PHENIX Collaboration

# Transverse-single-spin asymmetries of charged pions at midrapidity in
transversely polarized $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV

U.A. Acharya  Georgia State University, Atlanta, Georgia 30303, USA  C. Aidala
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040,
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  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  N.S.
Bandara  Department of Physics, University of Massachusetts, Amherst,
Massachusetts 01003-9337, 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  R. Belmont  University of Colorado, Boulder,
Colorado 80309, USA  Physics and Astronomy Department, University of North
Carolina at Greensboro, Greensboro, North Carolina 27412, USA  A. Berdnikov
Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia
Y. Berdnikov  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  L. Bichon  Vanderbilt University, Nashville, Tennessee 37235,
USA  B. Blankenship  Vanderbilt University, Nashville, Tennessee 37235, USA
D.S. Blau  National Research Center “Kurchatov Institute”, Moscow, 123098
Russia  National Research Nuclear University, MEPhI, Moscow Engineering
Physics Institute, Moscow, 115409, Russia  J.S. Bok  New Mexico State
University, Las Cruces, New Mexico 88003, USA  V. Borisov  Saint Petersburg
State Polytechnic University, St. Petersburg, 195251 Russia  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  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  M. Chiu  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  C.Y. Chi
Columbia University, New York, New York 10027 and Nevis Laboratories,
Irvington, New York 10533, USA  I.J. Choi  University of Illinois at Urbana-
Champaign, Urbana, Illinois 61801, USA  J.B. Choi  Deceased  Jeonbuk National
University, Jeonju, 54896, Korea  Z. Citron  Weizmann Institute, Rehovot
76100, Israel  M. Connors  Georgia State University, Atlanta, Georgia 30303,
USA  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  R. Corliss  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  N. Cronin
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  T. Csörgő  Eszterházy Károly University,
Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary  Institute for
Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian
Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49,
Budapest, Hungary  M. Csanád  ELTE, Eötvös Loránd University, H-1117 Budapest,
Pázmány P. s. 1/A, Hungary  T.W. Danley  Department of Physics and Astronomy,
Ohio University, Athens, Ohio 45701, USA  M.S. Daugherity  Abilene Christian
University, Abilene, Texas 79699, USA  G. David  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  K. DeBlasio  University of New Mexico, Albuquerque, New
Mexico 87131, USA  K. Dehmelt  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  A. Denisov
IHEP Protvino, State Research Center of Russian Federation, Institute for High
Energy Physics, Protvino, 142281, Russia  A. Deshpande  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  E.J. Desmond  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  A. Dion  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  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  H. En’yo  RIKEN Nishina Center for Accelerator-Based Science,
Wako, Saitama 351-0198, Japan  A. Enokizono  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  Physics Department,
Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan  R.
Esha  Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  S. Esumi  Tomonaga Center for the History of
the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  B. Fadem
Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA  W. Fan
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  N. Feege  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
D.E. Fields  University of New Mexico, Albuquerque, New Mexico 87131, USA  M.
Finger, Jr  Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech
Republic  M. Finger  Charles University, Ovocný trh 5, Praha 1, 116 36,
Prague, Czech Republic  D. Fitzgerald  Department of Physics, University of
Michigan, Ann Arbor, Michigan 48109-1040, USA  S.L. Fokin  National Research
Center “Kurchatov Institute”, Moscow, 123098 Russia  J.E. Frantz  Department
of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA  A. Franz
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  A.D. Frawley  Florida State University, Tallahassee, Florida
32306, USA  Y. Fukuda  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  P. Gallus  Czech Technical
University, Zikova 4, 166 36 Prague 6, Czech Republic  C. Gal  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  P. Garg  Department of Physics, Banaras Hindu University,
Varanasi 221005, India  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  H. Ge  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  M. Giles  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  F. Giordano
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  Y.
Goto  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, Japan  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  N. Grau  Department of Physics, Augustana
University, Sioux Falls, South Dakota 57197, USA  S.V. Greene  Vanderbilt
University, Nashville, Tennessee 37235, USA  M. Grosse Perdekamp  University
of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  T. Gunji  Center
for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1
Hongo, Bunkyo, Tokyo 113-0033, Japan  H. Guragain  Georgia State University,
Atlanta, Georgia 30303, USA  T. Hachiya  Nara Women’s University, Kita-uoya
Nishi-machi Nara 630-8506, Japan  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  RIKEN BNL Research Center, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  J.S. Haggerty  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
K.I. Hahn  Ewha Womans University, Seoul 120-750, Korea  H. Hamagaki  Center
for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1
Hongo, Bunkyo, Tokyo 113-0033, Japan  H.F. Hamilton  Abilene Christian
University, Abilene, Texas 79699, USA  J. Hanks  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
S.Y. Han  Ewha Womans University, Seoul 120-750, Korea  Korea University,
Seoul 02841, Korea  M. Harvey  Texas Southern University, Houston, TX 77004,
USA  S. Hasegawa  Advanced Science Research Center, Japan Atomic Energy
Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195,
Japan  T.O.S. Haseler  Georgia State University, Atlanta, Georgia 30303, USA
T.K. Hemmick  Department of Physics and Astronomy, Stony Brook University,
SUNY, Stony Brook, New York 11794-3800, USA  X. He  Georgia State University,
Atlanta, Georgia 30303, USA  J.C. Hill  Iowa State University, Ames, Iowa
50011, USA  K. Hill  University of Colorado, Boulder, Colorado 80309, USA  A.
Hodges  Georgia State University, Atlanta, Georgia 30303, USA  R.S. Hollis
University of California-Riverside, Riverside, California 92521, USA  K. Homma
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  B. Hong
Korea University, Seoul 02841, Korea  T. Hoshino  Hiroshima University,
Kagamiyama, Higashi-Hiroshima 739-8526, Japan  N. Hotvedt  Iowa State
University, Ames, Iowa 50011, USA  J. Huang  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  K. Imai  Advanced
Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane,
Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan  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  D. Ivanishchev  PNPI, Petersburg Nuclear Physics Institute, Gatchina,
Leningrad region, 188300, Russia  B.V. Jacak  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
M. Jezghani  Georgia State University, Atlanta, Georgia 30303, USA  X. Jiang
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Z. Ji
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  B.M. Johnson  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  Georgia State
University, Atlanta, Georgia 30303, USA  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  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  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, Korea  E.-J. Kim  Jeonbuk National University,
Jeonju, 54896, Korea  M. Kim  Department of Physics and Astronomy, Seoul
National University, Seoul 151-742, Korea  D. Kincses  ELTE, Eötvös Loránd
University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  A. Kingan  Department
of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  E. Kistenev  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  J. Klatsky  Florida State
University, Tallahassee, Florida 32306, 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  D.
Kotov  PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region,
188300, Russia  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  L. Kovacs  ELTE, Eötvös Loránd University, H-1117 Budapest,
Pázmány P. s. 1/A, Hungary  S. Kudo  Tomonaga Center for the History of the
Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  K. Kurita
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo
171-8501, Japan  Y. Kwon  Yonsei University, IPAP, Seoul 120-749, Korea  J.G.
Lajoie  Iowa State University, Ames, Iowa 50011, USA  D. Larionova  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  A.
Lebedev  Iowa State University, Ames, Iowa 50011, USA  S. Lee  Yonsei
University, IPAP, Seoul 120-749, Korea  S.H. Lee  Iowa State University, Ames,
Iowa 50011, USA  Department of Physics, University of Michigan, Ann Arbor,
Michigan 48109-1040, USA  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  M.J. Leitch  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Y.H. Leung
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  N.A. Lewis  Department of Physics, University
of Michigan, Ann Arbor, Michigan 48109-1040, USA  S.H. Lim  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  Pusan National
University, Pusan 46241, Korea  Yonsei University, IPAP, Seoul 120-749, Korea
M.X. Liu  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
X. Li  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
V.-R. Loggins  University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA  D.A. Loomis  Department of Physics, University of Michigan, Ann
Arbor, Michigan 48109-1040, USA  K. Lovasz  Debrecen University, H-4010
Debrecen, Egyetem tér 1, Hungary  D. Lynch  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  S. Lökös  ELTE, Eötvös
Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  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  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  M. Mendoza  University of California-Riverside,
Riverside, California 92521, USA  A.C. Mignerey  University of Maryland,
College Park, Maryland 20742, USA  A. Milov  Weizmann Institute, Rehovot
76100, Israel  D.K. Mishra  Bhabha Atomic Research Centre, Bombay 400 085,
India  J.T. Mitchell  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  M. Mitrankova  Saint Petersburg State
Polytechnic University, St. Petersburg, 195251 Russia  Iu. Mitrankov  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  Iu.
Mitrankov  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  G. Mitsuka  KEK, High Energy Accelerator Research Organization,
Tsukuba, Ibaraki 305-0801, Japan  RIKEN BNL Research Center, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  S. Miyasaka  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro,
Tokyo 152-8551, Japan  S. Mizuno  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  Tomonaga Center for the History of the
Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  M.M. Mondal
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  P. Montuenga  University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA  T. Moon  Korea University,
Seoul 02841, Korea  Yonsei University, IPAP, Seoul 120-749, Korea  D.P.
Morrison  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  B. Mulilo  Korea University, Seoul 02841, Korea  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
T. Murakami  Kyoto University, Kyoto 606-8502, Japan  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  J. Murata  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo
171-8501, Japan  K. Nagai  Department of Physics, Tokyo Institute of
Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan  K. Nagashima  Hiroshima
University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  T. Nagashima
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo
171-8501, Japan  J.L. Nagle  University of Colorado, Boulder, Colorado 80309,
USA  M.I. Nagy  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s.
1/A, Hungary  I. Nakagawa  RIKEN Nishina Center for Accelerator-Based Science,
Wako, Saitama 351-0198, Japan  RIKEN BNL Research Center, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  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  T. Niida
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  R. Nouicer  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  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  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  G. Nukazuka  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  A.S.
Nyanin  National Research Center “Kurchatov Institute”, Moscow, 123098 Russia
E. O’Brien  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  C.A. Ogilvie  Iowa State University, Ames, Iowa 50011,
USA  J.D. Orjuela Koop  University of Colorado, Boulder, Colorado 80309, USA
J.D. Osborn  Department of Physics, University of Michigan, Ann Arbor,
Michigan 48109-1040, USA  Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831, USA  A. Oskarsson  Department of Physics, Lund University, Box 118,
SE-221 00 Lund, Sweden  G.J. Ottino  University of New Mexico, Albuquerque,
New Mexico 87131, USA  K. Ozawa  KEK, High Energy Accelerator Research
Organization, Tsukuba, Ibaraki 305-0801, Japan  Tomonaga Center for the
History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
V. Pantuev  Institute for Nuclear Research of the Russian Academy of Sciences,
prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia  V. Papavassiliou  New
Mexico State University, Las Cruces, New Mexico 88003, USA  J.S. Park
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  S. Park  RIKEN Nishina Center for Accelerator-Based Science, Wako,
Saitama 351-0198, Japan  Department of Physics and Astronomy, Seoul National
University, Seoul 151-742, Korea  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  M. Patel  Iowa
State University, Ames, Iowa 50011, USA  S.F. Pate  New Mexico State
University, Las Cruces, New Mexico 88003, USA  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  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.P. Pisani  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  M. Potekhin  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  A. Pun  Department of Physics and
Astronomy, Ohio University, Athens, Ohio 45701, USA  M.L. Purschke  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
P.V. Radzevich  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  N. Ramasubramanian  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  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.
Runchey  Iowa State University, Ames, Iowa 50011, USA  A.S. Safonov  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  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  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  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  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  B.K. Singh  Department of Physics, Banaras
Hindu University, Varanasi 221005, India  C.P. Singh  Department of Physics,
Banaras Hindu University, Varanasi 221005, India  V. Singh  Department of
Physics, Banaras Hindu University, Varanasi 221005, India  M. Slunečka
Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic
K.L. Smith  Florida State University, Tallahassee, Florida 32306, USA  M.
Snowball  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
R.A. Soltz  Lawrence Livermore National Laboratory, Livermore, California
94550, USA  W.E. Sondheim  Los Alamos National Laboratory, Los Alamos, New
Mexico 87545, USA  S.P. Sorensen  University of Tennessee, Knoxville,
Tennessee 37996, USA  I.V. Sourikova  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  P.W. Stankus  Oak Ridge National
Laboratory, Oak Ridge, Tennessee 37831, USA  S.P. Stoll  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  T. Sugitate
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  A.
Sukhanov  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  T. Sumita  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  J. Sun  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
Z. Sun  Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  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  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  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.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  Y.S. Watanabe  Center for Nuclear Study, Graduate School of
Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  C.P.
Wong  Georgia State University, Atlanta, Georgia 30303, USA  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  C.L. Woody  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
L. Xue  Georgia State University, Atlanta, Georgia 30303, USA  C. Xu  New
Mexico State University, Las Cruces, New Mexico 88003, USA  Q. Xu  Vanderbilt
University, Nashville, Tennessee 37235, USA  S. Yalcin  Department of Physics
and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800,
USA  Y.L. Yamaguchi  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  I. Yoon  Department of Physics and Astronomy, Seoul National
University, Seoul 151-742, Korea  J.H. Yoo  Korea University, Seoul 02841,
Korea  I.E. Yushmanov  National Research Center “Kurchatov Institute”, Moscow,
123098 Russia  H. Yu  New Mexico State University, Las Cruces, New Mexico
88003, USA  Peking University, Beijing 100871, People’s Republic of China
W.A. Zajc  Columbia University, New York, New York 10027 and Nevis
Laboratories, Irvington, New York 10533, USA  A. Zelenski  Collider-
Accelerator Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  S. Zharko  Saint Petersburg State Polytechnic University, St.
Petersburg, 195251 Russia  L. Zou  University of California-Riverside,
Riverside, California 92521, USA

###### Abstract

In 2015, the PHENIX collaboration has measured single-spin asymmetries for
charged pions in transversely polarized $p$$+$$p$ collisions at the center of
mass energy of $\sqrt{s}=200$ GeV. The pions were detected at central
rapidities of $|\eta|<0.35$. The single-spin asymmetries are consistent with
zero for each charge individually, as well as consistent with the previously
published neutral-pion asymmetries in the same rapidity range. However, they
show a slight indication of charge-dependent differences which may suggest a
flavor dependence in the underlying mechanisms that create these asymmetries.

##  I Introduction

Single-spin asymmetries have been measured in hadronic collisions over a wide
range of energies for a number of final state particles [1, 2, 3, 4] and at
various rapidity regions. Initially, calculations that were based entirely on
perturbative quantum chromodynamics (pQCD) expected such asymmetries to be
suppressed as they generally required a helicity-flip which would be
proportional to the parton mass over the hard scale of the scattering process
[5], though recent calculations suggest that perturbative contributions may be
possible [6]. In contrast to the pQCD calculations, the measured single-spin
asymmetries, $A_{N}$ for pion production in the forward direction were found
to be quite sizeable [1, 2, 3].

Initially, two different mechanisms were suggested to describe these
asymmetries that attribute the effect to the nonperturbative parts of either
the parton distribution functions [7] or the fragmentation functions [8]. To
do so, the traditional concept of parton distribution and fragmentation
functions had to be extended to allow for explicit-transverse-momentum degrees
of freedom. In the transverse-momentum-dependent (TMD) framework, it is
however necessary that at least two scales are observed, the large scattering
scale and a smaller scale related to the intrinsic transverse momenta of
parton distribution and fragmentation. Both can be observed in semi-inclusive
deeply inelastic scattering (SIDIS), as was first successfully demonstrated in
[9] for both suggested effects.

Single-hadron final-state measurements in hadronic collisions have only one
scale, typically given by the transverse momentum of the detected hadron. As
such, a collinear framework that only relies on a single hard scale was
suggested to describe these asymmetries [10, 11]. In this framework, nonzero
asymmetries require nonperturbative higher-twist correlations either in the
initial state or the final state [12, 13]. Subsequently, it was suggested that
some of these correlation functions can be related to transverse-momentum
moments of the TMD functions [14], which unifies both approaches. Thus, global
fits of asymmetry measurements from SIDIS and hadron collisions have become
possible and provide additional precision on the underlying functions of
interest such as the quark transversity [15] or the Sivers [7] function in the
proton. The latest of these comes from [16], in which are found sizeable
contributions from both initial and final state effects. However, the final-
state effects dominate in hadronic collisions where the measured asymmetries
are large.

Pion transverse-single-spin asymmetries pick up both initial- and final-state
effects. While at forward rapidities, the asymmetries are quite sizeable in
the energy range of the Relativistic Heavy Ion Collider (RHIC) at Brookhaven
National Laboratory [2, 3], neutral-pion and $\eta$ mesons have been shown to
have vanishing asymmetries at central rapidities where the valence effects are
expected to be less pronounced [17]. In addition, in neutral-particle
asymmetries, potential cancellations between different parton flavors could
also cause these asymmetries to vanish. Charged pion asymmetries provide
different flavor sensitivity via the fragmentation functions and could test
whether such cancellations happen, as the dominant hard process at the
transverse momenta of this measurement is given by quark-gluon scattering. The
PHENIX detector at RHIC has measured charged pion single-spin asymmetries at
central rapidities in transversely polarized $p$$+$$p$ collisions at a center-
of-mass energy of $\sqrt{s}=200$ GeV.

In the following sections, the relevant detector systems and the accumulated
data sets will be described. The documentation of the charged pion selection
criteria, reconstruction efficiencies and various background corrections
follow before evaluating the various systematic uncertainties for the
asymmetry results which are then discussed.

##  II Data-sets

In 2015, the PHENIX experiment accumulated 60 pb-1 of transversely polarized
$p$$+$$p$ collision data. As both beams were polarized with average
polarizations of 60% (counter-clockwise, yellow beam) and 58% (clockwise, blue
beam) [18], two independent measurements were initially performed using the
spin information of one beam and averaging over the spin information of the
second beam. After confirming the consistency of the single-spin asymmetries
for each individual beam, the results were combined.

The PHENIX detector comprises a central Helmholtz double coil magnet that is
surrounded by two central detector arms that cover 90 degrees azimuthally
each, and a pseudorapidity range of $|\eta|<0.35$. A detailed detector
description can be found at [19], while only the detector sub-systems relevant
for this analysis will be presented in this paper. The central arms comprise
drift (DC) and pad chambers (PC) at radii of 2.02–2.46 m (DC), 2.50 m (PC1),
4.00 m (PC2), and 5.00 m (PC3) that measure charged-particle momenta via the
bending in the magnetic field. Between them, the gas ring-imaging Čerenkov
(RICH) detector is situated that helps identifying electrons, pions, and kaons
at momentum thresholds of 0.03, 4.7, and 16 GeV/$c$, respectively. Downstream
of the PCs, two types of electromagnetic calorimeters, EMCal, are located. Six
of eight sectors are instrumented with a lead-scintillator (PbSc) shashlik
calorimeter while the remaining two sectors are instrumented with a lead-glass
(PbGl) calorimeter. The EMCal measures the energy of electrons and photons, as
well as in part the energy of hadrons that start showering within the EMCal
detector. The PbSc (PbGl) EMCal corresponds to 0.85 (1.05) nuclear interaction
lengths. It also serves as a trigger detector for these particles, where
typically three different energy thresholds are set up with different
suppression factors in the data-taking.

Additionally, the beam-beam counters (BBCs), which comprise 64 quartz crystals
and photo-multipliers each, located at the forward and backward rapidities of
3.1$<|\eta|<$ 3.9 register hard collisions and the collision vertex position
and the start time for time-of-flight measurements. The BBCs also serve to log
the relative luminosities that have been accumulated in different spin states.
Zero-degree-calorimeters at rapidities of $|\eta|>6$ are used to cross check
these relative luminosities as well as the correct beam spin orientation using
the nonzero neutron single-spin asymmetries [20].

##  III Event and particle selection criteria

Pion-candidate events were selected if the lowest threshold of the EMCal
trigger condition was satisfied, which required that at least 1.4 GeV of
energy was deposited by the candidate particle in any of 4 $\times$ 4 EMCal
towers. The BBC reconstructed event vertex had to be within 30 cm of the
nominal beam interaction point along the beam axis. Pions were then selected
if their momentum was between 5 and 15 GeV/$c$ and the track matched the
energy deposit in the EMCal. The track had to fire the RICH, and the shower
shape in the EMCal had not to resemble that of an electromagnetic particle as
given by a likelihood ratio between electromagnetic and other particles. To
reduce the contamination by electrons in the pion data sample, the ratio of
deposited energy, $E$, in the EMCal and reconstructed momentum, $p$, had to be
$0.2<E/p<0.8$. At low $E/p$ values, electrons that are produced in decays
close to the EMCal and appear to have higher reconstructed momenta get
rejected. While other electrons deposit all of their energy in the EMCal and
typically get reconstructed at $E/p$ values around unity, pions only deposit a
fraction of their energy in the EMCal and can thus be selected.

To estimate the asymmetries for electron background an electron-enhanced
sample is selected in addition to the pion enhanced sample. For this sample
the $E/p$ and shower shape selections are inverted and even more RICH activity
was required. These two types of samples will be denoted as pion-enhanced and
electron-enhanced samples.

##  IV Asymmetry extraction

The charged-pion yields were extracted starting by selecting them with the
aforementioned criteria.

The single-spin asymmetries are then calculated for each beam, particle charge
and signal type as:

$A_{N}=\frac{1}{P}\frac{\sqrt{N_{L}^{\uparrow}N_{R}^{\downarrow}}-\sqrt{N_{L}^{\downarrow}N_{R}^{\uparrow}}}{\sqrt{N_{L}^{\uparrow}N_{R}^{\downarrow}}+\sqrt{N_{L}^{\downarrow}N_{R}^{\uparrow}}}\quad,$
(1)

where $N_{L/R}^{\uparrow/\downarrow}$ are the count rates to the left and
right with respect to the polarized beam direction and spin orientation, for
beams polarized up or down, respectively. $P$ is the average beam
polarization. Additionally, as the detector sits not exactly at 90 degrees to
the spin orientation, the asymmetry needs to be normalized with the average
cosine of the azimuthal angle $\langle|\cos\phi|\rangle$ of all particle
candidates $n$, $\langle|\cos\phi|\rangle=\sum_{i}|\cos\phi_{i}|/n$, where
$\phi_{i}$ is defined for each candidate $i$ relative to the spin orientation
of the polarized beam, along its beam axis.

To evaluate the signal and background fractions in each sample, the raw
candidate yields were corrected for the general reconstruction and acceptance
efficiencies that were evaluated in single-particle simulations in geant3
[21]. The trigger efficiencies were corrected by calculating the fraction of
minimum-bias events, for which pion candidates were also triggered by the
EMCal based trigger. The RICH efficiency was calculated similarly by comparing
the ratio of pion candidates that require the RICH selection criterion over
all candidates. Because electrons also fulfill the RICH requirements for lower
transverse momenta, the RICH efficiencies were corrected for this background
using pythia6 [22] simulations.

Given that pion candidates are triggered using an electromagnetic calorimeter,
the overall reconstruction efficiencies are much lower than for neutral pions
or electrons, see for example [23] for more details on pion cross section
measurements using PHENIX.

Figure 1: Transverse-momentum distribution of reconstructed particles from
data and MC simulation.

The composition of the raw data yields as a function of the transverse
momentum based on a pythia6 [22] Monte-Carlo (MC) simulation is shown in Fig.
1, which shows that overall the data is well-described by the MC. The
thresholds in the RICH for pions and kaons to emit Čerenkov light are clearly
visible at momenta of around 5 and 16 GeV/$c$, respectively. The simulations,
confirm that the selected sample is clearly dominated by pions, with electrons
being the main background. To calibrate the actual signal and background
fractions in the pion and electron enhanced data samples, the $E/p$
distributions in both pion and electron enhanced data samples were fit by the
shapes obtained from MC over an enlarged $E/p$ range. In particular, the
electron contribution can be obtained by fitting a Gaussian close to unity
which corresponds to the well-reconstructed electrons, that lose all their
energy in the calorimeter, while the shape for the pions was directly taken
from the simulation. The example for the raw yields and fits to the pion-
enhanced data sample can be seen in Fig. 2. The MC obtains the overall
magnitude of signal and background well, although slight differences between
MC and data based electron peaks are visible that are used to rescale the
background fraction. The background level in the pion-enhanced sample ranges
from 1 to 8% for the different transverse-momentum bins and charges.

Using the extracted electron background fractions in pion-enhanced ($r_{\pi}$)
and electron-enhanced ($r_{e}$) samples, as well as the sample’s respective
asymmetries ($A_{N}^{Sig}$, $A_{N}^{BG}$), the charged-pion asymmetries
$A_{N}^{\pi}$ can be obtained:

$A_{N}^{\pi}=\frac{r_{e}A_{N}^{Sig}-r_{\pi}A_{N}^{BG}}{r_{e}-r_{\pi}}\quad.$
(2)

The background asymmetries are consistent with zero, but their measured values
were taken and the statistical errors propagated. The uncertainties on the
signal to background fractions are assigned as systematic uncertainties as
described below.

Figure 2: Energy-over-momentum ratio distribution for negative pion and
electron candidates from data and MC simulation for the pion-enhanced data
sample.

##  V Systematic studies and cross checks

For the asymmetries, several methods were applied to ensure the validity of
the results. Apart from the previously discussed square root formula (Eq. 1),
the single-spin asymmetries were also extracted by the so-called relative
luminosity formula, where the relative luminosity
$\mathcal{R}=\mathcal{L}^{\uparrow}/\mathcal{L}^{\downarrow}$ between the
luminosities of the two spin orientations is applied to the count rate
differences and the count rate sum:

$A_{N}=\frac{1}{P}\frac{N_{L}^{\uparrow}-\mathcal{R}N_{L}^{\downarrow}}{N_{L}^{\uparrow}+\mathcal{R}N_{L}^{\downarrow}}\quad,$
(3)

and normalized by the acceptance factor $\langle|\cos\phi|\rangle$.

The asymmetries were additionally calculated as a function of the azimuthal
angle and fitted with a sine modulation, although the azimuthal acceptance is
limited at central rapidities in PHENIX. All three methods were compared using
T-tests and were found to be consistent with each other such that no further
systematic uncertainty was assigned.

The two polarized beams provide two independent measurements of the
asymmetries at central rapidities and can therefore be compared with each
other for consistency. Again using a T-test, the results were found to be
consistent with each other, such that both results could be combined in the
final result.

Another test is performed by randomizing the spin information of each of the
beam crossings and fills to artificially remove any physical asymmetry. This
so-called bunch-shuffling method is repeated many times and ideally should
produce a Gaussian distribution centered at zero with a width as large as the
statistical uncertainty. Any deviations would suggest additional systematic
uncertainties that had not been included. While the bunch-shuffled asymmetries
were on average consistent with zero, their widths were in some bins slightly
larger than the statistical uncertainties. This variation was assigned as
additional systematic uncertainty.

Lastly, the signal and background fractions that were described in the
previous section were varied according to the uncertainties obtained from the
fits to the $E/p$ distribution. These are the dominant systematic uncertainty,
but the measurements are dominated by the statistical uncertainties for both
charges and all transverse-momentum bins. Additionally, a global 3.4% scale
uncertainty exists due to the precision of the beam polarization evaluated by
the RHIC polarimetry group [18].

##  VI Results

The asymmetries are displayed in Fig. 3 as a function of the transverse
momentum and summarized in Table 1. As can be seen, the results are
statistically limited due to the fact that, in comparison to the neutral
pions, only a fraction of charged pions shower in the EMCal and fire triggers.
Nevertheless, smaller than one percent level precision can be reached at lower
transverse momenta, and the systematic uncertainties are generally much
smaller. While the asymmetries for each charge are consistent with zero, as
well as consistent with the previously measured neutral-pion asymmetries,
there are differences between positive and negative charges. The $\chi^{2}$
between $\pi^{+}$ and $\pi^{-}$ asymmetries is 9.04 for all five data points
together. This might indicate a dependence of the asymmetries on the
participating flavors of up and down quarks in particular, given that gluon-
related initial-state effects would show the same behavior for either pion
charge. Higher statistical precision, as is envisioned to be extracted with
the sPHENIX experiment [24], will tell whether different flavors produce
different asymmetries. It is worth noting that while the knowledge on the
higher-twist correlations is still very limited, both the Sivers functions as
well as the combinations of quark transversity and Collins fragmentation
functions, show clear differences for up- and down-quark related effects.

When comparing the asymmetries to the expected asymmetries based on the global
fit of data from SIDIS, other (predominantly forward single-spin asymmetries
in $p$$+$$p$ collisions and $e^{+}e^{-}$ data [16]), the PHENIX results at
higher transverse momenta are well described. In the midrapidity range, these
calculations are dominated by the higher twist quark-gluon-quark correlators
in the nucleon that are related to the quark Sivers functions. However, at
lower transverse momenta, the size and sign of the measured asymmetries,
especially for negative pions, appear to be slightly different.

Figure 3: Transverse-single-spin asymmetries as a function of transverse momentum for positive (closed [blue] triangles), negative (closed [red] circles), and the previously published neutral pions (open [black] boxes). The statistical uncertainties are shown by bars and the systematic uncertainties are shown by boxes. The lower [red] and upper [blue] curves show the predicted $A_{N}$ and their uncertainties based on Ref. [16].  Table 1: Final single-spin asymmetries for charged pions as a function of transverse momentum with statistical errors ($\Delta A_{N}$) and systematic uncertainties ($\delta A_{N}$). An additional 3.4% scaling uncertainty due to the beam polarization measurements is not shown.  | $\pi^{\pm}$ |  $p_{T}$ range | $A_{N}$ | $\Delta A_{N}$ | $\delta A_{N}$ |
---|---|---|---|---|---|---
|  | (GeV/$c$) | $(10^{-3})$ | $(10^{-3})$ | $(10^{-3})$ |
| $\pi^{-}$ | 5–6 | 6.30 | 4.67 | 0.03 |
|  | 6–7 | 9.98 | 4.73 | 0.95 |
|  | 7–8 | 3.71 | 6.60 | 0.55 |
|  | 8–11 | 0.44 | 6.85 | 0.10 |
|  | 11–15 | -9.27 | 11.76 | 5.60 |
| $\pi^{+}$ | 5–6 | -5.60 | 4.33 | 1.55 |
|  | 6–7 | -0.44 | 4.49 | 0.10 |
|  | 7–8 | -6.81 | 6.12 | 0.23 |
|  | 8–11 | 3.99 | 5.91 | 2.70 |
|  | 11–15 | 15.43 | 11.83 | 6.33 |

##  VII Summary

In summary, the PHENIX experiment has measured charged-pion transverse-single-
spin asymmetries at central rapidities. The precision has been greatly
improved from the previously published nonidentified charged-hadron
asymmetries [25] to a one-percent-level precision of charged pions over a
substantially larger range of transverse momenta. While the asymmetries
overall are consistent with zero, as well as the previously published neutral-
pion asymmetries in the same rapidity region, an indication for a charge-
dependent separation of the asymmetries is visible. If confirmed with higher
precision, it could indicate a flavor-dependent effect.

###### Acknowledgements.

We thank the staff of the Collider-Accelerator and Physics Departments at
Brookhaven National Laboratory and the staff of the other PHENIX participating
institutions for their vital contributions. We acknowledge support from the
Office of Nuclear Physics in the Office of Science of the Department of
Energy, the National Science Foundation, Abilene Christian University Research
Council, Research Foundation of SUNY, and Dean of the College of Arts and
Sciences, Vanderbilt University (USA), Ministry of Education, Culture, Sports,
Science, and Technology and the Japan Society for the Promotion of Science
(Japan), Natural Science Foundation of China (People’s Republic of China),
Croatian Science Foundation and Ministry of Science and Education (Croatia),
Ministry of Education, Youth and Sports (Czech Republic), Centre National de
la Recherche Scientifique, Commissariat à l’Énergie Atomique, and Institut
National de Physique Nucléaire et de Physique des Particules (France), J.
Bolyai Research Scholarship, EFOP, the New National Excellence Program (ÚNKP),
NKFIH, and OTKA (Hungary), Department of Atomic Energy and Department of
Science and Technology (India), Israel Science Foundation (Israel), Basic
Science Research and SRC(CENuM) Programs through NRF funded by the Ministry of
Education and the Ministry of Science and ICT (Korea). Ministry of Education
and Science, Russian Academy of Sciences, Federal Agency of Atomic Energy
(Russia), VR and Wallenberg Foundation (Sweden), the U.S. Civilian Research
and Development Foundation for the Independent States of the Former Soviet
Union, the Hungarian American Enterprise Scholarship Fund, the US-Hungarian
Fulbright Foundation, and the US-Israel Binational Science Foundation.

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