collisions
Adcox  _et al._ (2005); Adams  _et al._ (2005). Direct photons are produced
throughout the collision and carry information about the medium at the time
when the photons were emitted, because the only interaction is electromagnetic
David  _et al._ (2008). Direct photons are produced via interactions at
partonic and hadronic levels in either initial hard scatterings of the
collision or thermal radiation from the medium and, by definition, do not
originate from hadron decays Stankus (2005). In particular, thermal photons,
which contribute dominantly at low momentum Turbide  _et al._ (2004), are one
of the most important probes because they allow us direct access to the
thermodynamic properties of the created medium. However, photons from hadron
decays account for a large fraction in the inclusive photon yield, typically
more than 80% for heavy ion collisions. The large number of decay photons
makes the measurement challenging.

Two analysis methods, the virtual photon method Adare  _et al._ (2010a) and
the external conversion method Adare  _et al._ (2015a), have been established
to measure direct photons at low $p_{T}$ ($\mbox{$p_{T}$}<5~{}$GeV/$c$).
Low-$p_{T}$ direct photon measurements have been made in PHENIX and STAR
experiments at the Relativistic Heavy Ion Collider (RHIC) for not only in
Au$+$Au collisions Adare  _et al._ (2010a, 2015a); Adamczyk  _et al._ (2017)
but also in $p$$+$$p$ and $d$$+$Au Adare  _et al._ (2013) collisions. The
virtual photon method makes it possible to measure direct photons even if the
signal to background is only a few percent as in $p$$+$$p$ and $d$$+$Au
collisions, while in Au$+$Au collisions S/B reaches 15%. The $p$$+$$p$
measurement allows to determine the hard photon yield from initial hard
scatterings. No significant modification of the $p_{T}$ distribution of direct
photons due to cold nuclear effects is seen in the $d$$+$Au data. Finally, an
enhanced yield of low-$p_{T}$ direct photons, which is unexplainable by hard
photon production and cold nuclear matter effects, has been discovered in
Au$+$Au collisions in central and semi-central events at
$\mbox{$\sqrt{s_{{}_{NN}}}$}=200$ GeV Adare  _et al._ (2010a, 2015a).

The ALICE experiment at the Large Hadron Collider (LHC) has also succeeded in
measuring the low-$p_{T}$ direct photons with the external conversion method
in Pb$+$Pb collisions at $\mbox{$\sqrt{s_{{}_{NN}}}$}=2.76$ TeV Adam  _et al._
(2016) and observed a larger yield and a higher inverse slope of the spectrum
than at RHIC, implying that a larger and hotter thermalized medium is produced
at the LHC energy. Further understanding of the thermal properties of the
created hot medium can be realized through the systematic study of low-$p_{T}$
direct photon production within a wide range of system size and collision
energy.

In this paper, we present the measurement of low-$p_{T}$ direct photons in
Cu$+$Cu collisions at $\mbox{$\sqrt{s_{{}_{NN}}}$}=200$ GeV with the virtual
photon method. This measurement may provide additional information on the
system size dependence of low-$p_{T}$ direct photon production. This paper
focuses on two centrality classes, minimum bias (MB) and 0%–40% most central
collisions, for which the number of participants, $N_{\rm part}$, is similar
to peripheral Au$+$Au ($N_{\rm part}=34.6\pm 1.2$ Adare  _et al._ (2014) and
66.4$\pm$2.5 Adare  _et al._ (2016a)).

##  II The PHENIX detector

Figure 1:  The beam view of the PHENIX detector configuration in 2005.

The two PHENIX central arm spectrometers in conjunction with the beam-beam
counters (BBC) are used for this measurement. Figure 1 shows the beam view of
the PHENIX detector configuration for the 2005 run. The BBCs, with rapidity
coverage $3.1<|\eta|<3.9$, are located at $\pm 144~{}$cm away from the nominal
interaction point. They measure charged particles that are used to determine
the $z$-vertex position, centrality, and the event plane. They provide the MB
event trigger with a trigger efficiency of 94%. The two central arms cover
$|\eta|<0.35$ and an azimuthal angle range of $\pi/2$ per arm. Each arm is
instrumented with a drift chamber (DC) and pad chambers (PCs) that determine
the trajectories and, together with a magnetic field, measure the momenta of
charged particles. The material in front of the DC is minimal, 0.39% of a
radiation length, to allow for a good momentum resolution of $\delta
p/p=1\%\oplus 1.1\%\times p$ [GeV/$c$] above 0.2 GeV/$c$ Adcox  _et al._
(2003), and to minimize the amount of photon conversions. Eight separate
sectors of electromagnetic calorimeters (EMCals) composed of two lead-glass
(PbGl) calorimeters in the bottom sectors of the east arm and six lead-
scintillator (PbSc) calorimeters for the remainder, provide an electromagnetic
shower energy measurement with resolution $\Delta E/E$ of $2.1\%\oplus
8.1\%/\sqrt{E}$ for PbSc and of $0.8\%\oplus 5.9\%/\sqrt{E}$ for PbGl ($E$ in
GeV) Adcox  _et al._ (2003). Requiring energy-momentum matching with an
associated hit in the Ring Imaging Čerenkov counter (RICH) provides a hadron
rejection factor of better than 104, thus providing good electron
identification. The mass resolution for $e^{+}e^{-}$ pairs is determined with
a Monte Carlo simulation which is tuned to match the shape of the
reconstructed $e^{+}e^{-}$ mass distribution in the data below 90 MeV/$c^{2}$
Adare  _et al._ (2015b), where $e^{+}e^{-}$ pairs from $\pi^{0}$ Dalitz decays
are dominant. The calculated $e^{+}e^{-}$ mass resolution is
$\sigma_{ee}=3.1~{}$MeV/$c^{2}$ for $1<\mbox{$p_{T}$}<2~{}$GeV/$c$, and it
increases by about 1 MeV/$c^{2}$ per GeV/$c$ as $p_{T}$ increases.

##  III Analysis

Low-$p_{T}$ direct photons, measured using the virtual photon method, are the
subject of this analysis. Any production process of direct photons has a
higher order process producing a quasi-real virtual photon, which then
produces a low mass, high $p_{T}$ $e^{+}e^{-}$ pair. The relation between the
photon emission ($dN_{\gamma}$) and associate electron pair rates ($dN_{ee}$)
is expressed as:

$\frac{d^{2}N_{ee}}{dm_{ee}}=\frac{2\alpha}{3\pi}\frac{1}{m_{ee}}\sqrt{1-\frac{4m_{e}^{2}}{m_{ee}^{2}}}(1+\frac{2m_{e}^{2}}{m_{ee}^{2}})SdN_{\gamma},$
(1)

where $\alpha,m_{e},m_{ee}$ are the fine structure constant and masses for the
electron and the electron pair. $S$ is introduced to factor out the difference
between real and virtual photon emission. It is a process dependent factor
because it accounts for the effects of form factors, phase space and spectral
functions Adare  _et al._ (2010b). For direct virtual photons satisfying
$\mbox{$p_{T}$}\gg m_{ee}$, $S$ is almost unity, while it drops to 0 as
$m_{ee}$ approaches the parent hadron mass in case of hadron decays. As a
result, $S$ introduces a shape difference of the $e^{+}e^{-}$ mass
distributions for virtual photons and hadron decays. The key idea of this
measurement is to utilize this shape difference. Therefore, the contribution
of the $e^{+}e^{-}$ pairs internally converted via virtual photons is
determined as an excess yield over the known hadronic contributions in the
mass region above the $\pi^{0}$ mass, typically
$0.1<m_{ee}<0.3~{}$GeV/$c^{2}$, by a template fit. The direct photon fraction
at $m_{ee}=0$ is then obtained by extrapolation of the template fit result.
Finally, the obtained direct photon fraction can be converted to the real
direct photon yield using the measured inclusive photon yield. A detailed
description of the virtual photon method can be found in Ref. Adare  _et al._
(2010b).

This measurement is based on a MB sample of $4.95\times 10^{8}$ 200 GeV
Cu$+$Cu collisions with $z$-vertex within $25~{}$cm of the nominal interaction
point collected in 2005, equivalent to 0.44 nb-1. All electrons with
$p^{e}_{T}>0.3~{}$GeV/$c$ are paired in each event. These $e^{+}e^{-}$ pairs
are required to have $\mbox{$p_{T}$}>1~{}$GeV/$c$.

Figure 2:  The $E/p$ distribution for electrons from pairs with $p_{T}$ of 1–2
GeV/$c$ after applying all cuts for electron identification except for $E/p$.

Figure 2 shows the $E/p$ distribution for electrons from pairs with $p_{T}$ of
1–2 GeV/$c$, where $E$ is measured with the EMCal, and $p$ from the track
radius in the magnetic field. All electron identification cuts except for
$E/p$ are applied for this figure. Because hadrons do not deposit their full
energy in the EMCal, hadron contamination produces a tail in the negative
region. This plot indicates the excellent purity of the electron sample. All
electron candidates are required to have $(E/p-1)/\sigma_{E/p}>-2$, resulting
in negligible hadron contamination.

Undesired pairs from several background sources contaminate the foreground
pair distribution. The first source is fake pairs due to accidentally
overlapping hits in various detectors. RICH ring-sharing and cluster overlaps
in the PCs are the main sources for these fake pairs. They can be removed by
geometric analysis cuts Adare  _et al._ (2010b, 2016b). The RICH ring-sharing
cut requires separation of ring centers for the two electrons of a pair to be
greater than 25 cm, which is larger than the expected maximum diameter of a
RICH ring, $\sim 16.8~{}$cm. Tracks are also required to be separated by
$\Delta z>0.5~{}$cm and $\Delta\phi>0.02~{}$rad to remove overlap in the PCs.

The second background source is photon conversions in the detector material.
These can be eliminated because the PHENIX tracking algorithm, which assumes
all tracks come from the collision vertex, introduces an artificial opening
angle of the conversion pairs with the decay plane perpendicular to the
magnetic field.

###  III.1 Background evaluation

After removing the detector-oriented fake pairs and conversions, the
foreground distributions for unlike-sign (FG+-) and like-sign pairs (FG–,
FG++) can be expressed as:

$\displaystyle{\rm FG}_{--}$ $\displaystyle=$ $\displaystyle{\rm BG}^{\rm
CM}_{--}+{\rm BG}^{\rm JT}_{--}+{\rm BG}^{\rm XC}_{--}={\rm BG}^{\rm
SUM}_{--},$ (2) $\displaystyle{\rm FG}_{++}$ $\displaystyle=$
$\displaystyle{\rm BG}^{\rm CM}_{++}+{\rm BG}^{\rm JT}_{++}+{\rm BG}^{\rm
XC}_{++}={\rm BG}^{\rm SUM}_{++},$ (3) $\displaystyle{\rm FG}_{+-}$
$\displaystyle=$ $\displaystyle S+{\rm BG}^{\rm SUM}_{+-}+{\rm HD}_{+-}.$ (4)

Here FG refers to the data and BG refers to backgrounds whose shapes are
calculated as described below, but whose normalization comes from a fit to the
data (FG). $S$ refers to the direct virtual photon signal and HD refers to
correlated pairs from known hadron decays. It is notable that the like-sign
pair distributions are composed of only random combinations (BGCM), jet-
induced correlations (BGJT) and correlated fake pairs from double Dalitz
decays of the $\pi^{0},\eta$ (BGXC). The sum of these backgrounds is referred
to as BGSUM in this paper. Once compositions of these background contributions
are known in the like-sign combination sample, the unlike-sign combination
background, BG${}^{\rm SUM}_{+/-}$, can be determined within the same analysis
framework.

####  III.1.1 Combinatorial background

The combinatorial background can be reproduced by the event mixing technique
with event classification with respect to $z$-vertex position, event plane,
and centrality. However the modulation of the mass distribution by the
elliptic flow, which is apparent in the real events, is not fully introduced
in event mixing because of the limited reaction plane resolution. Thus, pairs
in the mixed events are weighted by a factor based on the measured azimuthal
anisotropy of single electrons Adare  _et al._ (2016b) for given reaction
plane classes. The weighting factor, $w$, depending on the opening angle of a
pair is calculated as:

$w(\Delta\phi)=1+2v_{2}^{a}v_{2}^{b}\cos 2(\Delta\phi),$ (5)

where $\Delta\phi,v_{2}^{a,b}$ are the pair opening angle and azimuthal
anisotropy of each electron in a pair, respectively. The flow modulation makes
at most a few percent difference in the mass shape.

####  III.1.2 Jet-induced correlation

Jet-induced correlations are pairs in which each electron is from a different
parent, but both parents are from the same jet or back-to-back jets. Such
events are simulated by pythia8 Sjostrand  _et al._ ; Sjostrand  _et al._
(2008) with cteq5l Lai  _et al._ (2000) parton distribution functions. The
pythia8-generated events are passed through a geant3 Brun  _et al._ (1987)
based simulation of the PHENIX detector in which all detector effects such as
the acceptance and efficiencies are taken into account. Uncorrelated
combinations are evaluated by the event mixing technique within the simulated
events. It is found that the shape of the like-sign mass distribution for the
uncorrelated combinations is consistent with that for the foreground
combinations in $0.6<m_{ee}<1.1~{}$GeV/$c^{2}$. Here, the true and other
correlated pairs are removed from the foreground distribution before the
comparison. Normalization of the uncorrelated combinations in a specific
region of a pair opening angle, where opening angle distributions for
correlated and uncorrelated pairs are consistent, gives a consistent result. A
detailed description can be found in Ref. Adare  _et al._ (2016b). Finally the
jet-induced correlations are obtained by removing uncorrelated combinations
from the simulated mass distribution.

####  III.1.3 Correlated Dalitz and Double Dalitz Cross Pairs

The other nonnegligible source of correlated background is cross combinations
from decays having two electron pairs in the final state, i.e. $\pi^{0}$ and
$\eta$ double Dalitz decays and Dalitz decays with a subsequent photon
conversion. These cross combinations are localized at the very low mass region
below the $\pi^{0}$ and $\eta$ masses. The mass distributions of these cross
combinations from $\pi^{0}$ and $\eta$ are calculated using the aforementioned
geant3 simulation with the $\pi^{0}$ and $\eta$ distributions measured by
PHENIX.

####  III.1.4 Background Normalization by BGSUM fit

The calculated BG–,++ distributions are the ingredients for a fit to FG–,++,
which then yields the contribution of each component to the background, BGSUM.
Pairs from the same jet and back-to-back jets are separately included in the
fit because they are influenced differently by jet quenching. The BGSUM fit to
FG–,++ works very well. Figure 3 shows the like-sign and unlike-sign mass
distributions of the data together with BGSUM normalized by the BGSUM fit for
$1<\mbox{$p_{T}$}<5~{}$GeV/$c$ where the virtual photon analysis is performed.
The normalized BGSUM is in good agreement with the data for like-sign pairs.
The contribution of the physically correlated pairs ($S+{\rm HD}_{+-}$ in Eq.
4) is significant in the foreground unlike-sign pair mass distribution below
0.3 GeV/$c^{2}$.

Figure 3:  The (a) like-sign and (c) unlike-sign mass distributions of the
data together with BGSUM normalized by the BGSUM fit for
$1<\mbox{$p_{T}$}<5~{}$GeV/$c$. (b) and (d) the ratios of data over BGSUM.

A cross check with the like-sign subtraction method Adare  _et al._ (2017) is
done to demonstrate that the BG${}^{\rm SUM}_{+-}$ properly accounts for all
backgrounds. To infer the background in unlike-sign distributions, a
correction must be made to account for the relative acceptance difference
between like- and unlike-sign pairs. Thus, the acceptance-corrected like-sign
pairs should be expressed as:

${\rm BG}^{\rm SUM}_{+-}=\alpha_{\rm acc}\times({\rm FG}_{--}+{\rm FG}_{++}).$
(6)

The acceptance correction factor, $\alpha_{\rm acc}$, is calculated as the
ratio of like- and unlike-sign pairs from mixed events.

Figure 4:  The background pair distributions of $e^{+}e^{-}$ determined by the
like-sign subtraction method, $\alpha_{\rm
acc}\times($FG${}_{--}+$FG${}_{++})$, (circle symbols) and BGSUM fit method
(solid curves) for (a) $\mbox{$p_{T}$}=$1–2 GeV/$c$ and (b) 2–3 GeV/$c$. The
resulting contributions to BG${}^{\rm SUM}_{+-}$ are also shown by dashed,
dotted, and dashed-dotted curves [see text and legend].

Figure 4 shows the background pair distributions of $e^{+}e^{-}$ determined by
the like-sign subtraction technique and the method used here for $p_{T}$ of
1–2 and 2–3 GeV/$c$, respectively. The two distributions are consistent within
the statistical errors. The present method yields a smaller uncertainty,
particularly at high $p_{T}$. The combinatorial background (dashed [red]
curves) has a much more significant contribution in BGSUM compared to those of
the cross pairs (dotted [blue] curves) and jet-induced correlations (dashed-
dotted [green] curves).

####  III.1.5 Correlated pairs from hadron decays

The last $e^{+}e^{-}$ background source (indicated as $HD_{+-}$) for the
direct virtual photon signal is the known hadron decays. The invariant yields
of $\pi^{0}$ in the 200 GeV Cu$+$Cu as measured by PHENIX Adare  _et al._
(2008a) have been successfully parameterized by a modified Hagedorn fit:

$E\frac{d^{3}\sigma}{dp^{3}}=A(e^{-(ap_{T}+bp_{T}^{2})}+p_{T}/p_{0})^{-n}.$
(7)

The resulting Hagedorn fit parameters for 0%–40% and MB samples are listed in
Table 1.

Table 1: Hagedorn fit parameters for the $\pi^{0}$ distribution in 0%–40% centrality and MB in Cu$+$Cu collisions. Fit parameter | 0%–40% | MB
---|---|---
$A$ [mb GeV${}^{-2}c^{3}$] | (3.5$\pm$2.8)$\times 10^{2}$ | (1.8$\pm$0.6)$\times 10^{2}$
$a$ [(GeV$/c$)-1] | 0.41$\pm$0.22 | 0.42$\pm$0.09
$b$ [(GeV$/c$)-2] | 0.22$\pm$0.16 | 0.20$\pm$0.07
$p_{0}$ [GeV$/c$] | 0.70$\pm$0.09 | 0.69$\pm$0.04
$n$ | 8.02$\pm$0.15 | 8.01$\pm$0.07

Note that the large uncertainty of the absolute scale parameter, $A$, does not
affect the direct photon result because only the shape enters in determining
the direct photon fraction. A detailed description of this analysis appears in
the next section, Sec. III.2. $m_{T}$-scaling of the parameterized $\pi^{0}$
yield has been shown to accurately reproduce the invariant yields of other
known hadrons Adare  _et al._ (2014). All known hadron decays producing
$e^{+}e^{-}$ are simulated with this parameterization by a Monte Carlo event
generator within the PHENIX framework Adare  _et al._ (2010b) and passed
through the PHENIX geant3 simulation. The simulated $e^{+}e^{-}$ pair mass
distributions for known hadrons are merged as a “cocktail” of the hadron decay
contributions. The particle compositions in the hadronic cocktail are based on
the measured yields. The particle ratios to the $\pi^{0}$ yield are identical
to the $p$$+$$p$ data Adler  _et al._ (2006).

An additional source of decay background is $e^{+}e^{-}$ pairs from open heavy
flavor decays. They hide behind the cocktail of photonic decays discussed
previously in the mass region of interest below $m_{ee}$=0.3 GeV/$c^{2}$.
Their contribution becomes significant only around 0.6 GeV/$c^{2}$, and then
dominant in the high mass region above 1 GeV/$c^{2}$ because of their large
opening angle. Their low mass contribution can be extrapolated using a model
fit to the data in the high mass region Adare  _et al._ (2017). PHENIX has
reported that the low mass distribution has a model dependence Adare  _et al._
(2016b). This model dependence results in a 100% uncertainty particularly on
the $c\bar{c}$ contribution. The open heavy flavor contribution is evaluated
by binary-scaling of the $d$$+$Au result Adare  _et al._ (2017). However, the
$c\bar{c}$ contribution is less than 0.1% at most in the mass region of
interest, $0.3~{}$GeV/$c^{2}$, even if 100% uncertainty from the model
dependence is taken into account.

###  III.2 Determination of direct photon fraction

The direct virtual photon signal is now extracted as the remainder of the
signal above the backgrounds described in the previous section, Sec. III.1. A
similar fitting procedure to the one described in Ref. Adare  _et al._ (2010a)
is employed, in which Eq. 8 is fit to the mass distribution, with the
following difference. In the previous analysis only the hadronic cocktail was
included in the fit. In the present measurement, the open heavy flavor and
BGSUM contributions, which were subtracted before the fit in the previous
measurements, are now included together with the hadronic cocktail as fixed
contributions in the fit as Eq. 8. This is done in order for a log-likelihood
fit to work properly even with limited statistics in the data, especially at
higher $p_{T}$.

$f(m_{ee})=(1-r_{\gamma})f_{c}(m_{ee})+r_{\gamma}f_{\rm dir}(m_{ee})+f_{\rm
BG}(m_{ee}),$ (8)

where $r_{\gamma}$ is the only fit parameter and $f_{c},f_{\rm BG}$ are the
hadronic cocktail and the fixed contribution of a sum of the open heavy flavor
and BGSUM pairs, respectively. The expected mass shape of the direct virtual
photons, $f_{\rm dir}$, is calculated by a Monte Carlo simulation based on Eq.
1. It does not show the drop that appears in the mass shapes of $e^{+}e^{-}$
pairs from $\pi^{0},\eta$ Dalitz decays because of $S\sim 1$ in Eq. 1. $f_{\rm
dir},f_{c}$ are normalized for $m_{ee}<0.03~{}$GeV/$c^{2}$ before the fit to
ensure the fit result matches the data at $m_{ee}=0$, where $f_{\rm
dir},f_{c}$ are identical. Finally a log-likelihood fit is performed within a
fit range of $0.1<m_{ee}<0.3~{}$GeV/$c^{2}$ to determine the direct virtual
photon fraction for several $p_{T}$ bins separately
[$1<p_{T}<1.5,1.5<p_{T}<2.0,2.0<p_{T}<3.0,3.0<p_{T}<5.0$ GeV/$c$].

Figure 5:  The $e^{+}e^{-}$ pair mass distribution in Cu$+$Cu MB collisions
for $1.5<\mbox{$p_{T}$}<2.0$ GeV$/c$. (a) The data (closed [black] circles),
fit to the data $(1-r_{\gamma})f_{c}+r_{\gamma}f_{\rm dir}+f_{\rm BG}$ (thick
[red] curve), hadronic contribution (thin [blue] curve), and BG${}^{\rm
SUM}_{+-}$ (shaded [red] region). (b) The data after BG${}^{\rm SUM}_{+-}$
subtraction (closed [black] circles), the fit (thick [red] curve), hadronic
contribution (thin [blue] curve), and cocktail components (indicated curves
[see legend]).

Figure 5 shows the $e^{+}e^{-}$ pair mass distributions in Cu$+$Cu MB
collisions for $1.5<\mbox{$p_{T}$}<2.0$ GeV$/c$. Figure 5a shows the data, the
fit, the hadronic contribution, and the background BG${}^{\rm SUM}_{+-}$.
Figure 5b shows the data and fit after BG${}^{\rm SUM}_{+-}$ subtraction, the
hadronic contribution, and cocktail components.

###  III.3 Systematic uncertainties

The major sources of systematic uncertainties of the direct photon fraction
are:

  1. 1.

the background normalization,

  2. 2.

the particle composition of the hadronic cocktail,

  3. 3.

the $e^{+}e^{-}$ mass range for the log-likelihood fit.

To evaluate the uncertainty of the direct photon fraction, the fraction is
recalculated by the same procedure varying each source within $\pm 1\sigma$ of
its uncertainty. The differences from the nominal value are quantified and
taken as contributions to the uncertainty of the direct photon fraction. An
uncertainty of about 15%–40% comes from the fit mass range with different fit
starting points from 0 to 0.15 GeV/$c^{2}$. The particle compositions,
dominantly $\pi^{0}/\eta$ add another 5%–15%. An additional 9.6% and 10%
uncertainties are introduced from the MB trigger efficiency and $e^{+}e^{-}$
pair acceptance when converting the direct photon fraction to the yield. Total
systematic uncertainties are calculated as a quadratic sum.

Figure 6:  Direct photon fraction measured with the virtual photon method for
different systems in $\mbox{$\sqrt{s_{{}_{NN}}}$}=200~{}$GeV collisions: (a)
$p$$+$$p$ Adare  _et al._ (2013), (b) $d$$+$Au (MB) Adare  _et al._ (2013),
(c) Cu$+$Cu (MB), (d) Au$+$Au (MB) Adare  _et al._ (2010a). Expectations from
NLO pQCD calculations Gordon and Vogelsang (1993) are also shown by curves
with different cutoff mass scales, $\mu$.

##  IV Results and Discussion

Figure 7:  The direct photon spectra (closed [black] circles) for 200 GeV Cu$+$Cu (a) MB and (b) 0%–40% centralities. The $T_{\rm AA}$-scaled $p$$+$$p$ data and fits together with uncertainties are shown as the open [red] circles symbols and the dotted [blue] curves and accompanying [red] boxes and [blue] bands. Au$+$Au 40%–60% centrality data points, which have a similar $N_{\rm part}$ as the Cu$+$Cu 0%-40% centrality data, are shown as the open [black] squares, where the Au$+$Au points are scaled by the $N_{\rm part}$ ratio (66.4/56.0). An exponential fit to the Cu$+$Cu data of the excess yield over the scaled $p$$+$$p$ fit (solid [red] curve) yields inverse slopes of 285$\pm$53(stat)$\pm$57(syst) MeV/$c$ for MB and 333$\pm$72(stat)$\pm$45(syst) MeV/$c$ for 0%–40%.  Table 2: $dN_{\rm ch}/d\eta$, $N_{\rm coll}$, $N_{\rm part}$, the inverse slope of the exponential fits, and $dN/dy(\mbox{$p_{T}$}>1~{}$GeV$/c)$ of the excess yield of direct photons over the scaled $p$$+$$p$ fits for 0%–40% and MB Cu$+$Cu collisions. Centrality | $dN_{\rm ch}/d\eta$ | $N_{\rm coll}$ | $N_{\rm part}$ | Inverse slope (MeV/$c$) |  $dN/dy(\mbox{$p_{T}$}>1~{}$GeV$/c)$
---|---|---|---|---|---
0%–40% | 109.3$\pm$7.8 | 108.2$\pm$12.0 | 66.4$\pm$2.5 | 333$\pm$72$\pm$45 | (1.3$\pm$0.5${}^{+0.9}_{-0.8})\times 10^{-1}$
MB | 51.7$\pm$3.6 | 51.8$\pm$5.6 | 34.6$\pm$1.2 | 285$\pm$53$\pm$57 | (5.4$\pm$1.9${}^{+3.6}_{-3.1})\times 10^{-2}$

###  IV.1 Direct-photon fraction

The direct photon fraction as a function of $p_{T}$ is obtained for two
different centrality classes, MB and 0%–40%. Figure 6 shows the comparison of
the direct photon fraction, $r_{\gamma}$, measured with the virtual photon
method for different collision systems at
$\mbox{$\sqrt{s_{{}_{NN}}}$}=200~{}$GeV from left to right: $p$$+$$p$ Adare
_et al._ (2013), $d$$+$Au (MB) Adare  _et al._ (2013), Cu$+$Cu (MB), and
Au$+$Au (MB) Adare  _et al._ (2010a).

The statistical and systematic uncertainties are shown together with the data
points. Curves indicate the expectations from a next-to-leading-order (NLO)
perturbative-quantum-chromodynamics (pQCD) calculation Gordon and Vogelsang
(1993) with different cutoff mass scales, $\mu$. While the $p$$+$$p$ and
$d$$+$Au results show agreements with the NLO pQCD calculation, an excess over
the NLO pQCD calculation is seen in the Cu$+$Cu data as well as in Au$+$Au.
The Cu$+$Cu excess is rather modest compared to Au$+$Au, possibly due to a
smaller volume of the created medium.

###  IV.2 Direct photon spectra

The obtained direct photon fractions are converted to direct photon yields
using the inclusive photon yields calculated by the same Monte Carlo
simulation used for the $e^{+}e^{-}$ pairs of the hadronic cocktail. Figure 7
shows the direct photon spectra for Cu$+$Cu MB and 0%–40% most central events.
The $p$$+$$p$ results Adare  _et al._ (2013) parameterized by a modified power
law function, $A_{pp}(1+\mbox{$p_{T}$}^{2}/B_{pp})^{n_{pp}}$, and its $T_{\rm
AA}$-scaled functions are shown as the dotted curves together with the data
points. The modified power law is an empirical parameterization describing the
$p$$+$$p$ result well, especially at low $p_{T}$. The same function has been
employed in previous low $p_{T}$ direct photon publications in heavy ion
collisions Adare  _et al._ (2010a, 2015a). We have performed a least square
analysis in which $p_{T}$-correlated and $p_{T}$-uncorrelated errors are
properly taken into account. A detail description on constraint
parameterization can be found in Ref. Adare  _et al._ (2008b). The $p$$+$$p$
data points measured by the EMCal in $4<\mbox{$p_{T}$}<10~{}$GeV/$c$ are
included in the fit in addition to the virtual photon measurement covering
$\mbox{$p_{T}$}<$ 6 GeV/$c$. Here the lowest $p_{T}$ data point is just an
upper limit. The best fit gives ${\chi}^{2}$/NDF=18.9/17, which is the minimum
obtained by variation of the $p_{T}$-correlated errors. The uncertainty of the
$p$$+$$p$ fit is calculated using the error matrix of the fit parameters and
is indicated as bands on the scaled $p$$+$$p$ fits. A different empirical
parameterization, employed in Ref. Adare  _et al._ (2013), was tested as well.
We treat the small deviation we find above 1 GeV/$c$ as a maximum-extend
error. We divide the deviation by $\sqrt{12}$ and add it in quadrature to the
uncertainty of the fit.

An exponential fit to the excess yield above the scaled $p$$+$$p$ fits gives
inverse slopes of 285$\pm$53(stat)$\pm$57(syst) MeV/$c$ for MB and
333$\pm$72(stat)$\pm$45(syst) MeV/$c$ for 0%–40% centrality. Furthermore, the
Cu$+$Cu 0%–40% centrality result is compared with the Au$+$Au 40%–60% data
scaled by the $N_{\rm part}$ ratio (66.4/56.0), which is consistent within
uncertainties [see Fig. 7(b)].

###  IV.3 Rapidity density

We further investigate the $N_{\rm part}$ dependence of the direct photon
yields as discussed in Ref. Adare  _et al._ (2015a). It has been reported that
the Au$+$Au results Adare  _et al._ show an increasing trend for $N_{\rm
part}$. The Cu$+$Cu data points help to have a closer look at the dependence
in the small $N_{\rm part}$ region. The rapidity density for
$\mbox{$p_{T}$}>1~{}$GeV/$c$ at midrapidity,
$dN/dy(\mbox{$p_{T}$}>1~{}$GeV$/c)$, is calculated by summing the direct
photon yields in given $p_{T}$ bins taking the bin-width correction into
account:

$\displaystyle\frac{dN}{dy}$ $\displaystyle=$ $\displaystyle
2\pi\sum_{\mbox{$p_{T}$}^{i}>1\rm{GeV}/c}(\mbox{$p_{T}$}^{i}\times
y_{\gamma}^{i}\times C_{bw}^{i}\times\Delta\mbox{$p_{T}$}^{i}),$ (9)
$\displaystyle C_{bw}^{i}$ $\displaystyle=$
$\displaystyle\int_{p_{T,min}}^{p_{T,max}}f_{fit}(\mbox{$p_{T}$})d\mbox{$p_{T}$}/(f_{fit}(\mbox{$p_{T}$}^{i})\times\Delta\mbox{$p_{T}$}^{i}),$
(10)

where $\mbox{$p_{T}$}^{i},y_{\gamma}^{i},\Delta\mbox{$p_{T}$}^{i}$ are the
mean $p_{T}$, the direct photon yield and the $p_{T}$-bin width for the $i$-th
$p_{T}$ bin. The bin-width correction, $C_{bw}$, is evaluated based on the fit
function, $f_{fit}$, to the data shown in Fig. 7. $C_{bw}$ contributes an
additional 3.5% uncertainty of $dN/dy$. Then, $dN/dy$ for the binary-scaled
$p$$+$$p$ fit Adare  _et al._ is subtracted. Figure 8 shows $dN/dy$ of the
excess yield over the scaled $p$$+$$p$ fit as a function of measured charged
multiplicity, $dN_{\rm ch}/d\eta$, at midrapidity. A simple power law fit with
the fixed power of 1.25, $(dN_{\rm ch}/d\eta)^{1.25}$, is done for both the
Cu$+$Cu and Au$+$Au results as done in Ref. Adare  _et al._ . It works very
well to describe the $dN_{\rm ch}/d\eta$ dependence.

Figure 8:  Rapidity densities of the excess yield of direct photons over the
scaled $p$$+$$p$ fits for $p_{T}>1~{}$GeV/$c$ at midrapidity as a function of
$dN_{\rm ch}/d\eta$. The Au$+$Au data points with different centralities Adare
_et al._ (2015a) and the power-law fit with the fixed power of 1.25 to both
Cu$+$Cu and Au$+$Au data points are shown together.

The inverse slope of the exponential fits and the rapidity density of the
excess yield of direct photons over the scaled $p$$+$$p$ fits for
$p_{T}>1~{}$GeV/$c$ are summarized together with $dN_{\rm ch}/d\eta$, $N_{\rm
coll}$, $N_{\rm part}$ corresponding to 0%–40%, MB Cu$+$Cu collisions in Table
2.

##  V Summary and Conclusions

Low-$p_{T}$ direct photons have been measured using the virtual photon method
for MB and 0%–40% most central collisions in $\mbox{$\sqrt{s_{{}_{NN}}}$}=200$
GeV Cu$+$Cu collisions. A clear excess yield of direct photons over the
binary-scaled $p$$+$$p$ baseline is seen for Cu$+$Cu as in the previously
reported Au$+$Au results. The Cu$+$Cu direct photon $p_{T}$ spectra are
consistent with the Au$+$Au data for similar $N_{\rm part}$. The exponential
fits to the excess over the binary-scaled $p$$+$$p$ baseline give inverse
slopes of 285$\pm$53(stat)$\pm$57(syst) MeV/$c$ for MB and
333$\pm$72(stat)$\pm$45(syst) MeV/$c$ for 0%–40% centrality. The Cu$+$Cu data
points improve our knowledge of the system size dependence of the excess yield
of the direct photons, especially in the small-$N_{\rm part}$ region. The
Cu$+$Cu results on $dN/dy$ for $\mbox{$p_{T}$}>1~{}$GeV/$c$ follow the same
$dN_{\rm ch}/d\eta$ dependence as the Au$+$Au data as described by a simple
power law.

###### Acknowledgements.

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 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), Croatian Science
Foundation and Ministry of Science and Education (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), J. Bolyai Research Scholarship,
EFOP, the New National Excellence Program (ÚNKP), NKFIH, and OTKA (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, the US-Hungarian Fulbright
Foundation, and the US-Israel Binational Science Foundation.

## References

  * Adcox  _et al._ (2005) K. Adcox _et al._ (PHENIX Collaboration), “Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX Collaboration,” Nucl. Phys. A 757, 184 (2005).
  * Adams  _et al._ (2005) John Adams _et al._ (STAR Collaboration), “Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions,” Nucl. Phys. A 757, 102 (2005).
  * David  _et al._ (2008) G. David, R. Rapp, and Z. Xu, “Electromagnetic Probes at RHIC-II,” Phys. Rept. 462, 176 (2008).
  * Stankus (2005) P. Stankus, “Direct photon production in relativistic heavy-ion collisions,” Ann. Rev. Nucl. Part. Sci. 55, 517 (2005).
  * Turbide  _et al._ (2004) S. Turbide, R. Rapp, and C. Gale, “Hadronic production of thermal photons,” Phys. Rev. C 69, 014903 (2004).
  * Adare  _et al._ (2010a) A. Adare _et al._ (PHENIX Collaboration), “Enhanced production of direct photons in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and implications for the initial temperature,” Phys. Rev. Lett. 104, 132301 (2010a).
  * Adare  _et al._ (2015a) A. Adare _et al._ (PHENIX Collaboration), “Centrality dependence of low-momentum direct-photon production in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV,” Phys. Rev. C 91, 064904 (2015a).
  * Adamczyk  _et al._ (2017) L. Adamczyk _et al._ (STAR Collaboration), “Direct virtual photon production in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Lett. B 770, 451 (2017).
  * Adare  _et al._ (2013) A. Adare _et al._ (PHENIX Collaboration), “Direct photon production in $d+$Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C 87, 054907 (2013).
  * Adam  _et al._ (2016) J. Adam _et al._ (ALICE Collaboration), “Direct photon production in Pb$-$Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV,” Phys. Lett. B 754, 235 (2016).
  * Adare  _et al._ (2014) A. Adare _et al._ (PHENIX Collaboration), “System-size dependence of open-heavy-flavor production in nucleus-nucleus collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV,” Phys. Rev. C 90, 034903 (2014).
  * Adare  _et al._ (2016a) A. Adare _et al._ (PHENIX Collaboration), “Transverse energy production and charged-particle multiplicity at midrapidity in various systems from $\sqrt{s_{NN}}=7.7$ to 200 GeV,” Phys. Rev. C 93, 024901 (2016a).
  * Adcox  _et al._ (2003) K. Adcox _et al._ (PHENIX Collaboration), “PHENIX detector overview,” Nucl. Instrum. Methods Phys. Res., Sec. A 499, 469 (2003).
  * Adare  _et al._ (2015b) A. Adare _et al._ (PHENIX Collaboration), “Search for dark photons from neutral meson decays in $p$$+$$p$ and $d$$+$Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C 91, 031901 (2015b).
  * Adare  _et al._ (2010b) A. Adare _et al._ (PHENIX Collaboration), “Detailed measurement of the $e^{+}e^{-}$ pair continuum in $p+p$ and Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and implications for direct photon production,” Phys. Rev. C 81, 034911 (2010b).
  * Adare  _et al._ (2016b) A. Adare _et al._ (PHENIX Collaboration), “Dielectron production in Au$+$Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C 93, 014904 (2016b).
  * (17) T. Sjostrand, S. Mrenna, and P. Z. Skands, “PYTHIA 6.4 Physics and Manual,” J. High Energy Phys. 05 (2006) 026\.
  * Sjostrand  _et al._ (2008) T. Sjostrand, S. Mrenna, and P. Z. Skands, “A Brief Introduction to PYTHIA 8.1,” Comput. Phys. Commun. 178, 852 (2008).
  * Lai  _et al._ (2000) H. L. Lai, J. Huston, S. Kuhlmann, J. Morfin, Fredrick I. Olness, J. F. Owens, J. Pumplin, and W. K. Tung (CTEQ Collaboration), “Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions,” Eur. Phys. J. C 12, 375 (2000).
  * Brun  _et al._ (1987) R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini, “geant3,” (1987).
  * Adare  _et al._ (2017) A. Adare _et al._ (PHENIX Collaboration), “Measurements of $e^{+}e^{-}$ pairs from open heavy flavor in $p$$+$$p$ and $d$$+$$A$ collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C 96, 024907 (2017).
  * Adare  _et al._ (2008a) A. Adare _et al._ (PHENIX Collaboration), “Onset of pi0 Suppression Studied in Cu+Cu Collisions at $\sqrt{s_{NN}}=22.4$, 62.4, and 200 GeV,” Phys. Rev. Lett. 101, 162301 (2008a).
  * Adler  _et al._ (2006) S. S. Adler _et al._ (PHENIX Collaboration), “Common suppression pattern of eta and pi0 mesons at high transverse momentum in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. Lett. 96, 202301 (2006).
  * Gordon and Vogelsang (1993) L. E. Gordon and W. Vogelsang, “Polarized and unpolarized prompt photon production beyond the leading order,” Phys. Rev. D 48, 3136 (1993).
  * Adare  _et al._ (2008b) A. Adare _et al._ (PHENIX Collaboration), “Quantitative Constraints on the Opacity of Hot Partonic Matter from Semi-Inclusive Single High Transverse Momentum Pion Suppression in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C 77, 064907 (2008b).
  * (26) A. Adare _et al._ (PHENIX Collaboration), “Beam energy and centrality dependence of direct-photon emission from ultra-relativistic heavy ion collisions,” arXiv:1805.04084.