PHENIX Collaboration

# Measurement of $J/\psi$ at forward and backward rapidity in $p$+$p$,
$p$$+$Al, $p$$+$Au, and 3He+Au collisions at $\sqrt{s_{{}_{NN}}}=200~{}{\rm
GeV}$

U. 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  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  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  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  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  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  C.Y. Chi  Columbia University,
New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533,
USA  M. Chiu  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  I.J. Choi  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  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  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
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.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  Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
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
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  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
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  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  H. En’yo  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, 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  Charles University, Ovocný trh
5, Praha 1, 116 36, Prague, Czech Republic  M. Finger, Jr  Charles University,
Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic  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  C. Gal  Department of Physics and Astronomy, Stony Brook University,
SUNY, Stony Brook, New York 11794-3800, USA  P. Gallus  Czech Technical
University, Zikova 4, 166 36 Prague 6, Czech Republic  E.A. Gamez  Department
of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, 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  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  S.Y. Han  Ewha Womans
University, Seoul 120-750, Korea  Korea University, Seoul, 02841  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
J. Hanks  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, 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  X.
He  Georgia State University, Atlanta, Georgia 30303, USA  T.K. Hemmick
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, 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  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  S. Huang  Vanderbilt University, Nashville,
Tennessee 37235, USA  K. Imai  Advanced Science Research Center, Japan Atomic
Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken
319-1195, Japan  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  S. Ishimaru  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  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  Chemistry Department, Stony Brook University, SUNY,
Stony Brook, New York 11794-3400, USA  X. Jiang  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  B.M. Johnson  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
Georgia State University, Atlanta, Georgia 30303, 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
C. Kim  University of California-Riverside, Riverside, California 92521, USA
Korea University, Seoul, 02841  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  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  Department of
Physics and Astronomy, Seoul National University, Seoul 151-742, Korea  B.
Kimelman  Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA  D.
Kincses  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  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  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  R. Lacey
Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York
11794-3400, USA  J.G. Lajoie  Iowa State University, Ames, Iowa 50011, USA  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 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  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  University of Colorado, Boulder, Colorado 80309,
USA  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Pusan
National University, Busan, 46241, South Korea  Yonsei University, IPAP, Seoul
120-749, Korea  M.X. Liu  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  Eszterházy Károly University, Károly
Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary  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  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  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
W.J. Metzger  Eszterházy Károly University, Károly Róbert Campus, H-3200
Gyöngyös, Mátrai út 36, Hungary  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
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 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. 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  P. Montuenga  University
of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  T. Moon  Korea
University, Seoul, 02841  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  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
RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198,
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. Nishitani  Nara Women’s University, Kita-uoya Nishi-
machi Nara 630-8506, 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  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  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  S.F. Pate  New Mexico State University, Las
Cruces, New Mexico 88003, USA  M. Patel  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  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  New Mexico State
University, Las Cruces, New Mexico 88003, USA  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  S. Sato  Advanced Science Research Center, Japan Atomic Energy
Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195,
Japan  C.Y. Scarlett  Florida A&M University, Tallahassee, FL 32307, USA  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.J. Skoby  Department of Physics, University of Michigan, Ann Arbor,
Michigan 48109-1040, USA  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  X. Sun  Georgia State University, Atlanta, Georgia 30303, USA  Z. Sun
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  S. Suzuki  Nara
Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan  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. 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  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  C.L. Woody
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  Y. Wu  University of California-Riverside, Riverside,
California 92521, 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  C. Xu  New Mexico State University, Las
Cruces, New Mexico 88003, USA  Q. Xu  Vanderbilt University, Nashville,
Tennessee 37235, USA  L. Xue  Georgia State University, Atlanta, Georgia
30303, 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  J.H. Yoo  Korea University, Seoul,
02841  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  I. Yoon  Department of Physics and Astronomy, Seoul
National University, Seoul 151-742, Korea  H. Yu  New Mexico State University,
Las Cruces, New Mexico 88003, USA  Peking University, Beijing 100871, People’s
Republic of China  I.E. Yushmanov  National Research Center “Kurchatov
Institute”, Moscow, 123098 Russia  W.A. Zajc  Columbia University, New York,
New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA  A.
Zelenski  Collider-Accelerator Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  Y. Zhai  Iowa State University, Ames, Iowa
50011, 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

Charmonium is a valuable probe in heavy-ion collisions to study the properties
of the quark gluon plasma, and is also an interesting probe in small collision
systems to study cold nuclear matter effects, which are also present in large
collision systems. With the recent observations of collective behavior of
produced particles in small system collisions, measurements of the
modification of charmonium in small systems have become increasingly relevant.
We present the results of $J/\psi$ measurements at forward and backward
rapidity in various small collision systems, $p$$+$$p$, $p$$+$Al, $p$$+$Au and
3He$+$Au, at $\sqrt{s_{{}_{NN}}}$=200 GeV. The results are presented in the
form of the observable $R_{AB}$, the nuclear modification factor, a measure of
the ratio of the $J/\psi$ invariant yield compared to the scaled yield in
$p$$+$$p$ collisions. We examine the rapidity, transverse momentum, and
collision centrality dependence of nuclear effects on $J/\psi$ production with
different projectile sizes $p$ and 3He, and different target sizes Al and Au.
The modification is found to be strongly dependent on the target size, but to
be very similar for $p$$+$Au and 3He$+$Au. However, for 0%–20% central
collisions at backward rapidity, the modification factor for 3He$+$Au is found
to be smaller than that for $p$$+$Au, with a mean fit to the ratio of $0.89\pm
0.03$(stat)${\pm}0.08$(syst), possibly indicating final state effects due to
the larger projectile size.

##  I Introduction

The cross section for production of charmonium in proton collisions with heavy
nuclei is strongly modified relative to that in $p$$+$$p$ collisions. The
effects that cause this modification are often referred to as cold nuclear
matter (CNM) effects because of the long-standing presumption that the energy
density and temperature produced in the collision of a single proton with a
nucleus were not sufficient to form a deconfined quark-gluon plasma, as
produced in ultra-relativistic heavy ion collisions at the Relativistic Heavy
Ion Collider (RHIC) and the Large Hadron Collider (LHC). A major motivation
for this work is to study CNM effects that can modify charm production in
$p$$+$$A$ collisions, which include modification of the nuclear-parton-
distribution functions (nPDFs) in a nucleus Eskola  _et al._ (2017); Kovarik
_et al._ (2016), initial state parton energy loss Vitev (2007), breakup of the
forming charmonium in collisions with target nucleons McGlinchey  _et al._
(2013); Arleo  _et al._ (2000), coherent gluon saturation Kharzeev and Tuchin
(2006); Fujii  _et al._ (2006), and transverse momentum broadening Cronin  _et
al._ (1975). These mechanisms are generally expected to act in the early
stages of the collision, and effect either the production rates of charm
quarks or their propagation through the nucleus. All of these processes are
strongly (and differently) dependent on the rapidity and transverse momentum
of the produced charmonium, and the collision energy. They are therefore best
studied using $p$$+$$A$ data covering the broadest possible range of collision
energy, rapidity and transverse momentum.

At RHIC, $p$$+$$p$, $d$$+$Au, $p$$+$Au, 3He$+$Au and $p$$+$Al collisions have
been studied at $\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$. The PHENIX experiment
published data on $J/\psi$ production in $d$$+$Au collisions over the rapidity
intervals $1.2<|y|<2.2$ and $|y|<0.35$ Adare  _et al._ (2011a, 2013a). PHENIX
also reported measurements of the $\psi(2S)$ in small collision systems, first
with nuclear modification in $d$$+$Au collisions ($|y|<0.35$) Adare  _et al._
(2013b), followed by measurements of the ratio of $\psi(2S)$ to $J/\psi$ in
$p$$+$Al, $p$$+$Au and 3He$+$Au collisions at
$\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$ ($1.2<|y|<2.2$) Adare  _et al._
(2017). The STAR collaboration has reported $J/\psi$ nuclear modification data
for $d$$+$Au collisions ($|y|<1$) Adamczyk  _et al._ (2016).

At the LHC, nuclear effects in $p$$+$Pb collisions have been studied at
$\sqrt{s_{{}_{NN}}}=5.02$ TeV. The ALICE collaboration has reported data for
$J/\psi$ Adam  _et al._ (2015); Abelev  _et al._ (2014a) and $\psi(2S)$ Abelev
_et al._ (2014b); Adam  _et al._ (2016) ($-4.46<y<-2.96$ and $2.03<y<3.53$).
The LHCb collaboration has reported $J/\psi$ Aaij  _et al._ (2014) and
$\psi(2S)$ data Aaij  _et al._ (2016) ($-5.0<y<-2.5$ and $1.5<y<4.0$). The CMS
collaboration has reported $J/\psi$ Sirunyan  _et al._ (2017) and $\psi(2S)$
Sirunyan  _et al._ (2019) data ($-2.4<y<1.93$ and $p_{T}>4~{}\mathrm{GeV}/c$).
The ATLAS collaboration has reported $J/\psi$ Aad  _et al._ (2015) and
charmonium Aaboud  _et al._ (2018) data ($|y|<2$ and $p_{T}>8$ GeV/$c$). These
measurements show a significant energy, rapidity and $p_{T}$ dependence of the
modification of charmonia production compared to the scaled $p$$+$$p$ results.

The assumption that effects due to soft particles produced in the collision
are not important in $p$ or $d$$+$$A$ collision at colliders was called into
question by the observation of strong suppression of the $\psi(2S)$ relative
to the $J/\psi$ in central $d$$+$Au collisions Adare  _et al._ (2013b), and
then in $p$$+$Pb collisions Abelev  _et al._ (2014b). Because CNM effects on
the production of charm quarks and their transport through the nucleus are
expected to affect both states similarly, they do not appear to be able to
explain this observation. However, it can be reproduced by the co-mover break
up model Ferreiro (2015), where charmonium is dissociated by interactions with
produced particles in the final state, which naturally gives a larger
suppression effect on the much more weakly bound $\psi(2S)$. The observation
of flow-like behavior in $p$$+$Pb collisions at LHC (see for example Dusling
_et al._ (2016)) and later in $d$$+$Au collisions at RHIC Adare  _et al._
(2013c, 2015a) suggested that a quark-gluon plasma of small size may be formed
in high energy collisions of these light systems. This led to the application
of transport models to $p$$+$Pb and $d$$+$Au data, which were originally
developed for charmonium production in heavy ion collisions Du and Rapp
(2015); Beraudo  _et al._ (2016). A plasma phase in these small collision
systems gives different suppression between the charmonia states and allows a
description of the data. In the case of most central midrapidity $d$$+$Au
collisions at $\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$, additional suppression
beyond CNM effects has been predicted of approximately 20% for the $J/\psi$,
and 55% for the $\psi(2S)$ Du and Rapp (2015), in good agreement with the data
Adare  _et al._ (2011a, 2013b).

In 2014 and 2015, RHIC provided collisions of $p$$+$Al, $p$$+$Au, and 3He$+$Au
for a systematic study of small systems. A comparison of flow data from
$p$$+$Au, $d$$+$Au, and 3He$+$Au with hydrodynamic models found that the data
were all consistent with hydrodynamic flow in the most central collisions
Aidala  _et al._ (2019a); Orjuela Koop  _et al._ (2015); Adare  _et al._
(2015b). An obvious question is whether increased energy density provided by
the 3He projectile in comparison to the proton produces any observable effect
on charmonium modification in collisions with a Au target.

In this paper we present PHENIX measurements of inclusive $J/\psi$ production
in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions at
$\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$. The inclusive $J/\psi$ cross section
includes feed-down from $\psi(2S)$ and $\chi_{c}$ states, and a smaller
contribution from B-meson decays. The results are directly compared to
$p$$+$$p$ collisions at the same center of mass energy by calculating the
nuclear modification factor $R_{AB}$. The $J/\psi$ data are presented as a
function of $p_{T}$, rapidity, and centrality and are compared to theoretical
models.

##  II Experimental Setup

The PHENIX detector Adcox  _et al._ (2003) comprises two central arm
spectrometers at midrapidity and two muon arm spectrometers at forward and
backward rapidity. The detector configuration during the data taking in 2014
and 2015 is shown in Fig. 1. The data presented here are from
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decays recorded with the muon arm
spectrometers. The muon spectrometers have full azimuthal acceptance, covering
$-2.2<\eta<-1.2$ (south arm) and $1.2<\eta<2.4$ (north arm), where the forward
arm has a slightly larger acceptance than the backward arm. For dimuons, the
analysis is restricted to $1.2<|y|<2.2$ in both arms. Each muon arm comprises
a Forward Silicon Vertex Tracker (FVTX), followed by a hadron absorber and a
muon spectrometer.

Figure 1:  Side view of the PHENIX detector in 2014 and 2015.

The FVTX Aidala  _et al._ (2014) is a silicon detector designed to measure a
precise collision vertex (also constrained by the Silicon Vertex Tracker (VTX)
at midrapidity), and to provide precise tracking for charged particles
entering the muon spectrometer before undergoing multiple scattering in the
hadron absorber. The FVTX was not used in this inclusive $J/\psi$ analysis,
because the acceptance is reduced when requiring muon arm tracks that match
tracks in the FVTX. Following the FVTX is the hadron absorber, composed of
layers of copper, iron, and stainless steel, corresponding to 7.2 nuclear
interaction lengths ($\lambda_{I}$). The absorber suppresses hadrons in front
of the muon arm by a factor of approximately 1000, thus significantly reducing
hadronic background for muon based measurements.

Each of the muon spectrometers is composed of a muon tracker (MuTr) embedded
in a magnetic field followed by a muon identifier (MuID). Each MuTr comprises
three stations of cathode strip chambers, inside a magnet with a radial field
integral of $\int{{\rm B}\cdot dl}=0.72~{}{\rm T}\cdot{\rm m}$. It provides a
momentum measurement for charged particles. Each MuID is composed of five
layers (referred to as gap 0–4) of steel absorber (4.8 (5.4) $\lambda_{I}$ for
south (north) arm) and two planes of Iarocci tubes. This enables the
separation of muons and hadrons based on their penetration depth at a given
reconstructed momentum. The MuID in each arm is also used to trigger events
containing two or more muon tracks per event, called a dimuon trigger, and
each muon track is required to have at least one hit in either gap 3 or gap
4\. A more detailed discussion of the PHENIX muon arms can be found in Ref.
Akikawa  _et al._ (2003); Adachi  _et al._ (2013).

The beam-beam counters (BBC) are used to determine the collision vertex
position along the beam axis ($z_{\rm BBC}$) with a resolution of roughly 2 cm
in $p$$+$$p$ collisions. Each BBC comprises two arrays of 64 quartz Čerenkov
detectors located at $z=\pm 144~{}{\rm cm}$ from the nominal interaction
point, and has an acceptance covering the full azimuth and $3.1<|y|<3.9$. They
also provide a minimum bias (MB) trigger by requiring at least one hit in each
BBC. The BBC trigger efficiency, determined from the Van der Meer scan
technique Drees  _et al._ (2003), is 55% $\pm$5% for inelastic $p$$+$$p$
events and 79% $\pm$2% for events with midrapidity particle production Adler
_et al._ (2003); Adare  _et al._ (2014). In $p$$+$Al, $p$$+$Au, and 3He$+$Au
collisions, charged particle multiplicity in the BBC in the Au/Al-going
direction ($-3.9<y<-3.1$) is used to categorize the event centrality. The BBC
trigger efficiency is 72% $\pm$4%, 84% $\pm$3%, and 88% $\pm$4% of inelastic
$p$$+$Al, $p$$+$Au, and 3He$+$Au collisions, respectively.

A Glauber model, combined with a simulation of the BBC response, is used to
relate charged particle multiplicity in the BBC to parameters that
characterize the collision centrality, as described in Adare  _et al._ (2014).
The analysis produces the average number of nucleon-nucleon collisions in each
centrality category. It also produces centrality dependent BBC bias correction
factors which account for the correlation between BBC charge and the presence
of a hard scattering in the event, and are applied as a multiplicative
correction on invariant yields. Table 1 shows the values of $\langle
N_{\mathrm{c}oll}\rangle$ and BBC bias correction factor from this analysis.

Table 1:  $\langle N_{\mathrm{c}oll}\rangle$ and BBC bias correction factors for different centrality bins of $p$$+$Al, $p$$+$Au and 3He$+$Au collisions.  Collision system | Centrality | $\langle N_{\mathrm{c}oll}\rangle$ | Bias factor
---|---|---|---
$p$$+$Al | 0%–20% | 3.4$\pm$0.3 | 0.81$\pm$0.01
| 20%–40% | 2.4$\pm$0.1 | 0.90$\pm$0.02
| 40%–72% | 1.7$\pm$0.1 | 1.04$\pm$0.04
| 0%–100% | 2.1$\pm$0.1 | 0.80$\pm$0.02
$p$$+$Au | 0%–5% | 9.7$\pm$0.6 | 0.86$\pm$0.01
| 5%–10% | 8.4$\pm$0.6 | 0.90$\pm$0.01
| 10%–20% | 7.4$\pm$0.5 | 0.94$\pm$0.01
| 0%–20% | 8.2$\pm$0.5 | 0.90$\pm$0.01
| 20%–40% | 6.1$\pm$0.4 | 0.98$\pm$0.01
| 40%–60% | 4.4$\pm$0.3 | 1.03$\pm$0.01
| 60%–84% | 2.6$\pm$0.2 | 1.00$\pm$0.06
| 0%–100% | 4.7$\pm$0.3 | 0.86$\pm$0.01
3He$+$Au | 0%–20% | 22.3$\pm$1.7 | 0.95$\pm$0.01
| 20%–40% | 14.8$\pm$1.1 | 0.95$\pm$0.01
| 40%–88% | 5.5$\pm$0.4 | 1.03$\pm$0.01
| 0%–100% | 10.4$\pm$0.7 | 0.89$\pm$0.01

##  III Data analysis

###  III.1 Data set

The data sets used in this analysis are 3He$+$Au data collected in 2014, and
$p$$+$$p$, $p$$+$Al, and $p$$+$Au data collected in 2015. All data sets were
recorded at a center of mass energy $\sqrt{s_{{}_{NN}}}$=200 GeV. The events
considered here are triggered by the dimuon trigger and are required to have a
vertex within $\pm 30~{}\mathrm{cm}$ of the center of the interaction region.
The corresponding integrated luminosity is 47 pb-1 for $p$$+$$p$, 590 nb-1 for
$p$$+$Al, 138 nb-1 for $p$$+$Au, and 18 nb-1 for 3He$+$Au collisions.

###  III.2 $J/\psi$ signal extraction

Figure 2:  Invariant mass distributions of unlike-sign and like-sign dimuons
in $p$$+$$p$ and integrated centrality of $p$$+$Au collisions in the south
muon arm. Fit results to extract the $J/\psi$ signal are also presented.

Yields of $J/\psi$ mesons were extracted from the invariant mass spectra
constructed from combinations of unlike-sign tracks that are identified as
muons (see Fig. 2). The mass spectra contain muon pairs from $J/\psi$ decays,
as well as significant contributions from combinations of real muons not from
a $J/\psi$, as well as misidentified hadrons. Details about the dimuon
selection to reduce the background contributions are described in Aidala  _et
al._ (2019b); Adare  _et al._ (2012).

The mass spectrum constructed from like-sign tracks was used to estimate the
background due to random combinations of kinematically unrelated tracks. A
modified Hagedorn function was used to represent the correlated background due
to kinematically related tracks. For $J/\psi$ signal extraction, Crystal-ball
functions Gaiser (1982) were used to describe the $J/\psi$ and $\psi(2S)$
peaks, similar to the previous analysis in small collision systems Adare  _et
al._ (2017):

$f(m)=N\cdot{\rm exp}\left(-\frac{(m-\bar{m})^{2}}{2\sigma^{2}}\right),\hskip
5.69054pt\small{{\rm for}\hskip 5.69054pt\frac{m-\bar{m}}{\sigma}>-\alpha}\\\
f(m)=N\cdot A\cdot\left(B-\frac{(m-\bar{m})^{2}}{\sigma}\right)^{-n},\hskip
5.69054pt\small{{\rm for}\hskip
5.69054pt\frac{m-\bar{m}}{\sigma}\leq-\alpha},\\\
A=\left(\frac{n}{|\alpha|}\right)^{n}\cdot{\rm
exp}\left(-\frac{|\alpha|^{2}}{2}\right),\hskip
5.69054ptB=\frac{n}{|\alpha|}-|\alpha|,$ (1)

where $\sigma$ and $\bar{m}$ are the width and mass centroid of the Gaussian
component of the line shape and $\alpha$ and $n$ are parameters describing the
tail.

The crystal-ball shape and tail parameters for the $\psi(2S)$ were fixed with
respect to the $J/\psi$ parameters, using the PDG database value Tanabashi
_et al._ (2018) for the energy difference and a width broadening factor taken
from simulations. In cases where the statistical precision of the data led to
poor definition of the $J/\psi$ signal shape, the mass and width of the
$J/\psi$ peak were fixed and a systematic uncertainty was assigned to the
yield based on tests made with higher statistics cases. The statistical
uncertainties related to the extraction of the $J/\psi$ yields were determined
from a covariance matrix in the fitting procedure.

###  III.3 Background estimation

The random combinatorial background in the unlike-sign mass spectrum was
approximated by combining all like-sign tracks from the same events. There is
a small correlated contribution to the like-sign pairs from jets and open
bottom; however, compared to the other background sources, this is small.

The correlated background comprises unlike-sign muon pairs from charm, bottom,
jets, and Drell-Yan. Because the correlated background cannot be estimated
independently from the data, it must be fitted to the mass spectrum when the
$J/\psi$ yield is extracted. Fitting the correlated background effectively
compensates for the small correlated component included in the like-sign
estimation of the combinatorial background.

We describe the correlated background using a modified Hagedorn function Adare
_et al._ (2011b); Aidala  _et al._ (2019b); Adare  _et al._ (2010):

$\frac{d^{2}N}{dm_{\mu\mu}d\mbox{$p_{T}$}}=\frac{p_{0}}{[\exp{(-p_{1}m_{\mu\mu}-p_{2}m_{\mu\mu}^{2})}+{m_{\mu\mu}}/{p_{3}}]^{p_{4}}},$
(2)

where $m_{\mu\mu}$ is the reconstructed $J/\psi$ mass, $p_{0}$ is a
normalization parameter, $p_{4}$ is the high mass tail parameter, and $p_{1}$,
$p_{2}$ and $p_{3}$ are additional fit parameters. It was found during the
analysis that when fitting mass spectra with poor statistical precision, the
shape of the correlated background was not well defined. This led to a
contribution of less than 10% to the point-to-point uncertainty in the
$J/\psi$ yields. Therefore, the shape of the correlated background as a
function of $p_{T}$ (determined by $p_{1}$, $p_{2}$ and $p_{3}$) was
constrained using simulation results based on a detailed study of dimuon mass
spectra Aidala  _et al._ (2019b); Leung (2019); Aidala  _et al._ (2020); Adare
_et al._ (2011a). A systematic uncertainty on the $J/\psi$ yield was assigned
for this procedure by refitting the data with various combinations of
correlated background parameters left free.

###  III.4 Efficiency correction

####  III.4.1 Acceptance and Reconstruction Efficiency

The study of acceptance and reconstruction efficiency of dimuons from $J/\psi$
decays has been performed using a geant4-based full detector simulation
Agostinelli  _et al._ (2003). In this simulation, the MuTr and MuID detector
efficiencies are set to values determined from the data. An emulator of the
dimuon trigger response is included in the simulation to account for the
trigger efficiency. As these efficiencies depend on the instantaneous
luminosity being sampled, each data set is divided into three groups with
different beam interaction rates, and corrected yields with separate
corrections are compared. A systematic uncertainty is assigned to the
extracted $J/\psi$ cross sections times branching fraction to $\mu^{+}\mu^{-}$
to reflect the differences, see Sec. III.7 for details.

The pythia8 event generator package Sj$\mathrm{\ddot{o}}$strand  _et al._
(2008) is utilized to generate $J/\psi$ events used for the full Geant4
detector simulation. To take into account effects from background hits, the
simulated hits of pythia8 $J/\psi$ events are embedded into real data events,
separated into centrality classes of the collision system. The track
reconstruction is then run on the data with embedded simulated hits to examine
the effects of the underlying event on the reconstruction efficiency. Figure 3
shows the acceptance and reconstruction efficiency for the $J/\psi$ as a
function of $p_{T}$ in $p$$+$$p$ collisions. The difference between the two
muon arms is mainly from different inefficient detector areas. There is little
multiplicity effect on the reconstruction efficiency in small collision
systems, the relative difference between 0%–20% and 40%–88% centrality bins at
backward rapidity in 3He$+$Au collisions is about 5%.

Figure 3:  Acceptance and reconstruction efficiency as a function of $p_{T}$
for dimuons from $J/\psi$ decays in $p$$+$$p$ collisions. GEANT simulations
evaluate detector acceptance$\times$efficiency simultaneously.

###  III.5 Invariant yield and nuclear modification factor

The invariant yield of dimuons from $J/\psi$ decays in a given rapidity and
centrality bin for the integrated $p_{T}$ range is

$B_{ll}\frac{dN}{dy}=\frac{1}{\Delta
y}\frac{c_{\mathrm{BBC}}}{\varepsilon_{\mathrm{Ae}}\varepsilon_{\mathrm{trig}}}\frac{N_{J/\psi}}{N_{\mathrm{evt}}},$
(3)

where $B_{ll}$ is the branching ratio of $J/\psi$ to dimuons, $\Delta y$ is
the width of the rapidity bin, $N_{J/\psi}$ is the number of $J/\psi$ obtained
from the fit procedure, $c_{\mathrm{BBC}}$ is the BBC bias correction factor
described in Table 1, $N_{\mathrm{evt}}$ is the number of sampled MB events in
the given centrality bin, $\varepsilon_{\mathrm{Ae}}$ is the $J/\psi$
acceptance and reconstruction efficiency, and $\varepsilon_{\mathrm{trig}}$ is
the dimuon trigger efficiency.

The invariant yield in a $y$, $p_{T}$, and centrality bin is

$\frac{B_{ll}}{2\pi
p_{T}}\frac{d^{2}N}{dydp_{T}}=\frac{1}{2\pi\mbox{$p_{T}$}\Delta\mbox{$p_{T}$}\Delta
y}\frac{c_{\mathrm{BBC}}}{\varepsilon_{\mathrm{Ae}}\varepsilon_{\mathrm{trig}}}\frac{N_{J/\psi}}{N_{\mathrm{evt}}},$
(4)

where $\Delta\mbox{$p_{T}$}$ is the width of the $p_{T}$ bin, and in this case
$N_{\mathrm{evt}}$ is the number of events in the centrality bin. Based on the
invariant yields calculated with Eq. 4, the $J/\psi$ nuclear modification
factor $R_{AB}$ for a given $y$, $p_{T}$, and centrality bin is formed to
quantify nuclear effects in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions. The
$R_{AB}$ is defined as

$R_{AB}=\frac{1}{\langle\mbox{$N_{\mathrm{c}oll}$}\rangle}\frac{d^{2}N^{AB}/dydp_{T}}{d^{2}N^{pp}/dydp_{T}},$
(5)

where $d^{2}N^{AB}/dyd\mbox{$p_{T}$}$ is the $J/\psi$ invariant yield for a
certain centrality bin of $A$$+$$B$ collisions,
$d^{2}N^{pp}/dyd\mbox{$p_{T}$}$ is the corresponding $J/\psi$ invariant yield
for $p$$+$$p$ collisions, and $\langle\mbox{$N_{\mathrm{c}oll}$}\rangle$ is
the mean number of binary collisions for that centrality bin in $A$$+$$B$
collisions.

###  III.6 $\langle p_{T}^{2}\rangle$ calculation

The $\langle p_{T}^{2}\rangle$ values for various centrality bins in all
collision systems have been calculated over the full measured $p_{T}$ range
($0<\mbox{$p_{T}$}<7$ GeV/$c$). We do not extrapolate the $p_{T}$ distribution
beyond 7 GeV/$c$. A previous study Adare  _et al._ (2013a) determined that
extrapolating to infinite $p_{T}$ increased the $\langle p_{T}^{2}\rangle$
values by 3%. The value of $\langle p_{T}^{2}\rangle$ is calculated
numerically using the following formula:

$\mbox{$\langle
p_{T}^{2}\rangle$}=\frac{\sum\limits^{N}_{i=0}p_{T,i}^{2}w_{i}}{\sum\limits^{N}_{i=0}w_{i}},$
(6)

where $p_{T,i}$ is the center of the i-th $p_{T}$ bin, and $w_{i}$ is the
weight factor proportional to the $J/\psi$ invariant yield in the $p_{T}$ bin:

$w_{i}=p_{T,i}dp_{T,i}\left(\frac{B_{ll}}{2\pi
p_{T}}\frac{d^{2}N}{dydp_{T}}\right)_{i},$ (7)

where $dp_{T,i}$ is the width of the bin.

###  III.7 Systematic Uncertainties

In the measurements we present in the next section, Type A uncertainties are
uncorrelated point to point uncertainties, and are dominated by the
statistical precision of the data. Type B systematic uncertainties are
correlated point to point uncertainties. Type C global uncertainties are
fractional uncertainties that apply to all measurements uniformly.

####  III.7.1 Signal extraction

As discussed in Sec. III.3, the modified Hagedorn function in Eq. 2 was used
to describe the correlated background. Initial parameters were estimated based
on the previous measurement of dimuon mass spectra Aidala  _et al._ (2019b);
Leung (2019), and two parameters, $p_{0}$ and $p_{4}$, were left free to
describe dimuon mass distributions in the data more properly. For the
systematic uncertainty study, additional parameters, $p_{1}$, $p_{2}$, and
$p_{3}$, in the modified Hagedorn function were also freed in the fit
procedure. We observe 1.4%–2.8% variations of $J/\psi$ counts depending on
rapidity, $p_{T}$, and centrality.

To describe the combinatorial background shape, the modified Hagedorn function
in Eq. 2, used for the correlated background component, was also used to fit
like-sign dimuon mass distributions. The effect of statistical fluctuations in
the like-sign dimuon mass distributions was studied by varying the shape based
on the statistical uncertainties of the fit parameters. We observe 1.0%–4.4%
variations of $J/\psi$ counts depending on rapidity, $p_{T}$, and centrality.

The uncertainty related to fixing the $J/\psi$ mass centroid and width was
evaluated by directly comparing the difference in yields with the parameters
free versus fixed, which ranges from 1.1%–2.9% uncertainty.

Table II lists all Type B uncertainties arising from the $J/\psi$ signal
extraction.

Table 2:  Fractional systematic uncertainties on the signal extraction in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions at forward (north arm) and backward (south arm) rapidity.  System | Source | Forward | Backward | Type
---|---|---|---|---
$p$$+$$p$ | Corr. bkg. | 1.4% | 1.8% | B
$p$$+$Al |  | 1.4% | 1.8% | B
$p$$+$Au |  | 1.9%–2.7% | 1.4%–2.8% | B
3He$+$Au |  | 2.3%–2.4% | 1.4%–2.8% | B
$p$$+$$p$ | Comb. bkg. |  $<$1.0% |  $<$1.0% | B
$p$$+$Al |  | 1.0% | 4.4% | B
$p$$+$Au |  | 1.0% | 1.0% | B
3He$+$Au |  | 1.0% | 2.7% | B
$p$$+$$p$ | Signal shape | - | - | B
$p$$+$Al |  | 1.1% | 1.1% | B
$p$$+$Au |  | 0%–1.5% | 0%–2.9% | B
3He$+$Au |  | 1.5% | 2.9% | B

####  III.7.2 Acceptance and efficiency correction

The acceptance and reconstruction efficiency correction and trigger efficiency
correction are obtained from simulation, so discrepancies between the data and
calculations can be a source of systematic uncertainty. The discrepancies can
be due to a variation in the detector performance during the data taking
period and/or inaccuracy of detector geometry and dead channel maps in the
simulation. To quantify these effects, we divide each data set into three
groups of different detector efficiency, based on the beam instantaneous
luminosity and calculated invariant yields with separate correction factors.
In this comparison we observe 1.5%–5.0% variations, depending on rapidity and
data set, and assign this variation as a systematic uncertainty. In addition,
we compare the azimuthal angle $\phi$ distribution of tracks in the MuTr
between the data and simulation, and assign a 2.5%–6.0% systematic uncertainty
depending on rapidity and data set.

In the simulation procedure, pythia8 was used to generate $J/\psi$ events, and
initial $J/\psi$ rapidity and $p_{T}$ shapes in pythia8 are tuned to match the
measurements in $p$$+$$p$ and $d$$+$Au collisions Adare  _et al._ (2012,
2013a, 2011a). These two different assumptions of the distributions are used
as bounds to estimate the sensitivity of this analysis to the shapes of these
distributions in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions, which are not
known $a$ $priori$. The variation of acceptance and reconstruction efficiency
between two sets of rapidity and $p_{T}$ distributions is less than 2%, so we
assigned a 2% conservative systematic uncertainty.

The uncertainty in the dimuon acceptance caused by lack of knowledge of the
$J/\psi$ polarization was studied as described in Adare  _et al._ (2012).
Because there is no precise measurement of $J/\psi$ polarization, a maximum
polarization value ($\pm 1$ in the helicity frame) was considered to study the
systematic uncertainty. The variation of dimuon acceptance becomes larger as
$J/\psi$ $p_{T}$ decreases, and 9%–20% systematic uncertainties are assigned
depending on $p_{T}$. We assumed that the $J/\psi$ polarization is not
significantly modified in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions, and
this uncertainty is canceled in the $R_{AB}$ calculation. This assumption was
also made in a similar PHENIX analysis for $J/\psi$ nuclear modification in
$d$$+$Au collisions Adare  _et al._ (2013a).

To evaluate a systematic uncertainty on the dimuon trigger efficiency, the
single muon trigger efficiency in the MB triggered data obtained with a large
number of muon samples was compared with the emulated single muon trigger
efficiency determined from simulation. This difference was propagated to the
uncertainty in the dimuon trigger efficiency based on a previous study Aidala
_et al._ (2019b), and a 1.0%–4.8% systematic uncertainty was assigned. The
Type B systematic uncertainties related to acceptance and efficiency
correction are shown in Table III.

Table 3:  Fractional systematic uncertainties on the acceptance and efficiency correction in $p$$+$$p$, $p$$+$Al, $p$$+$Au and 3He$+$Au collisions at forward (north arm) and backward (south arm) rapidity.  System | Source | Forward | Backward | Type
---|---|---|---|---
$p$$+$$p$ | Run variation | 4.0% | 4.7% | B
$p$$+$Al |  | 2.8% | 3.3% | B
$p$$+$Au |  | 1.6% | 3.5% | B
3He$+$Au |  | 1.5% | 5.0% | B
$p$$+$$p$ |  $\phi$ Matching | 5.8% | 5.0% | B
$p$$+$Al |  | 3.6% | 3.3% | B
$p$$+$Au |  | 3.4% | 4.0% | B
3He$+$Au |  | 3.1% | 2.5% | B
all | Initial shape | 2.0% | 2.0% | B
all |  $J/\psi$ pol. | 10%–20% | 9%–20% | B
$p$$+$$p$ | Trigger eff. | 1.0%–1.7% | 1.0%–2.6% | B
$p$$+$Al |  | 1.0%–1.8% | 2.0%–4.6% | B
$p$$+$Au |  | 1.0%–1.7% | 1.0%–4.8% | B
3He$+$Au |  | 1.0%–2.4% | 1.0%–2.4% | B
Figure 4:  $J/\psi$ invariant yields as a function of $p_{T}$ in $p$$+$$p$
collisions at $\sqrt{s}=200~{}\mathrm{GeV}$. The ratio between the values for
the two muon arms is presented in the bottom panel. Bars (boxes) around data
points represent point-to-point uncorrelated (correlated) uncertainties. There
is also a global systematic uncertainty of 10.1%

####  III.7.3 Multiple interaction

Due to the high instantaneous beam luminosity, particularly in $p$$+$$p$ and
$p$$+$Al runs, it is possible to have multiple inelastic collisions from a
single beam crossing, which can affect the invariant yield calculation. To
investigate this effect, the variation among invariant yields in three groups
of different instantaneous luminosity for each data set was studied, revealing
a yield variation smaller than 5%. However, the instantaneous luminosity
dependence of the acceptance and efficiency correction is already included as
a systematic uncertainty, and so no additional systematic uncertainty is
assigned.

####  III.7.4 $\langle p_{T}^{2}\rangle$

The $\langle p_{T}^{2}\rangle$ uncertainty is calculated based on the
systematic uncertainty of the invariant yield as a function of $p_{T}$. The
systematic uncertainties are mostly point-to-point correlated, and we assumed
that the uncertainties in different $p_{T}$ bins are linearly correlated. The
upper and lower limits of invariant yield in each $p_{T}$ bin are taken to
calculate the upper and lower limits of $\langle p_{T}^{2}\rangle$.

####  III.7.5 $\langle N_{\mathrm{c}oll}\rangle$ and BBC efficiency

The systematic uncertainties on the BBC efficiency and the determination of
$\langle N_{\mathrm{c}oll}\rangle$ in $p$$+$Al, $p$$+$Au, and 3He$+$Au
collisions described in Table 1 are evaluated by following the procedure
developed in the previous PHENIX analyses of $d$$+$Au data Adare  _et al._
(2014). These systematic uncertainties are considered as Type C (Type B)
systematic uncertainties in rapidity and $p_{T}$ (centrality) dependence
results. The systematic uncertainty on the BBC efficiency in $p$$+$$p$
collisions obtained in Adler  _et al._ (2003) is $10.1\%$, and this systematic
uncertainty is considered as a Type C systematic uncertainty.

##  IV Results

Figure 5:  Nuclear modification factor of inclusive $J/\psi$ as a function of
rapidity for 0%–100% $p$$+$Al (a), $p$$+$Au (b), and 3He$+$Au (c) collisions.
Bars (boxes) around data points represent point-to-point uncorrelated
(correlated) uncertainties. The theory bands are discussed in the text.

Figure 6:  Nuclear modification factor of inclusive $J/\psi$ as a function of
rapidity in three centrality bins for $p$$+$Al collisions. Bars (boxes) around
data points represent point-to-point uncorrelated (correlated) uncertainties.

Figure 7:  Nuclear modification factor of inclusive $J/\psi$ as a function of
rapidity in six centrality bins for $p$$+$Au collisions. Bars (boxes) around
data points represent point-to-point uncorrelated (correlated) uncertainties.

Figure 8:  Nuclear modification factor of inclusive $J/\psi$ as a function of
rapidity in three centrality bins for 3He$+$Au collisions. Bars (boxes) around
data points represent point-to-point uncorrelated (correlated) uncertainties.

Figure 9:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ at backward rapidity (Al/Au-going direction) for 0%–100% $p$$+$Al,
$p$$+$Au, and 3He$+$Au collisions. Bars (boxes) around data points represent
point-to-point uncorrelated (correlated) uncertainties. The theory bands are
discussed in the text.

Figure 10:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ at forward rapidity ($p$/3He-going direction) for 0%–100% $p$$+$Al,
$p$$+$Au, and 3He$+$Au collisions. Bars (boxes) around data points represent
point-to-point uncorrelated (correlated) uncertainties. The theory bands are
discussed in the text.

Figure 11:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ in three centrality bins for $p$$+$Al collisions. Bars (boxes) around
data points represent point-to-point uncorrelated (correlated) uncertainties.

Figure 12:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ at $-2.2<y<-1.2$ in six centrality bins for $p$$+$Au collisions. Bars
(boxes) around data points represents point-to-point uncorrelated (correlated)
uncertainties. The theory bands are discussed in the text. Note that the
theory bands compared with the 0%–5% and 5%–10% centrality data are for
0%–10%.

Figure 13:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ at $1.2<y<2.2$ in six centrality bins for $p$$+$Au collisions. The
theory bands are discussed in the text. Note that the theory bands compared
with the 0%–5% and 5%–10% centrality data are for 0%–10%.

Figure 14:  Nuclear modification factor of inclusive $J/\psi$ as a function of
$p_{T}$ in three centrality bins for 3He$+$Au collisions.

Figure 15:  Comparison of nuclear modification factor of $J/\psi$ as a
function of $p_{T}$ in 0%–20% centrality $p$$+$Al and $p$$+$Au collisions.
Bars (boxes) around data points represent point-to-point uncorrelated
(correlated) uncertainties. Figure 16:  Comparison of nuclear modification
factor of $J/\psi$ as a function of $p_{T}$ in 0%–20% centrality $d$$+$Au
Adare  _et al._ (2013a) and $p$$+$Au collisions. Bars (boxes) around data
points represent point-to-point uncorrelated (correlated) uncertainties.
Figure 17:  Comparison of nuclear modification factor of $J/\psi$ as a
function of $p_{T}$ in 0%–20% centrality $p$$+$Au and 3He$+$Au collisions.
Bars (boxes) around data points represent point-to-point uncorrelated
(correlated) uncertainties. Figure 18:  Nuclear modification factor of
$J/\psi$ as a function of $\langle\mbox{$N_{\mathrm{c}oll}$}\rangle$ for
$p$$+$Al, $p$$+$Au, and 3He$+$Au collisions. Bars (boxes) around data points
represent point-to-point uncorrelated (correlated) uncertainties. Figure 19:
Nuclear modification factor of $J/\psi$ as a function of
$\langle\mbox{$N_{\mathrm{c}oll}$}\rangle$ for $p$$+$Au collisions compared
with the transport model. Bars (boxes) around data points represent point-to-
point uncorrelated (correlated) uncertainties. Figure 20:  Nuclear
modification factor of $J/\psi$ as a function of the mean target thickness
sampled by charmonium production in the centrality bin, for $p$$+$Al, $p$$+$Au
and 3He$+$Au collisions. Bars (boxes) around data points represent point-to-
point uncorrelated (correlated) uncertainties. Figure 21:  $\langle
p_{T}^{2}\rangle$ of $J/\psi$ for $\mbox{$p_{T}$}<7~{}\mathrm{GeV}/c$ as a
function of $\langle\mbox{$N_{\mathrm{c}oll}$}\rangle$ for $p$$+$Al, $p$$+$Au,
and 3He$+$Au collisions. Bars (boxes) around data points represent point-to-
point uncorrelated (correlated) uncertainties.

In this section, we present invariant yield, nuclear modification factor, and
$\langle p_{T}^{2}\rangle$ results at forward and backward rapidity. There
have been significant changes to the muon arm configuration and to the
simulation framework since the $d$$+$Au data set was recorded. Figure 4 shows
the $J/\psi$ invariant yield as a function of $p_{T}$ in $p$$+$$p$ collisions
at $\sqrt{s}=200~{}\mathrm{GeV}$ at forward and backward rapidity, where bars
(boxes) represent point-to-point uncorrelated (correlated) uncertainties. The
global systematic uncertainty is 10.1%. The ratio of invariant yields between
the forward and backward rapidity regions is presented in the bottom panel,
where the systematic uncertainty due to the $J/\psi$ polarization cancels in
the ratio. The invariant yields at forward and backward rapidity are
consistent within the systematic uncertainties, confirming that the detector
efficiency is well understood in $p$$+$$p$ collisions.

Plots and tables of invariant yield are presented for the other collision
systems in the Appendix. We focus here on the nuclear modification factors.

Figure 8 shows the rapidity dependence of the nuclear modification factor for
0%–100% centrality in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions. The
rapidity dependence of the nuclear modification for different centrality
classes is shown for $p$$+$Al in Fig. 8, for $p$$+$Au in Fig. 8, and for
3He$+$Au in Fig. 8.

Figures 11 and 11 show the nuclear modification factor as a function of
$p_{T}$ for 0%–100% $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions at backward
and forward rapidity. The $p_{T}$ dependence in different centrality classes
is presented for $p$$+$Al in Fig. 11, for $p$$+$Au in Figs. 14 and 14, and for
3He$+$Au in Fig. 14. The modification as a function of $p_{T}$ in 0%–20%
central collisions is compared between $p$$+$Al and $p$$+$Au in Fig. 15.
Similar comparisons where the target is identical, but the projectile is
different are shown for 0%–20% central collisions comparing $d$$+$Au and
$p$$+$Au in Fig. 16 and comparing 3He$+$Au and $p$$+$Au in Fig. 17.

The $p_{T}$ integrated nuclear modification factor for $p$$+$Al, $p$$+$Au and
3He$+$Au as a function of $\langle N_{\mathrm{c}oll}\rangle$ is shown at both
forward and backward rapidity in Figs. 18 and 19. A comparison between
$p$$+$Al, $p$$+$Au and 3He$+$Au modifications when plotted as a function of
the average nuclear thickness sampled by the charmonium production is
presented in Fig. 20. Figure 21 shows the mean $p_{T}$ squared values for the
three systems $p$$+$Al, $p$$+$Au, and 3He$+$Au as a function of $\langle
N_{\mathrm{c}oll}\rangle$ for $\mbox{$p_{T}$}<7~{}\mathrm{GeV}/c$ at forward
and backward rapidity.

##  V Discussion

###  V.1 Rapidity dependence

The rapidity dependence of the modification for 0%–100% centrality, seen in
Fig. 8, shows only weak modification for $p$$+$Al collisions. For both
$p$$+$Au and 3He$+$Au significant suppression is seen at forward rapidity,
with less suppression at backward rapidity. The modifications for $p$$+$Au and
3He$+$Au are very similar.

The rapidity dependence in three centrality bins for $p$$+$Al collisions, seen
in Fig. 8, shows only weak modification in all centrality bins, both at
forward and backward rapidity.

The $p$$+$Au data presented here contain finer centrality binning for central
collisions than was previously available from $d$$+$Au. The rapidity
dependence in six centrality bins for $p$$+$Au collisions, seen in Fig. 8,
shows a factor of more than two suppression at the most forward rapidity in
the 0%–5% centrality bin, and a marked increase in suppression with increasing
rapidity in the forward direction. At backward rapidity, the modifications in
all centrality bins show little centrality dependence, all being somewhat
suppressed.

The rapidity dependence in three centrality bins for 3He$+$Au collisions is
shown in Fig 8. In comparison with the $p$$+$Al results shown in Fig. 8 for
the 0%–20% centrality bin, which show little modification, the 3He$+$Au
results show a suppression at both forward and backward rapidity. The
modification becomes less pronounced in the 20%–40% centrality range, and
approaches unity for the most peripheral collisions within uncertainties.

The rapidity dependence of the 0%–100% centrality data is compared in Fig. 8
with model calculations from R. Vogt Vogt (2015); Nelson  _et al._ (2013) and
Shao et al. Kusina  _et al._ (2018); Shao (2013, 2016); Lansberg and Shao
(2017) showing the effect of nPDF modifications using the Eskola-Paakkinen-
Paukkunen-Salgado (EPPS16) Eskola  _et al._ (2017) next-to-leading order (NLO)
and/or nuclear coordinated theoretical and experimental tests of quantum
chromodynamics (nCTEQ15) NLO parameterizations Kovarik  _et al._ (2016). The
Vogt EPPS16 NLO shadowing calculations in general follow the methods described
in Vogt (2015), while the $J/\psi$ mass and scale parameters are discussed in
Nelson  _et al._ (2013). The Shao, et al. model calculations for $p$$+$Au
collisions are based on a Bayesian reweighting method which uses $J/\psi$
constraints from $p$$+$Pb data at the LHC Kusina  _et al._ (2018). The
dominant uncertainty in the reweighting method is the factorization scale
dependence $\mu_{F}$ of the gluon modification factor
R${}^{Au}_{g}(x,\mu_{F})$, where $\mu_{F}=\xi\mu_{0}$, with
$\mu_{0}^{2}=M^{2}+\mbox{$p_{T}$}^{2}$ for the $J/\psi$ transverse mass, and
$\xi$ = 0.5, 1, 2 for the factorization scale. The reweighting however is not
applied for lighter 3He and Al nuclei, with the predictions for these nuclei
based on the original method described in Shao (2013, 2016); Lansberg and Shao
(2017). For these predictions, the previous PHENIX $J/\psi$ measurement in
$p$$+$$p$ collisions Adare  _et al._ (2012) is used as a baseline. The
calculations were performed at all three factorization scales ($\mu_{0}$,
$0.5~{}\mu_{0}$, and $2~{}\mu_{0}$) and provide two different confidence
levels (68% and 90% CL). The uncertainty band shown is for the 68% CL, and we
have taken the envelope of the uncertainty bands from the calculations at the
three scales.

In Fig. 8, the calculations describe the data very well at forward rapidity
for all three collision systems, and for $p$$+$Al at backward rapidity. For
$p$$+$Au and 3He$+$Au at backward rapidity the calculated modifications are
too large by roughly 40%. However, the calculations do not contain effects of
nuclear absorption, which is expected to be important at backward rapidity at
$\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$ McGlinchey  _et al._ (2013), where the
nuclear crossing time is comparable with the charmonium formation time. That
is not expected to be the case at forward rapidity at
$\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$, or at the rapidities of interest at
LHC energies. Because nuclear absorption is not included in the model
calculations, they should be expected to overpredict the modification in
$p$$+$Au and 3He$+$Au at backward rapidity.

An estimate of the effect of nuclear absorption at backward rapidity can be
obtained from a model Arleo  _et al._ (2000) fitted to absorption cross
sections derived from shadowing corrected data measured at a broad range of
beam energies McGlinchey  _et al._ (2013). The model assumes that the
$c\bar{c}$ pair size grows linearly with time until it reaches the size of a
fully formed charmonium meson. Then the absorption cross section depends on
the proper time before the pair escapes the target. The effect of the
modification due to nuclear absorption at backward rapidity from this model is
added to Fig. 8, by folding it into the shadowing calculation. The results
indicate that the measured modifications are reasonably consistent with
shadowing plus nuclear absorption.

###  V.2 $p_{T}$ dependence

The $p_{T}$ dependence for 0%–100% centrality, seen at backward rapidity in
Fig. 11 and at forward rapidity in Fig. 11, shows little modification for
$p$$+$Al but shows strong, and similar, $p_{T}$ dependence for $p$$+$Au and
3He$+$Au. These data are also compared with the calculations of Shao et al.
Kusina  _et al._ (2018). As for the rapidity dependence, the calculations
describe the forward rapidity data well for all three collision systems and
for the backward rapidity $p$$+$Al. But the backward rapidity modification for
$p$$+$Au and 3He$+$Au is overpredicted. Significant nuclear absorption is
expected at backward rapidity and low $p_{T}$, and calculations that do not
include it should overpredict the modification there.

The $p$$+$Au modifications vs $p_{T}$, seen at forward rapidity in Fig. 14 for
all centrality bins, shows very strong dependence on centrality. The
modification falls to 0.35 at low $p_{T}$ for the 5% most central collisions.
At backward rapidity, as shown in Fig. 14, the suppression is considerably
weaker at low $p_{T}$ for the most central collisions, but it changes more
slowly with centrality. The result is that for collision centralities above
20% the behavior of the modification versus $p_{T}$ becomes rather similar at
forward and backward rapidity. The $p_{T}$ dependence of the nuclear
modification factors in $p$$+$Al and 3He$+$Au collisions are shown in Figs. 11
and 14, respectively. We see little modification across all three centrality
ranges of $p$$+$Al collisions, as was the case for the rapidity dependent
results shown in Fig. 8. The $p$$+$Al nuclear modification factor for the 6–7
GeV/$c$ data point seen in Fig. 11 (a) is quite low. However, the 6 GeV/$c$
(5–7 GeV/$c$ bin) points for the three backward rapidity centrality bins shown
in Fig. 11 do not exhibit the same behavior. We have therefore interpreted
this last data point as being a deviation from the trend. In 0%–20% 3He$+$Au
collisions, a suppression is observed at both forward and backward rapidity,
and the modification becomes weaker in higher $p_{T}$. The modification is
strongest in most central collisions, and the $R_{AB}$ approaches unity for
the most peripheral collisions. As seen with $p$$+$Al, the last data point
(5–7 GeV/$c$ bin) for 3He$+$Au is also quite low. Likewise, we have
interpreted this behavior as being a deviation from the trend, considering the
measurements shown in Fig. 11 c) do not produce a similar effect.

The theory predictions shown in Figs. 14 and 14 are the results of adapted
transport models provided by X. Du and R. Rapp, based on the original
transport model by Zhao & Rapp for $A$+$A$ collisions Zhao and Rapp (2010).
The theory was extended for $d$+$A$ collisions Du and Rapp (2015) and most
recently for $p$+$A$ collisions Du and Rapp (2019). The transport model
includes a fireball generated by a Monte-Carlo Glauber model Loizides  _et
al._ (2015) in addition to shadowing from Eskola-Paukkunen-Salgado (EPS09)
Eskola  _et al._ (2009) NLO, a broadening parameter Zhao and Rapp (2009), and
an absorption cross section constrained by PHENIX $d$$+$Au data Adare  _et
al._ (2013b). The $J/\psi$ production cross section is described in Du and
Rapp (2019), and charged particle multiplicity Adare  _et al._ (2018),
hadronic dissociation rates Du and Rapp (2015), and open charm production
cross sections Du and Rapp (2019) are also considered. The calculations
reproduce the data at high $p_{T}$, but generally underpredict the suppression
at low $p_{T}$ at forward rapidity. Because the modification of $J/\psi$
production in the transport model is not very strong at forward rapidity, the
suppression there is dominated by the EPS09 shadowing contribution.

In a previous PHENIX measurement of charged particle multiplicity Adare  _et
al._ (2018), it was found that twice as many particles are produced in 0%–20%
central $p$$+$Au collisions than in 0%–20% central $p$$+$Al collisions, and
the multiplicity in 0%–20% 3He$+$Au collisions is about a factor of two larger
than in 0%–20% $p$$+$Au collisions. To look for evidence of an effect from
this, Figs. 15, 16, and 17 show direct comparisons between the modifications
in the 0%–20% centrality bin of different projectile ($p/d/^{3}\mathrm{He}$)
and target sizes (Al/Au). The ratio of nuclear modification factors is
included in the bottom panel. In the comparisons among $p$$+$Al, $p$$+$Au, and
3He$+$Au collisions, all systematic uncertainties from each collision system
are included except the initial shape uncertainty, which cancels upon taking
the ratio, and all systematic uncertainties stemming from the $p$$+$$p$ system
cancel. In the comparison between $p$$+$Au and $d$$+$Au, the two systems do
not share the same $p$$+$$p$ reference, therefore all systematic uncertainties
are included in the ratio. Note the $d$$+$Au data set was recorded in 2008,
while the $p$$+$Au data was recorded in 2015 with a new detector. Simulations
for $d$$+$Au were also performed using methods that differ from those used for
the new small systems study. For $p$$+$Au, $d$$+$Au and 3He$+$Au comparisons,
a mean value has been fitted to the ratios, and the result is shown on the
plot together with the fit uncertainty and the uncertainty from the systematic
errors. The systematic uncertainty was determined by repeating the fit with
all points moved to the upper or lower limits of their systematic uncertainty.

The comparison in Fig. 15 of 0%–20% $p$$+$Al with 0%–20% $p$$+$Au
modifications contrasts the weak modification in central $p$$+$Al collisions
with the strong modification, particularly at forward rapidity, in central
$p$$+$Au collisions. Figure 15 (a) shows $p$$+$Au with a nuclear modification
factor of about 0.85 at 6 GeV/$c$ (5–7 GeV/$c$ bin). A drop in modification at
high $p_{T}$ is expected due to shadowing (and possibly also kT broadening).
The comparison in Fig. 16 of 0%–20% $p$$+$Au with 0%–20% $d$$+$Au
modifications highlights the similarity between the two systems. A fit to the
ratio of $d$$+$Au to $p$$+$Au at forward rapidity was found to be 1.13 $\pm$
0.03(stat) $\pm$ 0.13(syst) and at backward rapidity is 0.94 $\pm$ 0.02(stat)
$\pm$ 0.07(syst).

In the comparison between 0%–20% $p$$+$Au and 0%–20% 3He$+$Au collisions shown
in Fig. 17, the ratio at forward rapidity is

$\overline{R_{{}^{3}{\rm HeAu}}/R_{{\rm pAu}}}=0.96\pm 0.03{\rm(stat)}\pm
0.05{\rm(syst)},$

which is consistent with unity. At backward rapidity the ratio is

$\overline{R_{{}^{3}{\rm HeAu}}/R_{{\rm pAu}}}=0.89\pm 0.03{\rm(stat)}\pm
0.08{\rm(syst)}.$

There may be deviations from the trend in the highest $p_{T}$ bin, but large
statistical uncertainties preclude firm conclusions. The results are
consistent with $J/\psi$ production being reduced for the 3He projectile, with
the backward rapidity ratio having a probability of 90% of being less than
one.

###  V.3 $\langle N_{\mathrm{c}oll}\rangle$ dependence

The $p_{T}$ integrated modifications as a function of $\langle
N_{\mathrm{c}oll}\rangle$ in each centrality bin are shown in Fig. 18 for the
three systems $p$$+$Al, $p$$+$Au and 3He$+$Au. No scaling with $\langle
N_{\mathrm{c}oll}\rangle$ is expected between $p$$+$Au and 3He$+$Au, because
3He$+$Au will have roughly three times as many collisions as $p$$+$Au in the
same centrality class. The $\langle N_{\mathrm{c}oll}\rangle$ dependence of
the $p$$+$Au modification is shown again in Fig. 19, where it is compared with
the $p_{T}$ integrated modification predicted by Du and Rapp. The theory
calculation shows both the CNM baseline and the result of the transport
calculations. At backward rapidity some nuclear absorption is expected. At
forward rapidity, it appears that the CNM effects are not strong enough to
explain the data. However, the model predicts a suppression beyond CNM effects
at backward rapidity for central collisions of approximately 10%.

Modifications that are due to CNM effects (including nuclear absorption) would
be expected to depend on the thickness of the target nucleus at the impact
parameter of the nucleon that was involved in the hard process. The nuclear
thickness can be written

$T_{A}(r_{T})=\int\rho_{A}(z,r_{T})~{}dz,$ (8)

where $\rho_{A}(z,r_{T})$ is the density distribution of nucleons in nucleus A
taken from the Woods-Saxon distribution used in the Glauber model discussed in
section II. The parameter $z$ is the location in the nucleus along the beam
direction, and $r_{T}$ is the transverse distance from the center of the
nucleus. $T_{A}(r_{T})$ is the average number of nucleons per unit area at the
projectile nucleon impact parameter $r_{T}$. To get the average value of
$T_{A}$ sampled for charmonium production within a given centrality bin, the
values of $T_{A}(r_{T})$ are weighted by the distribution of $r_{T}$ values
within the centrality bin, to reflect the number of projectile nucleons having
one or more inelastic collisions at that $r_{T}$, and additionally by the
probability of a hard process at that $r_{T}$ – which is proportional to
$T_{A}(r_{T})$.

Figure 20 shows the $p$$+$Al, $p$$+$Au and 3He$+$Au modifications plotted
versus $\langle T_{A}\rangle$, in each centrality bin. The modifications seem
to fall on a common curve within uncertainties, as would be expected if they
were primarily due to CNM effects.

The $\langle p_{T}^{2}\rangle$ values versus $\langle
N_{\mathrm{c}oll}\rangle$, shown in Fig. 21, fall on a common curve for all
three systems. The $\langle N_{\mathrm{c}oll}\rangle$ dependence is mild, with
$\langle p_{T}^{2}\rangle$ increasing from 3.3 in $p$$+$$p$ collisions to
approximately 4.0 in $p$$+$Au and 3He$+$Au collisions. The $\langle
p_{T}^{2}\rangle$ is very similar between forward and backward rapidity, as
was also observed in $d$$+$Au collisions Adare  _et al._ (2013a).

##  VI Summary and conclusions

We have presented invariant yields for inclusive $J/\psi$ production in
$p$$+$$p$, $p$$+$Al, $p$$+$Au and 3He$+$Au collisions at
$\sqrt{s_{{}_{NN}}}=200~{}\mathrm{GeV}$, and the corresponding nuclear
modifications for $p$$+$Al, $p$$+$Au and 3He$+$Au. The new $p$$+$Au results
are found to agree within uncertainties with the previous PHENIX $d$$+$Au
results Adare  _et al._ (2011a).

The $p$$+$Al modifications are found to be much weaker at all centralities
than those in $p$$+$Au. The 0%–100% centrality data for $p$$+$Al are found to
be well described in rapidity and $p_{T}$ by calculations containing only
shadowing effects from the EPPS16 NLO and nCTEQ15 NLO parameterizations, aside
from slightly underpredicting the modification at 4–6 GeV/$c$ at forward
rapidity.

The 0%–100% centrality $p$$+$Au and 3He$+$Au data are also compared with
calculations based on the EPPS16 NLO and nCTEQ15 NLO shadowing
parameterizations. At forward rapidity, the calculations describe the $p$$+$Au
and 3He$+$Au modifications well in both rapidity and $p_{T}$, again with the
exception of slightly underpredicting the modification at 4–6 GeV/$c$ at
forward rapidity. At backward rapidity, the calculations overpredict the
modifications. We found that adding the predicted nuclear absorption
modification taken from previous work to the backward rapidity $p_{T}$
integrated data reduced the modifications to values consistent with the data.

The ratio of the 3He$+$Au and $p$$+$Au modifications for the 0%–20% centrality
bin at forward rapidity is

$\overline{R_{{}^{3}{\rm HeAu}}/R_{{\rm pAu}}}=0.96\pm 0.03{\rm(stat)}\pm
0.05{\rm(syst)},$

which is smaller but consistent with unity. At backward rapidity it is

$\overline{R_{{}^{3}{\rm HeAu}}/R_{{\rm pAu}}}=0.89\pm 0.03{\rm(stat)}\pm
0.08{\rm(syst)}.$

The results are consistent with a reduction in the modification for the
heavier projectile case. Given the systematic uncertainty, the backward
rapidity ratio has a 90% probability of being less than 1.0.

For $p$$+$Au at forward rapidity, the nuclear modification vs $p_{T}$ shows
very strong centrality dependence, dropping to approximately 0.35 at low
$p_{T}$ in the most central 5% of collisions. At backward rapidity the
suppression is weaker for central collisions, but it changes more slowly.
Comparison with theory calculations that include EPS09 shadowing and a final
state transport model are able to reproduce the general shape of the $p_{T}$
dependence at each centrality, but greatly underpredict the suppression at low
$p_{T}$ for central collisions.

The $p_{T}$ integrated modification for $p$$+$Au drops steeply with centrality
at forward rapidity, reaching approximately 0.5 for the 5% most central
collisions. The modification at backward rapidity is found to have weak
centrality dependence. Because nuclear absorption is evidently important at
backward rapidity, the weak centrality dependence there is likely due to a
trade-off between anti-shadowing and nuclear absorption. It was found that
plotting the modification vs $\langle T_{A}\rangle$ for each centrality bin
caused them to fall on a common line for all three systems, as would be
expected if CNM effects dominate.

###### 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 also thank H.-S. Shao and J.-P.
Lansberg, et al., R. Vogt, X. Du, and R. Rapp for useful discussions and
providing unpublished predictions. 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 and SRC(CENuM) Programs through
NRF funded by the Ministry of Education and the Ministry of Science and ICT
(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.

## appendix

Figure 22:  $J/\psi$ invariant yield as a function of $y$ in MB $p$$+$$p$,
$p$$+$Al, $p$$+$Au, and 3He$+$Au collisions. Bars (boxes) around data points
represents point-to-point uncorrelated (correlated) uncertainties. There is
also a global uncertainty of 10.1%, 11.5%, 12.1% and 12.2% corresponding to
$p$$+$$p$, $p$$+$Al, $p$$+$Au and 3He$+$Au yields.

The invariant yields for all data sets are presented in this appendix. Figure
22 shows inclusive $J/\psi$ invariant yield as a function of rapidity in MB
$p$$+$$p$, $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions, and the invariant
yields in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions are scaled with $\langle
N_{\mathrm{c}oll}\rangle$ to compare with the invariant yield in $p$$+$$p$
collisions. In this and the following figures showing results of invariant
yield measurement, the bars (boxes) around data points represent point-to-
point uncorrelated (correlated) uncertainties. Figures. 25, 25, and 25 show
inclusive $J/\psi$ invariant yield as a function of rapidity in different
centrality of $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions, respectively.
Invariant yields in $p$$+$Al, $p$$+$Au, and 3He$+$Au collisions are scaled
with $\langle N_{\mathrm{c}oll}\rangle$, and the $p$$+$$p$ result is also
presented in each panel. Figures 28, 28, and 28 show inclusive $J/\psi$
invariant yield as a function of $p_{T}$ in different centrality of $p$$+$Al,
$p$$+$Au, and 3He$+$Au collisions, respectively.

At $\mbox{$p_{T}$}>2.5~{}\mathrm{GeV}/c$, $p_{T}$ binning was changed for
different data sets depending on statistics as described in Table 4. When
calculating the nuclear modification factor for $p_{T}$ bins of different
$\Delta\mbox{$p_{T}$}$ from the $p$$+$$p$ data, additional fits to the
$p$$+$$p$ data were performed to match the $p_{T}$ binning of the
$p/^{3}\mathrm{He}$+$A$ data.

Table 4:  $p_{T}$ bins in different data sets and centrality bins. All values are in $\mathrm{GeV}/c$.  $p$$+$$p$ | $p$$+$Al | $p$$+$Al | $p$$+$Au | $p$$+$Au | 3He$+$Au | 3He$+$Au
---|---|---|---|---|---|---
| 0%–100% | Centrality | 0%–100% | Centrality | 0%–100% | Centrality
0.00–0.25 | 0.00–0.25 | 0.00–0.25 | 0.00–0.25 | 0.00–0.25 | 0.00–0.25 | 0.00–0.25
0.25–0.50 | 0.25–0.50 | 0.25–0.50 | 0.25–0.50 | 0.25–0.50 | 0.25–0.50 | 0.25–0.50
0.50–0.75 | 0.50–0.75 | 0.50–0.75 | 0.50–0.75 | 0.50–0.75 | 0.50–0.75 | 0.50–0.75
0.75–1.00 | 0.75–1.00 | 0.75–1.00 | 0.75–1.00 | 0.75–1.00 | 0.75–1.00 | 0.75–1.00
1.00–1.25 | 1.00–1.25 | 1.00–1.25 | 1.00–1.25 | 1.00–1.25 | 1.00–1.25 | 1.00–1.25
1.25–1.50 | 1.25–1.50 | 1.25–1.50 | 1.25–1.50 | 1.25–1.50 | 1.25–1.50 | 1.25–1.50
1.50–1.75 | 1.50–1.75 | 1.50–1.75 | 1.50–1.75 | 1.50–1.75 | 1.50–1.75 | 1.50–1.75
1.75–2.00 | 1.75–2.00 | 1.75–2.00 | 1.75–2.00 | 1.75–2.00 | 1.75–2.00 | 1.75–2.00
2.00–2.25 | 2.00–2.25 | 2.00–2.25 | 2.00–2.25 | 2.00–2.25 | 2.00–2.25 | 2.00–2.25
2.25–2.50 | 2.25–2.50 | 2.25–2.50 | 2.25–2.50 | 2.25–2.50 | 2.25–2.50 | 2.25–2.50
2.50–2.75 | 2.50–2.75 | 2.50–2.75 | 2.50–2.75 | 2.50–2.75 | 2.50–2.75 | 2.50–3.00
2.75–3.00 | 2.75–3.00 | 2.75–3.00 | 2.75–3.00 | 2.75–3.00 | 2.75–3.00 | 3.00–3.50
3.00–3.25 | 3.00–3.25 | 3.00–3.25 | 3.00–3.25 | 3.00–3.25 | 3.00–3.25 | 3.50–4.00
3.25–3.50 | 3.25–3.50 | 3.25–3.50 | 3.25–3.50 | 3.25–3.50 | 3.25–3.50 | 4.00–5.00
3.50–3.75 | 3.50–3.75 | 3.50–3.75 | 3.50–3.75 | 3.50–3.75 | 3.50–3.75 | 5.00–7.00
3.75–4.00 | 3.75–4.00 | 3.75–4.00 | 3.75–4.00 | 3.75–4.00 | 3.75–4.00 |
4.00–4.25 | 4.00–4.50 | 4.00–5.00 | 4.00–4.25 | 4.00–4.50 | 4.00–4.50 |
4.25–4.50 | 4.50–5.00 | 5.00–7.00 | 4.25–4.50 | 4.50–5.00 | 4.50–5.00 |
4.50–4.75 | 5.00–6.00 |  | 4.50–4.75 | 5.00–7.00 | 5.00–7.00 |
4.75–5.00 | 6.00–7.00 |  | 4.75–5.00 |  |  |
5.00–5.25 |  |  | 5.00–5.25 |  |  |
5.25–5.50 |  |  | 5.25–5.50 |  |  |
5.50–5.75 |  |  | 5.50–5.75 |  |  |
5.75–6.00 |  |  | 5.75–6.00 |  |  |
6.00–6.50 |  |  | 6.00–6.50 |  |  |
6.50–7.00 |  |  | 6.50–7.00 |  |  |

Figure 23:  $J/\psi$ invariant yield as a function of $y$ in various
centrality bins of $p$$+$Al collisions. Bars (boxes) around data points
represents point-to-point uncorrelated (correlated) uncertainties. There is
also a global uncertainty of 13.6%, 12.2%, and 12.3% corresponding to 0%–20%,
20%–40% and 40%–72% centrality.

Figure 24:  $J/\psi$ invariant yield as a function of $y$ in various
centrality bins of $p$$+$Au collisions. Bars (boxes) around data points
represents point-to-point uncorrelated (correlated) uncertainties. There is
also a global uncertainty of 11.9%, 11.8%, 12.2%, 12.1%, 12.2% and 14.0%
corresponding to 0%–5%, 5%–10%, 10%–20%, 20%–40%, 40%–60%, and 60%–84%
centrality.

Figure 25:  $J/\psi$ invariant yield as a function of $y$ in various
centrality bins of 3He$+$Au collisions. Bars (boxes) around data points
represents point-to-point uncorrelated (correlated) uncertainties. There is
also a global uncertainty of 12.7%, 12.6%, and 13.4% corresponding to 0%–20%,
20%–40%, and 40%–88% centrality.

Figure 26:  $J/\psi$ invariant yield as a function of $p_{T}$ in various
centrality bins of $p$$+$Al collisions, and the yields in each centrality bin
are scaled for better visibility. Bars (boxes) around data points represents
point-to-point uncorrelated (correlated) uncertainties. There is also a global
uncertainty of 10.2%, 10.3%, 10.9%, and 10.4% corresponding to 0%–20%,
20%–40%, 40%–72%, and 0%–100% centrality.

Figure 27:  $J/\psi$ invariant yield as a function of $p_{T}$ in various
centrality bins of $p$$+$Au collisions, and the yields in each centrality bin
are scaled for better visibility. Bars (boxes) around data points represents
point-to-point uncorrelated (correlated) uncertainties. There is also a global
uncertainty of 11.8% for 60%–84% centrality and 10.2% for all remaining
centralities.

Figure 28:  $J/\psi$ invariant yield as a function of $p_{T}$ in various
centrality bins of 3He$+$Au collisions, and the yields in each centrality bin
are scaled for better visibility. Bars (boxes) around data points represents
point-to-point uncorrelated (correlated) uncertainties. There is also a global
uncertainty of 10.7% for 40%–88% centrality and 10.2% for all remaining
centralities.

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