PHENIX Collaboration

# Kinematic dependence of azimuthal anisotropies in $p$$+$Au, $d$$+$Au, 3He+Au
at $\sqrt{s_{{}_{NN}}}$ = 200 GeV

U.A. Acharya  Georgia State University, Atlanta, Georgia 30303, USA  A. Adare
University of Colorado, Boulder, Colorado 80309, USA  C. Aidala  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  M. Alfred  Department of Physics and Astronomy, Howard
University, Washington, DC 20059, USA  V. Andrieux  Department of Physics,
University of Michigan, Ann Arbor, Michigan 48109-1040, USA  K. Aoki  KEK,
High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801,
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  H. Asano  Kyoto University, Kyoto 606-8502,
Japan  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, Japan  C. Ayuso  Department of Physics, University of Michigan, Ann
Arbor, Michigan 48109-1040, 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
N.S. Bandara  Department of Physics, University of Massachusetts, Amherst,
Massachusetts 01003-9337, 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  S. Bathe  Baruch College, City University of New York, New York, New
York, 10010 USA  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  A. Bazilevsky  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  M. Beaumier  University
of California-Riverside, Riverside, California 92521, USA  S. Beckman
University of Colorado, Boulder, Colorado 80309, USA  R. Belmont  University
of Colorado, Boulder, Colorado 80309, USA  Department of Physics, University
of Michigan, Ann Arbor, Michigan 48109-1040, USA  Physics and Astronomy
Department, University of North Carolina at Greensboro, Greensboro, North
Carolina 27412, USA  A. Berdnikov  Saint Petersburg State Polytechnic
University, St. Petersburg, 195251 Russia  Y. Berdnikov  Saint Petersburg
State Polytechnic University, St. Petersburg, 195251 Russia  L. Bichon
Vanderbilt University, Nashville, Tennessee 37235, USA  B. Blankenship
Vanderbilt University, Nashville, Tennessee 37235, USA  D.S. Blau  National
Research Center “Kurchatov Institute”, Moscow, 123098 Russia  National
Research Nuclear University, MEPhI, Moscow Engineering Physics Institute,
Moscow, 115409, Russia  M. Boer  Los Alamos National Laboratory, Los Alamos,
New Mexico 87545, USA  J.S. Bok  New Mexico State University, Las Cruces, New
Mexico 88003, USA  V. Borisov  Saint Petersburg State Polytechnic University,
St. Petersburg, 195251 Russia  K. Boyle  RIKEN BNL Research Center, Brookhaven
National Laboratory, Upton, New York 11973-5000, 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
University of California-Riverside, Riverside, California 92521, USA  V.
Bumazhnov  IHEP Protvino, State Research Center of Russian Federation,
Institute for High Energy Physics, Protvino, 142281, Russia  C. Butler
Georgia State University, Atlanta, Georgia 30303, USA  S. Campbell  Columbia
University, New York, New York 10027 and Nevis Laboratories, Irvington, New
York 10533, USA  Iowa State University, Ames, Iowa 50011, USA  V. Canoa Roman
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  R. Cervantes  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  M. Chiu  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  C.Y. Chi  Columbia University,
New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533,
USA  I.J. Choi  University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA  J.B. Choi  Deceased  Jeonbuk National University, Jeonju, 54896,
Korea  T. Chujo  Tomonaga Center for the History of the Universe, University
of Tsukuba, Tsukuba, Ibaraki 305, Japan  Z. Citron  Weizmann Institute,
Rehovot 76100, Israel  M. Connors  Georgia State University, Atlanta, Georgia
30303, USA  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton,
New York 11973-5000, USA  R. Corliss  Department of Physics and Astronomy,
Stony Brook University, SUNY, Stony Brook, New York 11794-3800, 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  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
M. Csanád  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A,
Hungary  L. D. Liu  Peking University, Beijing 100871, People’s Republic of
China  T.W. Danley  Department of Physics and Astronomy, Ohio University,
Athens, Ohio 45701, USA  A. Datta  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  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
K. DeBlasio  University of New Mexico, Albuquerque, New Mexico 87131, USA  K.
Dehmelt  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  A. Dion  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  P.B. Diss
University of Maryland, College Park, Maryland 20742, USA  D. Dixit
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  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  M. Dumancic  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  T. Elder  Georgia State
University, Atlanta, Georgia 30303, USA  H. En’yo  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  A. Enokizono  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  R. Esha  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  S. Esumi  Tomonaga
Center for the History of the Universe, University of Tsukuba, Tsukuba,
Ibaraki 305, Japan  B. Fadem  Muhlenberg College, Allentown, Pennsylvania
18104-5586, 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  M. Finger, Jr  Charles University, Ovocný trh 5, Praha 1,
116 36, Prague, Czech Republic  M. Finger  Charles University, Ovocný trh 5,
Praha 1, 116 36, Prague, Czech Republic  D. Fitzgerald  Department of Physics,
University of Michigan, Ann Arbor, Michigan 48109-1040, USA  S.L. Fokin
National Research Center “Kurchatov Institute”, Moscow, 123098 Russia  J.E.
Frantz  Department of Physics and Astronomy, Ohio University, Athens, Ohio
45701, USA  A. Franz  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  A.D. Frawley  Florida State University,
Tallahassee, Florida 32306, USA  Y. Fukuda  Tomonaga Center for the History of
the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  P. Gallus
Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic  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  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  H. Ge
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  M. Giles  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
F. Giordano  University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA  A. Glenn  Lawrence Livermore National Laboratory, Livermore,
California 94550, USA  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  N. Grau  Department of
Physics, Augustana University, Sioux Falls, South Dakota 57197, USA  S.V.
Greene  Vanderbilt University, Nashville, Tennessee 37235, USA  M. Grosse
Perdekamp  University of Illinois at Urbana-Champaign, Urbana, Illinois 61801,
USA  T. Gunji  Center for Nuclear Study, Graduate School of Science,
University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  H. Guragain
Georgia State University, Atlanta, Georgia 30303, USA  T. Hachiya  Nara
Women’s University, Kita-uoya Nishi-machi Nara 630-8506, 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  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  H.F. Hamilton
Abilene Christian University, Abilene, Texas 79699, USA  J. Hanks  Department
of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  S.Y. Han  Ewha Womans University, Seoul 120-750, Korea  Korea
University, Seoul 02841, Korea  M. Harvey  Texas Southern University, Houston,
TX 77004, USA  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  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  T.K. Hemmick  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  X. He  Georgia State University, Atlanta, Georgia 30303, USA
J.C. Hill  Iowa State University, Ames, Iowa 50011, USA  K. Hill  University
of Colorado, Boulder, Colorado 80309, USA  A. Hodges  Georgia State
University, Atlanta, Georgia 30303, USA  R.S. Hollis  University of
California-Riverside, Riverside, California 92521, USA  K. Homma  Hiroshima
University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  B. Hong  Korea
University, Seoul 02841, Korea  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  K. Imai  Advanced Science Research Center,
Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun,
Ibaraki-ken 319-1195, Japan  J. Imrek  Debrecen University, H-4010 Debrecen,
Egyetem tér 1, Hungary  M. Inaba  Tomonaga Center for the History of the
Universe, 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  Y. Ito
Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan  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. Jezghani
Georgia State University, Atlanta, Georgia 30303, USA  X. Jiang  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  Z. Ji  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  B.M. Johnson  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  Georgia State University,
Atlanta, Georgia 30303, USA  V. Jorjadze  Department of Physics and Astronomy,
Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA  D. Jouan
IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406,
Orsay, France  D.S. Jumper  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  S. Kanda  Center for Nuclear Study, Graduate
School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033,
Japan  J.H. Kang  Yonsei University, IPAP, Seoul 120-749, Korea  D. Kapukchyan
University of California-Riverside, Riverside, California 92521, USA  S.
Karthas  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  D. Kawall  Department of Physics,
University of Massachusetts, Amherst, Massachusetts 01003-9337, USA  A.V.
Kazantsev  National Research Center “Kurchatov Institute”, Moscow, 123098
Russia  J.A. Key  University of New Mexico, Albuquerque, New Mexico 87131, USA
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  A.
Khatiwada  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
B. Kimelman  Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA  C.
Kim  University of California-Riverside, Riverside, California 92521, USA
Korea University, Seoul 02841, Korea  D.J. Kim  Helsinki Institute of Physics
and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland  E.-J.
Kim  Jeonbuk National University, Jeonju, 54896, Korea  G.W. Kim  Ewha Womans
University, Seoul 120-750, Korea  M. Kim  Department of Physics and Astronomy,
Seoul National University, Seoul 151-742, Korea  M.H. Kim  Korea University,
Seoul 02841, Korea  D. Kincses  ELTE, Eötvös Loránd University, H-1117
Budapest, Pázmány P. s. 1/A, Hungary  A. Kingan  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
E. Kistenev  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  R. Kitamura  Center for Nuclear Study, Graduate School
of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
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  T. Koblesky  University of Colorado,
Boulder, Colorado 80309, USA  B. Komkov  PNPI, Petersburg Nuclear Physics
Institute, Gatchina, Leningrad region, 188300, Russia  D. Kotov  PNPI,
Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300,
Russia  Saint Petersburg State Polytechnic University, St. Petersburg, 195251
Russia  L. Kovacs  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P.
s. 1/A, Hungary  S. Kudo  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  B. Kurgyis  ELTE, Eötvös
Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  K. Kurita
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  J.G. Lajoie  Iowa State University,
Ames, Iowa 50011, USA  E.O. Lallow  Muhlenberg College, Allentown,
Pennsylvania 18104-5586, USA  D. Larionova  Saint Petersburg State Polytechnic
University, St. Petersburg, 195251 Russia  A. Lebedev  Iowa State University,
Ames, Iowa 50011, USA  S. Lee  Yonsei University, IPAP, Seoul 120-749, Korea
S.H. Lee  Iowa State University, Ames, Iowa 50011, USA  Department of Physics,
University of Michigan, Ann Arbor, Michigan 48109-1040, USA  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  M.J. Leitch  Los Alamos National Laboratory, Los Alamos, New
Mexico 87545, USA  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  S.H. Lim  Los Alamos National Laboratory, Los Alamos, New Mexico 87545,
USA  Pusan National University, Pusan 46241, Korea  Yonsei University, IPAP,
Seoul 120-749, Korea  M.X. Liu  Los Alamos National Laboratory, Los Alamos,
New Mexico 87545, 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  V.-R. Loggins  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  S. Lökös  ELTE, Eötvös Loránd University, H-1117
Budapest, Pázmány P. s. 1/A, Hungary  D.A. Loomis  Department of Physics,
University of Michigan, Ann Arbor, Michigan 48109-1040, USA  K. Lovasz
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  D. Lynch
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, 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  M. Makek  Department of Physics,
Faculty of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb,
Croatia  M. Malaev  PNPI, Petersburg Nuclear Physics Institute, Gatchina,
Leningrad region, 188300, Russia  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  H. Masuda  Physics Department, Rikkyo University,
3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan  M. McCumber  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, 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  C. McKinney
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  A.
Meles  New Mexico State University, Las Cruces, New Mexico 88003, USA  M.
Mendoza  University of California-Riverside, Riverside, California 92521, USA
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  A. Milov  Weizmann Institute, Rehovot
76100, Israel  D.K. Mishra  Bhabha Atomic Research Centre, Bombay 400 085,
India  J.T. Mitchell  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  M. Mitrankova  Saint Petersburg State
Polytechnic University, St. Petersburg, 195251 Russia  Iu. Mitrankov  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  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  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  S. Mizuno  RIKEN Nishina Center for Accelerator-Based Science, Wako,
Saitama 351-0198, Japan  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A.K. Mohanty  Bhabha
Atomic Research Centre, Bombay 400 085, India  M.M. Mondal  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  P. Montuenga  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  T. Moon  Korea University, Seoul 02841, Korea
Yonsei University, IPAP, Seoul 120-749, Korea  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  B. Mulilo  Korea University, Seoul 02841, Korea  RIKEN Nishina Center
for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  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  K. Nagai  Department of Physics, Tokyo
Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan  K.
Nagashima  Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
T. Nagashima  Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro,
Toshima, Tokyo 171-8501, Japan  J.L. Nagle  University of Colorado, Boulder,
Colorado 80309, USA  M.I. Nagy  ELTE, Eötvös Loránd University, H-1117
Budapest, Pázmány P. s. 1/A, 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  H.
Nakagomi  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, Japan  Tomonaga Center for the History of the Universe, University
of Tsukuba, Tsukuba, Ibaraki 305, 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
S. Nelson  Florida A&M University, Tallahassee, FL 32307, USA  P.K. Netrakanti
Bhabha Atomic Research Centre, Bombay 400 085, India  T. Niida  Tomonaga
Center for the History of the Universe, University of Tsukuba, Tsukuba,
Ibaraki 305, Japan  S. Nishimura  Center for Nuclear Study, Graduate School of
Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, 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  T. Novák  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  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  Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  R. Novotny  Czech Technical University, Zikova 4,
166 36 Prague 6, Czech Republic  G. Nukazuka  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.S.
Nyanin  National Research Center “Kurchatov Institute”, Moscow, 123098 Russia
E. O’Brien  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  C.A. Ogilvie  Iowa State University, Ames, Iowa 50011,
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  Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831, USA  A. Oskarsson  Department of Physics, Lund University, Box 118,
SE-221 00 Lund, Sweden  G.J. Ottino  University of New Mexico, Albuquerque,
New Mexico 87131, USA  K. Ozawa  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  V. Pantuev  Institute for Nuclear Research of the Russian
Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia
V. Papavassiliou  New Mexico State University, Las Cruces, New Mexico 88003,
USA  J.S. 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  M. Patel  Iowa State University, Ames, Iowa
50011, USA  S.F. Pate  New Mexico State University, Las Cruces, New Mexico
88003, USA  J.-C. Peng  University of Illinois at Urbana-Champaign, Urbana,
Illinois 61801, USA  W. Peng  Vanderbilt University, Nashville, Tennessee
37235, USA  D.V. Perepelitsa  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  University of Colorado, Boulder,
Colorado 80309, USA  G.D.N. Perera  New Mexico State University, Las Cruces,
New Mexico 88003, USA  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
J. Perry  Iowa State University, Ames, Iowa 50011, USA  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  M. Phipps  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  University of Illinois
at Urbana-Champaign, Urbana, Illinois 61801, USA  C. Pinkenburg  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
R. Pinson  Abilene Christian University, Abilene, Texas 79699, USA  R.P.
Pisani  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  M. Potekhin  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  A. Pun  Department of Physics and
Astronomy, Ohio University, Athens, Ohio 45701, USA  M.L. Purschke  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, 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  N. Ramasubramanian
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  B.J. Ramson  Department of Physics,
University of Michigan, Ann Arbor, Michigan 48109-1040, USA  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  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  D.
Richford  Baruch College, City University of New York, New York, New York,
10010 USA  T. Rinn  University of Illinois at Urbana-Champaign, Urbana,
Illinois 61801, USA  Iowa State University, Ames, Iowa 50011, USA  S.D.
Rolnick  University of California-Riverside, Riverside, California 92521, USA
M. Rosati  Iowa State University, Ames, Iowa 50011, USA  Z. Rowan  Baruch
College, City University of New York, New York, New York, 10010 USA  J.G.
Rubin  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  J. Runchey  Iowa State University, Ames, Iowa 50011, USA
A.S. Safonov  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  B. Sahlmueller  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  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  K. Sato  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  S. Sato  Advanced Science
Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-
mura, Naka-gun, Ibaraki-ken 319-1195, Japan  B. Schaefer  Vanderbilt
University, Nashville, Tennessee 37235, USA  B.K. Schmoll  University of
Tennessee, Knoxville, Tennessee 37996, USA  K. Sedgwick  University of
California-Riverside, Riverside, California 92521, USA  R. Seidl  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. Sen  Iowa State University, Ames, Iowa 50011, 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  A. Sexton  University of
Maryland, College Park, Maryland 20742, USA  D. Sharma  Department of Physics
and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800,
USA  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  T. Shioya  Tomonaga Center for the History of the Universe, University
of Tsukuba, Tsukuba, Ibaraki 305, 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  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  D. Silvermyr
Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden  Oak
Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA  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. Slunečka  Charles University, Ovocný trh 5, Praha 1, 116 36, Prague,
Czech Republic  K.L. Smith  Florida State University, Tallahassee, Florida
32306, USA  M. Snowball  Los Alamos National Laboratory, Los Alamos, New
Mexico 87545, 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
P.W. Stankus  Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
M. Stepanov  Deceased  Department of Physics, University of Massachusetts,
Amherst, Massachusetts 01003-9337, USA  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  T. Sumita  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  J. Sun  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
Z. Sun  Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  S. Syed
Georgia State University, Atlanta, Georgia 30303, 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  A. Takeda  Nara Women’s University, Kita-uoya Nishi-
machi Nara 630-8506, 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  K. Tanida
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata
Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, 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  Vanderbilt University,
Nashville, Tennessee 37235, USA  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  G. Tarnai  Debrecen
University, H-4010 Debrecen, Egyetem tér 1, Hungary  R. Tieulent  Georgia
State University, Atlanta, Georgia 30303, USA  IPNL, CNRS/IN2P3, Univ Lyon,
Université Lyon 1, F-69622, Villeurbanne, France  A. Timilsina  Iowa State
University, Ames, Iowa 50011, USA  T. Todoroki  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
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  M. Tomášek  Czech Technical University, Zikova 4,
166 36 Prague 6, Czech Republic  C.L. Towell  Abilene Christian University,
Abilene, Texas 79699, USA  R. Towell  Abilene Christian University, Abilene,
Texas 79699, USA  R.S. Towell  Abilene Christian University, Abilene, Texas
79699, USA  I. Tserruya  Weizmann Institute, Rehovot 76100, Israel  Y. Ueda
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  B. Ujvari
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  H.W. van Hecke
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  S. Vazquez-
Carson  University of Colorado, Boulder, Colorado 80309, USA  J. Velkovska
Vanderbilt University, Nashville, Tennessee 37235, USA  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  N. Vukman  Department of Physics, Faculty
of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb, Croatia
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  Z. Wang  Baruch College, City University of New York, New
York, New York, 10010 USA  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  KEK, High Energy Accelerator
Research Organization, Tsukuba, Ibaraki 305-0801, Japan  F. Wei  New Mexico
State University, Las Cruces, New Mexico 88003, USA  A.S. White  Department of
Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA  C.P.
Wong  Georgia State University, Atlanta, Georgia 30303, USA  Georgia State
University, Atlanta, Georgia 30303, USA  Los Alamos National Laboratory, Los
Alamos, New Mexico 87545, USA  C.L. Woody  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  M. Wysocki  Oak Ridge
National Laboratory, Oak Ridge, Tennessee 37831, USA  B. Xia  Department of
Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA  L. Xue
Georgia State University, Atlanta, Georgia 30303, USA  C. Xu  New Mexico State
University, Las Cruces, New Mexico 88003, USA  Q. Xu  Vanderbilt University,
Nashville, Tennessee 37235, USA  S. Yalcin  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, 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 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  H. Yamamoto  Tomonaga Center for the History
of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A.
Yanovich  IHEP Protvino, State Research Center of Russian Federation,
Institute for High Energy Physics, Protvino, 142281, Russia  P. Yin
University of Colorado, Boulder, Colorado 80309, USA  I. Yoon  Department of
Physics and Astronomy, Seoul National University, Seoul 151-742, Korea  J.H.
Yoo  Korea University, Seoul 02841, Korea  I.E. Yushmanov  National Research
Center “Kurchatov Institute”, Moscow, 123098 Russia  H. Yu  New Mexico State
University, Las Cruces, New Mexico 88003, USA  Peking University, Beijing
100871, People’s Republic of China  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  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  L. Zou  University of California-Riverside,
Riverside, California 92521, USA

###### Abstract

There is strong evidence for the formation of small droplets of quark-gluon
plasma in $p/d/^{3}$He+Au collisions at the Relativistic Heavy Ion Collider
(RHIC) and in $p$+$p$/Pb collisions at the Large Hadron Collider. In
particular, the analysis of data at RHIC for different geometries obtained by
varying the projectile size and shape has proven insightful. In the present
analysis, we find excellent agreement with the previously published PHENIX at
RHIC results on elliptical and triangular flow with an independent analysis
via the two-particle correlation method, which has quite different systematic
uncertainties and an independent code base. In addition, the results are
extended to other detector combinations with different kinematic
(pseudorapidity) coverage. These results provide additional constraints on
contributions from nonflow and longitudinal decorrelations.

##  I Introduction

The Relativistic Heavy Ion Collider (RHIC) was built and the Large Hadron
Collider (LHC) heavy-ion program initiated to study the formation of nucleus-
sized droplets of quark-gluon plasma (QGP) in the laboratory. This focused
scientific enterprise has been remarkably successful. The now standard model
of heavy-ion collisions includes the formation of QGP that expands
hydrodynamically before the phase transition to hadrons with confined quarks
and gluons. Refs. [1, 2, 3] provide useful reviews. Over the past ten years,
experiments have employed multiple techniques to assess whether such QGP
droplets are also formed in smaller collisions of $p$$+$$A$ and even $p$$+$$p$
collisions; see Ref. [4] for a recent review.

A specific proposal was to collide proton, deuteron, and helium-3 projectiles
on nuclear targets at RHIC, utilizing the unique capabilities of that
facility, to discern whether “flow-like” patterns are indeed attributable to
mini-QGP droplet formation [5]. In the years 2014, 2015, and 2016, RHIC
provided collisions of 3He$+$Au, $p$$+$Au, and $d$$+$Au at
$\sqrt{s_{{}_{NN}}}$ = 200 GeV, extending earlier results from 2003 and 2008
$d$$+$Au running. The PHENIX Collaboration has published a suite of results on
small systems including transverse momentum ($p_{T}$) spectra of identified
particles (indicating “baryon anomaly” results in small collision systems)
[6], pseudorapidity dependence of particle production and anisotropy
coefficients [7, 8], multiparticle cumulants [9], and anisotropy coefficients
at midrapidity as a function of $p_{T}$ for charged hadrons [10, 11, 12, 13]
and for identified particles [14, 15]. The full set of elliptic and triangular
azimuthal anisotropy coefficients ($v_{2}$ and $v_{3}$, respectively) for all
three collision geometries were published in Nature Physics [16].

The elliptical and triangular azimuthal anisotropy coefficients in all three
collision geometries are quantitatively predicted by viscous hydrodynamic
calculations published prior to the data [5, 17]. After intense theoretical
work [18, 19] and intense scientific scrutiny [20], calculations with initial-
state correlations in the color glass condensate framework are definitively
ruled out as the dominant source of the observed correlations. More recent
calculations indicate that prehydrodynamization evolution, either in the weak
[21] or strong [22] coupling limit, may have a significant impact on the
shortest lifetime systems—including the smallest systems or any size system at
the lowest energies—particularly for triangular flow. Additionally,
calculations within parton transport frameworks such as AMPT qualitatively
reproduce the flow coefficient ordering [23]. Finally, the initial geometry
has contributions from both intrinsic geometry and from geometric fluctuations
(originating from nucleonic and subnucleonic position-space fluctuations), and
from the statistics of particle production. As an example, the initial spatial
eccentricities $\varepsilon_{2}$ and $\varepsilon_{3}$ for central collisions
(impact parameter $b<2~{}{\rm fm}$) in different frameworks are given in Table
1. Additional negative binomial distribution fluctuations in particle
production and sub-nucleonic structure tend to increase the eccentricities
overall and reduce the differences, i.e. reducing the relative contribution
from intrinsic geometry; however, significant intrinsic contributions remain
in almost all cases. Additional measurements and theoretical work are needed
to gain insight on the relative contributions to the initial geometry and thus
further constrain both the hydrodynamic and prehydrodynamization stages.

Table 1:  Summary of various initial geometry calculations quantified by the average eccentricities $\varepsilon_{2,3}$ in central (impact parameter $b<2~{}{\rm fm}$) $p$$+$Au, $d$$+$Au, and 3He$+$Au events. The ”Nucl. w/o NBD Fluc.” column refers to Monte Carlo Glauber with nucleon position fluctuations [5]. The ”Nucl. w/ NBD Fluc.” column refers to Monte Carlo Glauber with nucleon position fluctuations and Negative Binomial Distribution (NBD) fluctuations in particle production [24]. The ”Quarks w/ NBD Fluc.” column refers to Monte Carlo Glauber with constituent quark position fluctuations and NBD fluctuations [24]. The last two columns use the IP-Glasma framework including gluon field fluctuations [25] in publicly available code with nucleon and constituent quark position fluctuations.  |  | Nucl. | Nucl. | Quarks | IP-G | IP-G
---|---|---|---|---|---|---
$\left<\varepsilon_{2,3}\right>$ | Collision | w/o | w/ | w/ | w/ | w/
| system | NBD | NBD | NBD | Nucl. | Quarks
|  | Fluc. | Fluc. | Fluc. |  |
$\left<\varepsilon_{2}\right>$ |  $p$$+$Au | 0.23 | 0.32 | 0.38 | 0.10 | 0.50
|  $d$$+$Au | 0.54 | 0.48 | 0.51 | 0.58 | 0.73
| 3He$+$Au | 0.50 | 0.50 | 0.52 | 0.55 | 0.64
$\left<\varepsilon_{3}\right>$ |  $p$$+$Au | 0.16 | 0.24 | 0.30 | 0.09 | 0.32
|  $d$$+$Au | 0.18 | 0.28 | 0.31 | 0.28 | 0.40
| 3He$+$Au | 0.28 | 0.32 | 0.35 | 0.34 | 0.46

Figure 1: PHENIX detector system layout. The Beam-Beam Counters (BBCS and
BBCN), the Forward Vertex Tracker (FVTXS and FVTXN), and the central
spectrometer arms (CNT) are shown with their respective pseudorapidity
coverage (horizontal) and azimuthal coverage (vertical). For the FVTX, the
lighter shaded region corresponds to the cluster acceptance while the darker
shaded region corresponds to the reconstructed track acceptance.

Figure 2: PHENIX relative acceptance and efficiency for reconstructed tracks
in the FVTX as a function of pseudorapidity and transverse momentum ($p_{T}$).
The pseudorapidity and $p_{T}$ acceptances depend on the collision $z$-vertex,
and the $z$-vertex distribution is included in generating this map. The
tracking quality selection significantly reduces the efficiency for tracks
with $p_{T}<0.5~{}{\rm GeV}/c$, again pseudorapidity dependent.

Given the importance of these results, the PHENIX Collaboration has carried
out a new analysis of the same data sets using combinations of three sets of
detector combinations to extract two-particle correlations (2PC), called the
3$\times$2PC method, to check the published results [16] and to provide
additional information via correlations between particles from different
kinematic regions. Because this makes use of three different two-particle
correlations, it is called the 3$\times$2PC method. In addition, as the PHENIX
experiment collected its final data in 2016, we provide an archival set of
correlation function data for future examination. In this paper, we do not
compare the experimental results with the latest theoretical calculations and
rather focus solely on the measurements and their quantified uncertainties.

##  II Analysis Method

The following subsections detail the PHENIX detector and the correlation
analysis.

###  II.1 Detector description

The PHENIX detector is composed of multiple spectrometers and detector
subsystems [26, 27]. The detectors used in this analysis are highlighted in
Fig. 2 and detailed here. The central arm spectrometers (CNT) measure charged
hadrons with pseudorapidity $|\eta|<0.35$. There are two CNT spectrometers,
referred to as “east” and “west”, each subtending $\Delta\phi=\pi/2$. The
beam-beam counters (BBC) [28] comprise two sets of 64 quartz Čerenkov
radiators with photomultiplier readout, each set covering $3.1<|\eta|<3.9$—the
BBC covering $-3.9<\eta<-3.1$ is referred to as the “south” side (BBCS), and
likewise the BBC covering $3.1<\eta<3.9$ is called the “north” side (BBCN). No
individual particle information is available and the light output for each
counter is normalized to the expected single charged particle response. We
note that approximately half of the particles hitting the BBC are scattered
from the beam pipe and the poles of the axial field magnet. The forward
silicon vertex detector (FVTX) [29] comprises silicon strips oriented in the
azimuthal direction and covers both forward and backward rapidity
$1.0<|\eta|<3.0$. The FVTX can be used to count hits via clusters or via
reconstructed tracks in the four-layers on each side. The acceptance for FVTX
tracks is significantly more constrained than the acceptance for clusters, and
has a strong dependence on the $z$-vertex of the collision (the direction
along the beam line). Due to the orientation of the strips, there is no
momentum information available with the FVTX tracks. The FVTX acceptance for
tracks is shown in Fig. 2 and is dominated by tracks with $1.2<|\eta|<2.2$ and
$p_{T}>0.5~{}{\rm GeV}/c$.

The BBC is used for triggering on minimum bias (MB) $p$$+$Au, $d$$+$Au, and
3He$+$Au collisions by requiring a fast reconstructed $z$-vertex within
$|z|<10$ cm and at least one hit on each side of the collision point.
Additionally, a high-multiplicity trigger was employed to enhance the 0%–5%
highest BBC multiplicity events by more than an order of magnitude. The BBC
information in the Au-going direction is also used offline to select events in
the 0%–5% centrality category. Full details are available in Refs. [16, 14,
10, 11].

###  II.2 Event plane method

Previous PHENIX publications, including Ref. [16], utilized the event plane
method [30] for measuring azimuthal anisotropies. The second- and third-
harmonic event planes are determined in the BBC in the Au-going direction
(referred to as the BBC “south” or BBCS) and in the Au-going FVTX (referred to
as the FVTX “south” or FVTXS). The standard Q-vector recentering and event
plane flattening techniques [31] are applied. Because the collision system is
asymmetric, one cannot determine the event plane resolutions by comparing
forward and backward detectors alone. Thus, the event plane resolutions are
determined utilizing the three-detector combination BBCS-FVTXS-CNT.

It was recently pointed out that the third-harmonic event plane resolutions
for the BBCS and FVTXS published in Ref. [16] do not follow the expected
simple scaling of $R(\psi_{n})\propto v_{n}\sqrt{N_{\rm hit}}$, where $N_{\rm
hit}$ is the number of particles striking the event plane detector and $v_{n}$
is the azimuthal anisotropy of those particles. We have carefully investigated
this observation by running a full simulation of the event plane procedure,
including the fact that the beam has nonzero angle and offset with respect to
the detector coordinate system. The beam angles and offsets for the different
running periods are given in Table 2. An additional issue is that the PHENIX
central carriage, which was moved between operation periods, has modest
position offsets of order 1–2 mm relative to nominal. We find that the event
plane flattening procedure in the rotated frame creates a distortion on the
triangular anisotropy due to the elliptic anisotropy. The simulation
qualitatively reproduced the event plane “bias” seen in real data; the effect
largely cancels in the final $v_{3}$, because the bias is opposite between the
BBCS and FVTXS. The effect is dependent on the size of the real signal
$v_{3}$, the beam angle, beam offset, event multiplicity, and Q-vector
recentering applied, and is much larger in $p$$+$Au and $d$$+$Au, where the
smaller $v_{3}$ induces higher sensitivity to these effects.

Table 2: System beam angles and offsets. Year | System | $x_{{\rm offset}}$ | $y_{{\rm offset}}$ |  $x$-$z$ angle
---|---|---|---|---
|  | (mm) | (mm) | (mrad)
2014 | 3He$+$Au | 3.9 | 0.02 | 1.8
2015 | $p$$+$Au | 2.1 | 0.5 | 3.6
2016 | $d$$+$Au | 3.0 | 0.2 | 1.0

Because the experimental results for $v_{3}$ in $p$$+$Au and $d$$+$Au, where
the distortion is largest, are important, we have carried out an independent
analysis to examine the validity of the previous results. In the Monte Carlo
simulation, two-particle correlation functions were successfully obtained when
using an event-mixing acceptance correction in very fine bins in collision
$z$-vertex. Thus, we have carried out a new analysis of all three collision
systems using three sets of two-particle correlations (3$\times$2PC). In the
limit of low event plane resolution, which is the case for all three systems,
the event plane physics result and the 3$\times$2PC physics result should
agree [30]—this is because they are both estimators of
$\left<v_{2}\right>^{1/2}$ in this case, which means the sensitivity to both
fluctuations and nonflow is the same.

We highlight that the analysis is independent of the published event plane
results in the following ways: (1) a completely different code base is used;
(2) the FVTX clusters are used in the event plane result but only FVTX tracks
with good quality are used in the 3$\times$2PC analysis; (3) additional
systematic uncertainty checks are carried out as detailed below. Note that a
subset of these 3$\times$2PC checks were carried out in the $d$$+$Au published
analyses detailed in Refs. [16, 8]. In this paper, we also extend the
kinematics from the original analysis to utilize different combinations of
detectors in the 3$\times$2PC method.

###  II.3 3$\times$2PC method

Here we detail the methodology used for the 3$\times$2PC method. The 2PC
technique utilized here follows the standard methodology [30]; the difference
only coming in requiring three such 2PC because the collision systems are
asymmetric. We measure the $\Delta\phi$ distribution of three different sets
of pairs. In each pair, one particle is required to be in one subevent, and
the other is required to be in another subevent. The manner in which the three
different pairs of subevents are used is qualitatively very similar to the
three subevent method for determining the event plane resolution. In the limit
of small event plane resolution, the techniques should yield the same results
as they are sensitive to flow, flow fluctuations, and nonflow in the same
manner [30].

The correlation function $C(\Delta\phi)$ is defined by

$C(\Delta\phi)=\frac{S(\Delta\phi)}{M(\Delta\phi)}\frac{\int_{0}^{2\pi}M(\Delta\phi)}{\int_{0}^{2\pi}S(\Delta\phi)},$
(1)

where $\Delta\phi$ is the difference in the azimuthal angles between the two
particles in the pair; $S(\Delta\phi)$ is the signal distribution, which is
constructed from pairs in which both particles are taken from the same event;
and $M(\Delta\phi)$, which is the mixed event distribution, which is
constructed from pairs of particles in which each particle is required to be
from a different event. It is essential that particles from mixed events come
from the same event category, which includes centrality class and collision
$z$-vertex class (i.e. the collision $z$-vertices of both particles must be in
the same collision $z$-vertex bin, typically 1 cm or 2 cm in width).

Once the correlation function is obtained, it can be decomposed via a Fourier
series with coefficients $c_{n}$:

$\displaystyle C(\Delta\phi)=1+\sum_{n=1}c_{n}\cos\Delta\phi,$ (2)

where $n$ is the harmonic number. Letting the superscripts denote subevents
$A$, $B$, and $C$, the $c_{n}$ coefficients mathematically represent

$\displaystyle c_{n}^{AB}$
$\displaystyle=\langle\cos(n(\phi_{A}-\phi_{B}))\rangle=\langle
v_{n}^{A}v_{n}^{B}\rangle,$ (3) $\displaystyle c_{n}^{AC}$
$\displaystyle=\langle\cos(n(\phi_{A}-\phi_{C}))\rangle=\langle
v_{n}^{A}v_{n}^{C}\rangle,$ (4) $\displaystyle c_{n}^{BC}$
$\displaystyle=\langle\cos(n(\phi_{B}-\phi_{C}))\rangle=\langle
v_{n}^{B}v_{n}^{C}\rangle.$ (5)

Finally, the $v_{n}$ in a single subevent can be determined as

$v_{n}^{C}(p_{T})=\sqrt{\frac{c_{n}^{AC}(p_{T})c_{n}^{BC}(p_{T})}{c_{n}^{AB}}}.$
(6)

Note that it is also possible to determine the $v_{n}$ in a different way,
using only one correlation in the numerator and all three in the denominator:

$\displaystyle v_{n}^{C}(p_{T})$
$\displaystyle=\frac{c_{n}^{AC}(p_{T})}{\sqrt{c_{n}^{AB}c_{n}^{AC}/c_{n}^{BC}}},$
(7) $\displaystyle v_{n}^{C}(p_{T})$
$\displaystyle=\frac{c_{n}^{BC}(p_{T})}{\sqrt{c_{n}^{AB}c_{n}^{BC}/c_{n}^{AC}}};$
(8)

where all of the correlations in the denominator are $p_{T}$-integrated. For
the detectors without momentum information (BBCS, FVTXS, FVTXN), this simply
means all tracks or hits. For the detectors with momentum information (CNT),
this means all tracks in the momentum range considered ($0.2<p_{T}<3.0~{}{\rm
GeV}/c$). Because this method is sometimes used by the LHC experiments, we
will informally refer to it as the LHC-style $v_{n}$, in contrast to the
PHENIX-style discussed previously. Note that the PHENIX-style $v_{n}$ is the
geometric mean of the two possible LHC-style $v_{n}$. For that reason, the
PHENIX-style presents certain advantages, particularly for reduced systematic
uncertainties.

###  II.4 Systematic uncertainties

The systematic uncertainties on the extracted $v_{2}$ and $v_{3}$ coefficients
have multiple contributions. In previous analyses utilizing CNT tracks [16,
14, 10, 11, 12], contributions from variations in track quality criteria, run-
to-run variations, etc. are quite modest and subdominant. The two dominant
sources of systematic uncertainty result from comparing results with different
collision $z$-vertex ranges and from comparing the two individual arms of the
CNT. The uncertainty associated with the collision $z$-vertex is assessed by
comparing the nominal result with $|z|<10~{}{\rm cm}$ to cases with
$+4.0~{}{\rm cm}<z<+10.0~{}{\rm cm}$ and $-10.0~{}{\rm cm}<z<-4.0~{}{\rm cm}$,
because the changes in the FVTXS acceptance are significant over this range.
We also consider the variation of only using “east” arm CNT tracks and only
using “west” arm CNT tracks. The differences found in the systematic
variations are taken to be the maximal possible deviations, representing
asymmetric distributions about the central value. These differences are
divided by $\sqrt{3}$ to give one standard deviation uncertainties, and then
those individual uncertainties are added in quadrature.

For the results utilizing the FVTXS and FVTXN detectors, we have repeated the
analyses using only one half, i.e. $1.2<|\eta|<1.7$, or the other half, i.e.
$1.7<|\eta|<2.2$. These give similar results; however, we do not include the
differences in the systematic uncertainties as the results may have differing
contributions from nonflow and longitudinal decorrelations. These results are
presented in the Appendix.

##  III Results

Figure 3:  The extracted $v_{2}$ coefficient as a function of $p_{T}$ in 0%–5%
central $p$$+$Au, $d$$+$Au, and 3He+Au collisions from the 3$\times$2PC method
using the BBCS-FVTXS-CNT detector combination are shown as solid circles. Also
shown as open crosses are the published Nature Physics [16] results that were
obtained via the event plane method and the same combination of detectors.

Figure 4:  The extracted $v_{3}$ coefficient as a function of $p_{T}$ in 0%–5%
central $p$$+$Au, $d$$+$Au, and 3He+Au collisions from the 3$\times$2PC method
using the BBCS-FVTXS-CNT detector combination are shown as solid circles. Also
shown as open crosses are the published Nature Physics [16] results that were
obtained via the event plane method and the same combination of detectors.

Figure 5:  The extracted $v_{2}$ coefficient as a function of $p_{T}$ in 0%–5%
central $p$$+$Au, $d$$+$Au, and 3He+Au collisions from the 3$\times$2PC method
using the FVTXS-CNT-FVTXN detector combination are shown as solid squares. For
comparison we also show the previously plotted results from the BBCS-FVTXS-CNT
combination as open circles.

The main physics results from the 3$\times$2PC analysis are the extracted
$v_{2,3}$ coefficients as a function of charged hadron $p_{T}$ at midrapidity
$|\eta|<0.35$. However, these values may depend on the other two detectors
used in combination with the CNT tracks. A set of example two-particle
correlations and a complete set of extracted Fourier coefficients ($c_{1}$,
$c_{2}$, $c_{3}$, $c_{4}$) and their statistical uncertainties are given in
supplemental material [32].

We highlight that care should be employed when comparing $c_{n}$ coefficients
directly as the $p_{T}$ acceptance of the BBCS and FVTXS differ, as well as
their relative particle (direct and scattered) contributions. Thus, even
though in principle one can extract $v_{2}$ and $v_{3}$ values in the BBCS and
FVTXS, by the same procedure as in the CNT, they do not have a straightforward
physics interpretation. In the case of reconstructed, high quality FVTXS
tracks, a full acceptance and efficiency correction as a function of collision
$z$-vertex is possible, as done for example in Ref. [7]. However, a similar
procedure has not been done for the BBCS, where approximately half the hits
are from scattered particles.

###  III.1 $v_{n}$ vs $p_{T}$ results

Figure 5 shows the elliptic $v_{2}$ coefficients as a function of $p_{T}$ from
the 3$\times$2PC method utilizing the three-detector combination BBCS-FVTXS-
CNT. The results for the most central 0%–5% events are shown for all three
collision geometries with statistical uncertainties as vertical lines and
systematic uncertainties as open boxes. The systematic uncertainties have a
high degree of point-to-point correlation. Also shown are the previously
published $v_{2}$ coefficients [16] utilizing the event plane method. We
highlight that the earlier publication includes an asymmetric systematic
uncertainty estimate for nonflow based on a simple multiplicity scaling of
coefficients from $p$$+$$p$ collisions at $\sqrt{s}$ = 200 GeV; here we do not
include this uncertainty, as we focus on what is directly measured from the
correlation functions with all physics contributions included. The analysis
presented here is in excellent agreement with the previously published
results.

Figure 5 shows the third harmonic coefficient $v_{3}$ as a function of
$p_{T}$. It is otherwise identical to the previous figure, showing a
comparison between the present 3$\times$2PC analysis and the previously
published event plane analysis [16] for the most central 0%–5% events for all
three collision systems and, as before, the vertical lines represent the
statistical uncertainties and the boxes indicate the point-to-point correlated
systematic uncertainties. There is good agreement within uncertainties between
the two analyses, with the 3He$+$Au $v_{3}$ values from the 3$\times$2PC
method slightly lower than the event plane results, though well within
systematic uncertainties, which are largely independent between the two
methods.

We highlight that the correlation coefficients $c_{2}$ and $c_{3}$ from all
collision geometries follow the approximate expected scaling based on each
detector’s multiplicity and $v_{n}$ using inputs from Ref. [7]. Thus the
puzzle involving the nonscaling of the event plane values mentioned above is
resolved.

###  III.2 Additional kinematic ranges

The above results are presented as $v_{2}$ and $v_{3}$ at midrapidity
$|\eta|<0.35$, but they can depend on the other two detectors used in the
analysis, namely the BBCS and FVTXS. Nonflow contributions, longitudinal
decorrelations, and potentially other effects can make the extraction
dependent on the kinematic coverage of the other detectors – see for example
Ref. [33]. The original motivation for utilizing the BBCS and FVTXS is based
on their higher multiplicity and significant pseudorapidity gap from the CNT
tracks. Note that the gap should be thought of not in simple terms of the
extreme $|\Delta\eta|>X$ value, but rather the distribution of possible
$|\Delta\eta|$ values. Thus, the average $\left<|\Delta\eta|\right>\approx
3.5,2.0,1.8$ for the BBCS-CNT, FVTXS-CNT, BBCS-FVTXS detector combinations.

We have also analyzed the detector combination FVTXS-CNT-FVTXN for the
3$\times$2PC. Note that now the average values are
$\left<|\Delta\eta|\right>\approx 2.0,2.0,3.4$ for the FVTXS-CNT, CNT-FVTXN,
and FVTXS-FVTXN detector combinations. However, based on measurements as a
function of pseudorapidity in Ref. [7], the $v_{2}$ values are less than half
the magnitude in the FVTXN compared to FVTXS and the multiplicity of tracks is
also less than half. Thus, nonflow contributions relative to flow
contributions are expected to be substantially larger in the FVTXN. Again,
additional example correlation functions and the full set of extracted $c_{n}$
coefficients are given in the Appendix.

Tables 4 and 4 list the pseudorapidity acceptances of the different detectors
and two-detector combinations. In Fig. 5 the pseudorapidity acceptance of the
BBCS-FVTXS-CNT combination is listed as
$-3.9<\eta<-3.1,-3.0<\eta<-1.0,|\eta|<0.35$. In Fig. 5 the pseudorapidity
acceptance of the FVTXS-CNT-FVTXN combination is listed as
$-3.0<\eta<-1.0,|\eta|<0.35,1.0<\eta<3.0$. While the full FVTX acceptance for
clusters is $1.0<|\eta|<3.0$, this analysis predominantly uses tracks that are
from $1.2<|\eta|<2.2$.

Table 3: Pseudorapidity acceptances of individual detectors.

Detector | $\eta_{{\rm min}}$ | $\eta_{{\rm max}}$
---|---|---
BBCS (tubes) | -3.9 | -3.1
FVTXS (clusters) | -3.0 | -1.0
FVTXS (tracks) | -2.2 | -1.2
CNT (tracks) | -0.35 | 0.35
FVTXN (clusters) | 1.0 | 3.0
FVTXN (tracks) | 1.2 | 2.2

Table 4: Pseudorapidity acceptances of two-detector combinations.

Detector combination | $|\Delta\eta|_{{\rm min}}$ | $|\left<\Delta\eta\right>|$
---|---|---
BBCS-FVTXS (tubes-clusters) | 0.1 | 1.8
BBCS-FVTXS (tubes-tracks) | 0.9 | 1.8
BBCS-CNT (tubes-tracks) | 2.75 | 3.5
FVTXS-CNT (clusters-tracks) | 0.65 | 2.0
FVTXS-CNT (tracks-tracks) | 0.85 | 2.0
FVTXN-CNT (clusters-tracks) | 0.65 | 2.0
FVTXN-CNT (tracks-tracks) | 0.85 | 2.0
FVTXS-FVTXN (clusters-clusters) | 2.0 | 3.4
FVTXS-FVTXN (tracks-tracks) | 2.4 | 3.4

Figure 5 shows the elliptic $v_{2}$ coefficients as a function of $p_{T}$ from
the 3$\times$2PC method utilizing the three-detector combination FVTXS-CNT-
FVTXN. The results for the most central 0%–5% events are shown for all three
collision geometries with statistical uncertainties as vertical lines and
systematic uncertainties as open boxes. The systematic uncertainties have a
high degree of point-to-point correlation. For comparison, the 3$\times$2PC
values from the BBCS-FVTXS-CNT combination are shown. Shown in Figure 6 is the
ratio of the $v_{2}$ in the FVTXS-CNT-FVTXN combination to the $v_{2}$ in the
BBCS-FVTXS-CNT combination. We observe a modest 5%–15% difference in the
3He$+$Au case, growing to a 10%–20% difference in the $d$$+$Au case, and then
a rather large 35%–80% difference in the $p$$+$Au case. Qualitatively this
difference could result from substantially larger nonflow contributions in the
FVTXS-CNT-FVTXN combination, and this would be expected to be largest in the
$p$$+$Au system which has the smallest multiplicity as well as the lowest
expected elliptic flow itself. Nonflow effects are also expected to play a
larger role at larger $p_{T}$, and we observe a modest rise in the ratios with
$p_{T}$.

Figure 6:  Ratio of $v_{2}$ in the FVTXS-CNT-FVTXN combination (numerator) to
$v_{2}$ in the BBCS-FVTXS-CNT combination (denominator) as a function of
$p_{T}$ for $p$$+$Au (red squares), $d$$+$Au (blue crosses), and 3He$+$Au
(black diamonds).

Figure 7:  The extracted $v_{3}$ coefficient as a function of $p_{T}$ in 0%–5%
central $p$$+$Au, $d$$+$Au, and 3He+Au collisions from the 3$\times$2PC method
using the FVTXS-CNT-FVTXN detector combination are shown as solid squares. For
comparison we also show the previously plotted results from the BBCS-FVTXS-CNT
combination as open circles.

Figure 8:  Two-particle correlation $c_{2}$ and $c_{3}$ coefficients from
0%–5% central $p$$+$Au, $d$$+$Au, 3He$+$Au collisions. The markers are located
at the pseudorapidity average from the two detectors (i.e.
$(\eta_{1}+\eta_{2})/2$) and the associated horizontal line extends between
the two detectors (i.e. from $\eta_{1}$ to $\eta_{2}$). The vertical bars
indicate the statistical uncertainties. See text for details.

Figure 8 shows the third harmonic coefficient $v_{3}$ as a function of $p_{T}$
from the 3$\times$2PC using the FVTXS-CNT-FVTXN method, shown in solid
squares, and also the BBCS-FVTXS-CNT detector combination, shown in open
circles, for comparison. The statistical uncertainties are shown as vertical
lines and the systematic uncertainties as open boxes. In the case of 3He$+$Au,
the results agree for the two detector combination sets within uncertainties.
However, in the case of $p$$+$Au and $d$$+$Au, one of the $c_{3}$ coefficients
is negative, and thus the mathematical calculation of $v_{3}$ results in an
imaginary value. These imaginary values are shown along the negative $y$-axis
in the figure.

These negative values of $c_{3}$ observed in the $p$$+$Au and $d$$+$Au systems
are consistent with the observation that nonflow contributions in $p$$+$$p$
collisions extrapolated to these systems drive $c_{3}$ towards negative
values. This effect is consistent with nonflow dominance in the FVTXS-CNT-
FVTXN result. It is striking how much larger the effect is in $p$$+$Au and
$d$$+$Au compared to negligible in 3He$+$Au. Also, the difference in potential
nonflow in the $v_{2}$ shown above is quite different between the systems and
will also depend on the real triangular flow in these different geometries.

From the two-particle correlations and extracted coefficients (tabulated in
the supplemental material [32]) one can examine the patterns between the two-
particle kinematics and between collision systems. Access to the full suite of
Fourier coefficients is critical to enable future analysis techniques to be
applied and comparison with new theoretical tools that might more fully
incorporate flow, nonflow, and longitudinal dynamics. Figure 8 shows the
$c_{2}$ and $c_{3}$ coefficients from 0%–5% central $p$$+$Au, $d$$+$Au,
3He$+$Au collisions from left to right. The markers are located at the
pseudorapidity average from the two detectors (i.e. $(\eta_{1}+\eta_{2})/2$)
and the associated horizontal line extends between the two detectors (i.e.
from $\eta_{1}$ to $\eta_{2}$). Correlations involving tracks in the CNT (e.g.
where one of the horizontal line end points is at $\eta=0$) are for the
inclusive range in $0.2<p_{T}<3.0~{}{\rm GeV}/c$. As discussed in the
supplemental material [32], the $c_{n}$ coefficients should not be viewed as
strict physics quantities because the charge in the BBC and tracks in the FVTX
are not corrected for variations in acceptance, efficiency, and backgrounds,
all of which can vary between running periods.

Starting with the $c_{2}$ values, one observes significant variation amongst
the values from the different detector combinations used for the two-particle
correlations. This arises naturally from the pseudorapidity dependence of the
flow $v_{2}$ itself, and also from the different $p_{T}$ coverage of the
different detectors and different contributions from background, particularly
in the BBCS. Overall one observes that the relative ordering of $c_{2}$ values
from different combinations is qualitatively similar for the three collision
systems, with the dominant feature that all of the $p$$+$Au values are lower.

For the $c_{3}$ values, the ordering of the detector combinations in 3He$+$Au
collisions is qualitatively similar to that of the $c_{2}$ values. In striking
contrast, all of the $c_{3}$ coefficients (so all detector combinations) are
significantly lower in $p$$+$Au and $d$$+$Au compared with 3He$+$Au. This
means that the conclusion of lower triangular flow in $p$$+$Au and $d$$+$Au is
independent of any single detector used in the two-particle detector
combination, i.e. it is seen in all combinations. In particular, $c_{3}$
values where the FVTXN is utilized, i.e. where the horizontal line extends to
$\eta=+1.7$, are very low and in some cases actually negative, though with
large statistical uncertainties. It is the negative value for $c_{3}$ between
the CNT-FVTXN that results in the imaginary calculated $v_{3}$ in the FVTXS-
CNT-FVTXN combination for $p$$+$Au and $d$$+$Au systems. Noting that the
multiplicity is lowest in these systems at forward rapidity, i.e. the proton
or deuteron-going direction, and the $v_{3}$ may be the smallest, the
explanation may be from a large nonflow contribution toward negative values of
$c_{3}$.

##  IV Summary

In this paper we have presented an independent analysis of the flow
coefficients $v_{2}$ and $v_{3}$ as a function of $p_{T}$ in 0%–5% central
$p$$+$Au, $d$$+$Au, and 3He$+$Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
using the 3$\times$2PC method. The results are in excellent agreement with the
published Nature Physics results from the PHENIX Collaboration using the event
plane method [16]. In addition, variations in the kinematic selection for the
three detector combinations reveals an important role for nonflow and
longitudinal decorrelations, particularly at forward rapidity, i.e. in the
small projectile direction. To support future analyses, this paper includes an
archival documentation of correlation functions from $p$$+$$p$ through
3He$+$Au systems.

###### 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), 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), 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 and SRC(CENuM) Programs through NRF funded by
the Ministry of Education and the Ministry of Science and ICT (Korea).
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.

## APPENDIX: $v_{n}$ coefficients with two different subsets of FVTX
acceptance

We have repeated the analyses of 3$\times$2PC and dividing the FVTXS and FVTXN
into halves, either selecting tracks with $1.2<|\eta|<1.7$ or
$1.7<|\eta|<2.2$. Thus, the detector combinations will have increased or
decreased rapidity gaps from the default analysis.

Figures 12 and 12 show the comparison of $v_{2}$ as a function of $p_{T}$ at
midrapidity using the two different FVTXN and FVTXS pseudorapidity ranges, in
addition to the default use of the entire FVTX acceptance range. In all cases,
the differences are modest. There is a general pattern that the $v_{2}$
calculated with the BBCS-FVTXS-CNT combination is slightly higher when using
the FVTXS $1.2<|\eta|<1.7$ instead of FVTXS $1.7<|\eta|<2.2$. This may
indicate a slight increase in nonflow contribution to the FVTXS-CNT
correlation that dominates over a possible slight decrease in nonflow in the
BBCS-FVTXS correlation. A similar effect is seen in the $v_{2}$ values with
the FVTXS-CNT-FVTXN combination, which again may related to slightly larger
nonflow contributions due to all correlations having a smaller rapidity gap.

Figure 9:  Calculated midrapidity $v_{2}$ as a function of $p_{T}$ for 0%–5%
central $p$$+$Au, $d$$+$Au, 3He$+$Au collisions. Shown are results from the
BBCS-FVTXS-CNT combination including variations in the pseudorapidity
selection of tracks in the FVTXS.

Figure 10:  Calculated midrapidity $v_{2}$ as a function of $p_{T}$ for 0%–5%
central $p$$+$Au, $d$$+$Au, 3He$+$Au collisions. Shown are results from the
FVTXS-CNT-FVTXN combination including variations in the pseudorapidity
selection of tracks in the FVTXS and FVTXN.

Figure 11:  Calculated midrapidity $v_{3}$ as a function of $p_{T}$ for 0%–5%
central $p$$+$Au, $d$$+$Au, 3He$+$Au collisions. Shown are results from the
BBCS-FVTXS-CNT combination including variations in the pseudorapidity
selection of tracks in the FVTXS.

Figure 12:  Calculated midrapidity $v_{3}$ as a function of $p_{T}$ for 0%–5%
central $p$$+$Au, $d$$+$Au, 3He$+$Au collisions. Shown are results from the
FVTXS-CNT-FVTXN combination including variations in the pseudorapidity
selection of tracks in the FVTXS and FVTXN.

Figures 12 and 12 show the comparison of $v_{3}$ as a function of $p_{T}$ at
midrapidity using the two different FVTXN and FVTXS pseudorapidity ranges, in
addition to the default use of the entire FVTX acceptance range. In all cases,
the differences are modest, though with larger statistical uncertainties when
splitting the FVTX acceptance. The larger statistical uncertainties preclude
any strong conclusions regarding a pattern with the different selections.

We do not include these differences as systematic uncertainties in the default
$v_{2}$ and $v_{3}$ results as modest differences are expected. We can however
rule out any large uncertainty from detector effects in the FVTX from the
lower and higher rapidity acceptances.

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  * [32] See Supplemental Material at [URL will be inserted by publisher] for a set of example two-particle correlations and a complete set of extracted Fourier coefficients ($c_{1}$, $c_{2}$, $c_{3}$, $c_{4}$) and their statistical uncertainties.
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