PHENIX Collaboration

# Transverse momentum dependent forward neutron single spin asymmetries 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  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  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  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  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  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. Firak  Debrecen University, H-4010 Debrecen, Egyetem tér 1,
Hungary  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  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  S.Y. Han  Ewha Womans
University, Seoul 120-750, Korea  Korea University, Seoul 02841, Korea  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  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, 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
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  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  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  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  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  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  M. 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  X. Li  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  S.H. Lim  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  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  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  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  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  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  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 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  S.I. Morrow  Vanderbilt
University, Nashville, Tennessee 37235, 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  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
S.F. Pate  New Mexico State University, Las Cruces, New Mexico 88003, USA  M.
Patel  Iowa State University, Ames, Iowa 50011, 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  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  X. Sun  Georgia State University, Atlanta,
Georgia 30303, 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  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 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
Y. Wu  University of California-Riverside, Riverside, California 92521, 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  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, Korea  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  L. Zou  University of
California-Riverside, Riverside, California 92521, USA

###### Abstract

In 2015, the PHENIX collaboration has measured very forward ($\eta>6.8$)
single spin asymmetries of inclusive neutrons in transversely polarized
proton-proton and proton-nucleus collisions at a center of mass energy of 200
GeV. A previous publication from this data set concentrated on the nuclear
dependence of such asymmetries. In this measurement the explicit transverse
momentum dependence of inclusive neutron single spin asymmetries for proton-
proton collisions is extracted using a bootstrapping unfolding technique on
the transverse momenta. This explicit transverse momentum dependence will help
improve the understanding of the mechanisms that create these asymmetries.

##  I Introduction

At the beginning of the era of polarized proton collisions at the relativistic
heavy ion collider (RHIC), a dedicated experiment based on a prototype zero-
degree calorimeter (ZDC) Adler  _et al._ (2001) was set up to initially study
very forward neutral pion asymmetries in transversely polarized proton
collisions in relation to earlier results that showed nonzero results Adams
_et al._ (1991). Instead of finding a neutral pion asymmetry, that was only
recently discovered at low transverse momentum by the RHICf experiment Kim
_et al._ (2020), a sizable neutron asymmetry was found in the forward
direction of the transversely polarized proton beam Fukao  _et al._ (2007).

Earlier theoretical studies related very forward neutron production to the
one-pion-exchange (OPE) model Soffer and Tornqvist (1992); D’Alesio and Pirner
(2000); Kopeliovich  _et al._ (1996) in which the exchange of one pion between
the proton and another colliding particle can create the outgoing neutron.
Such a model was reasonably successful in describing unpolarized, very forward
neutron production as previously observed at the ISR Flauger and Monnig
(1976). However, a simple pion exchange model would not be able to describe
any spin dependence of the observed neutron distributions. To accommodate
that, an interference with another particle exchange would be necessary to
have helicity-flip and nonflip amplitudes available that can create a single
spin left-right asymmetry. Within the general framework of Regge theory
Collins (2009), such an interference could be accomplished when adding also a
scalar meson exchange and the resulting pseudoscalar-scalar meson interference
would then create the asymmetry. Recent calculations of such an OPE based
description of very forward neutron single spin asymmetries Kopeliovich  _et
al._ (2011) are able to qualitatively describe the RHIC measurements which, by
now, include transversely polarized proton-proton collisions at $\sqrt{s}=$ 62
GeV, 200 GeV, as well as 500 GeV Adare  _et al._ (2013), although the
transverse momentum information enters only indirectly via the different
collision energies.

The very different asymmetries observed in proton-nucleus collisions Aidala
_et al._ (2018), with different sign and much larger magnitude, indicate that
at high impact parameters and at least for high-Z nuclei ultraperipheral
collisions (UPC) Mitsuka (2017) also contribute to these asymmetries in a very
different way. This data together with the recent very forward nonzero neutral
pion result Kim  _et al._ (2020) may provide crucial information to the
underlying mechanisms that create these asymmetries.

So far, none of these results have been extracted with an explicit transverse
momentum dependence while the different collision energies provide some
indirect information on it. Obtaining it can directly test the proposed
mechanism and the dependence that results from its theory calculation
Kopeliovich  _et al._ (2011). Therefore, extracting the actual transverse
momentum dependence is the focus of this publication. A substantial
understanding is required of the transverse momentum smearing in the PHENIX
ZDCs. Also needed are determinations of systematic uncertainties in unfolding
transverse momenta, which were studied via a Monte Carlo (MC) bootstrap method
as described later.

In the following sections, the detector description, analyzed data sets and
the forward neutron selection are covered. Next are described the procedure
for unfolding the neutron single spin asymmetries as a function of the
reconstructed transverse momenta to obtain the true transverse momentum
dependence. Then, the final results are presented before summarizing.

##  II Data sets

In 2015, the PHENIX experiment recorded polarized proton-proton and proton-
nucleus collision data at a center of mass energy of 200 GeV. In the proton-
proton collision data, the beams were transversely polarized with the spin
direction pointing vertically up or down with respect to the plane defined by
the accelerator ring.

Inclusive neutrons were detected with the ZDC, which comprise 3 modules of
Cu-W alloy absorbers layered with optical fibers of 1.7 nuclear interaction
lengths each (51 radiation lengths per module), covering a projected area of
10 cm by 10 cm transverse to the beam direction. The absorber layers of the
ZDC are tilted 45 degrees upward to maximize the light yield from Čerenkov
light. The location of the ZDCs is 18 m up and downstream of the PHENIX beam
interaction point, thus covering a range of pseudorapidity $\eta>6.8$. The ZDC
is used to measure the energy of forward neutrons, and its energy resolution
is about 20% for neutron energies of 100 GeV. Between the first and the second
module, approximately at the position of the maximal hadronic shower are
located scintillator strip detectors with a projected width of 15 mm
horizontally and vertically. This shower max detector (SMD) is used to
determine the position of the neutrons that are selected by calculating the
weighted average of the deposited energy for all strip positions. The position
resolution of the SMD for neutrons is $\approx 1$ cm. Additionally, the SMD is
used for local polarimetry of the polarized beams by making use of the nonzero
neutron asymmetries in proton-proton collisions and allowed to track the
transverse spin orientation or confirm the spin orientation to be rotated in
the longitudinal direction. See Ref. Adcox  _et al._ (2003) for a more
detailed detector description.

Collision events were selected for this result by a logical OR of north and
south ZDCs that require approximately an energy deposit of more than 15 GeV on
either detector. Within the proton collisions were accumulated about 35M
neutron events that were triggered by the ZDCs.

##  III Event and particle selection criteria

Neutron candidates in the north ZDC were selected by requiring more than 3% of
the total deposited energy to be in the second ZDC module. This effectively
rejects photon candidates, that deposited their energy in the first module due
to being electromagnetic showers. Also nonzero hits in both horizontal and
vertical SMDs are required to reliably estimate the neutron position and
transverse momentum. Furthermore, the reconstructed neutron energies were
selected between 40 and 120 GeV. The hit position as defined by the SMDs has
to be within 0.5 to 4 cm in radius from the nominal beam position.
Additionally, data under stable running conditions with no problems in the
polarized beam diagnostics were selected. The transverse momentum $P_{T}$ is
reconstructed from the neutron energy $E$, the radius of the average hit
position $r$ and the distance from the interaction point $z_{ZDC}$:

$P_{T}=\frac{r}{z_{ZDC}}E.$ (1)

The events that fulfill the above conditions are then binned in 4 transverse
momentum bins of [0.01, 0.06, 0.11, 0.16, 0.21] GeV/$c$ and 6 equidistant
azimuthal angular bins that cover full azimuth around the polarized beam
direction. The two spin states are kept separated for the unfolding, but to
obtain the asymmetries needed in the bootstrap method of the MC, they are also
directly calculated here as:

$A_{N}(\phi)=\frac{1}{\langle
P\rangle}\frac{N^{+}(\phi)-\mathcal{R}N^{-}(\phi)}{N^{+}(\phi)+\mathcal{R}N^{-}(\phi)},$
(2)

where $\langle P\rangle$ is the average beam polarization (for this running
period 52% RHIC Polarimetry Group (2013)) and $N^{\pm}$ are the yields of
neutrons in the up/down spin state as a function of azimuthal angle $\phi$
that is defined relative to the spin-up direction. $\mathcal{R}$ is the ratio
of accumulated luminosities for the down and up spin states, and is close to
unity in this analysis. The actual $A_{N}$ is then calculated by fitting a
sine modulation to it with magnitude and phase as free parameters.

As systematic uncertainties, the amount of charged particle background
(dominated by protons) and the uncertainty of the beam center position need to
be evaluated. Unlike other years, no charge veto counter in front of the ZDC
was installed in this running period. This resulted in a rather asymmetric
charged hadron background predominantly from protons that are swept into the
ZDC by the dipole magnet which joins and separates the two beams. The fraction
of charged hadron background was statistically subtracted on the spin
dependent yield level by applying the background fractions that were obtained
in the 2008 running period when the charge veto counter was installed. The
statistical uncertainties on these background fractions were then assigned as
systematic uncertainties on the resulting raw asymmetries.

The central beam position relative to the ZDC also cannot be perfectly
determined due to the large lever arm as well as varying beam conditions. As
such, the assigned beam position was artificially varied by 1 cm horizontally
and 0.5 cm vertically around the nominal beam position, respectively. All
neutron positions, transverse momenta, and azimuthal angles were recalculated
before evaluating the asymmetries. These variations were motivated by the
uncertainties based on two independent methods of reconstructing the beam
center positions using the ZDCs. The combined uncertainties on the asymmetries
from charged background and beam position are then used as a basis for
variation of the bootstrap MC method of unfolding the asymmetries as discussed
in the next section. The uncertainties due to charged background and beam
position remain negligible compared to the large systematic uncertainties this
unfolding introduces.

##  IV Transverse momentum unfolding

As hadronic showers develop a substantial size and the segmentation of the
SMDs is limited, the reconstructed neutron energy and in particular the
transverse momentum are smeared. The transverse momentum dependence of the
single spin asymmetries is however of much interest for the understanding of
the mechanism that creates these asymmetries.

We have performed detailed MC simulations using 5 different types of event
generators as input to full geant3 Brun  _et al._ (1994) simulations of the
forward region of PHENIX Togawa (2008); Adare  _et al._ (2014) including the
ZDCs, SMDs, the beam-pipe as well as the dipole magnet that merges and
separates the incoming and outgoing beams and is responsible for an asymmetric
spray from charged particles. These geant simulations have been shown to
describe these effects, as well as differences between top and bottom that
originate from the light collection and back scattering in the top part of the
ZDC. The composition, energy and momentum distributions of particles in the
far forward region are not very well understood in general, and therefore
different types of generators were used to gauge the impact of these
differences on the unfolded asymmetries. The three full generators pythia6.1
Sjostrand  _et al._ (2001), pythia8.2 Sjöstrand  _et al._ (2015) and dpmjet3.1
Roesler  _et al._ (2000) were applied, where in particular diffractive
processes are handled very differently.

Additionally, an empirical distribution of forward neutrons in longitudinal
and transverse momentum was used to mimic an OPE model. In this case, a pion
that balances the energy and momentum between the incoming proton and the
thrown neutron (i.e. $p\rightarrow\pi^{+}+n$) was collided with the other beam
using pythia8 again (i.e. $\pi+p$). Moreover, as the forward pA results have
indicated Aidala  _et al._ (2018), ultraperipheral collisions can also play a
role in forward neutron production although that will be more prominent in
proton-nucleus collisions. Therefore, the yield and distribution of photons
from the other beam was simulated using starlight Klein  _et al._ (2017) and
collided with the proton beam using pythia8 again.

As none of these generators is intrinsically spin dependent, spin effects ($w$
in the following expression) were simulated by reweighting generated events as
a function of true transverse momentum and azimuthal angle where the spin
state was randomly assigned. Three different functional forms were used in the
reweighting to provide as much flexibility as possible for the true transverse
momentum dependence of the single spin asymmetries. The most general
parameterization is a 3rd order polynomial in the transverse momentum with a
vanishing constant term due to the requirement for the asymmetry to vanish at
zero transverse momentum:

$w=\left(a\cdot P_{T,g}+b\cdot P_{T,g}^{2}+c\cdot
P_{T,g}^{3}\right)\sin(\phi_{g}+\lambda\cdot\pi),$ (3)

where $P_{T,g}$ and $\phi_{g}$ are the true transverse momenta and azimuthal
angles, respectively and $\lambda$ ($\pm 1$) is the spin state while $a$, $b$
and $c$ are free parameters that are varied. A second functional form (with
$a$ and $b>0$ free parameters) is based on a power-law behavior:

$w=\left(a\cdot P_{T,g}^{b}\right)\sin(\phi_{g}+\lambda\cdot\pi),$ (4)

and the last parameterization (with $a$ and $b$ free parameters) follows an
exponential form that eventually reaches an asymptotic constant:

$w=a\left(1-{\rm e}^{b\cdot P_{T,g}}\right)\sin(\phi_{g}+\lambda\cdot\pi).$
(5)

In the power law parameterization, only positive powers are allowed to avoid
unphysical nonzero asymmetries at zero transverse momentum.

For each set of parameters, functional form, and MC generator, the single spin
asymmetries were extracted from the reconstructed kinematic variables that
included these weights based on the true variables.

In a first step, the reconstructed asymmetries that were obtained from the
data are compared to the reconstructed asymmetries from MC for a large number
of variations of the parameters. The quality of a set of parameters,
functional form and MC generator in reproducing the data asymmetries was
evaluated by calculating the $\chi^{2}$ between the actual data points and the
smeared asymmetry points. While the MC statistics are generally large enough,
many functional forms can describe the data within the experimentally measured
uncertainties.

Figure 1: True asymmetry parameterizations as a function of transverse
momentum for (a) a 3rd order polynomial dependence ”Pol3,” (b) a power-law
dependence ”Power Law,” and (c) an exponential dependence ”Exponential”. The
shaded regions represent the regions where the $\chi^{2}$ between the smeared
asymmetries related to this parameterization and the asymmetries reconstructed
from data (solid [blue] squares) is below 10 units. The dashed lines represent
the best matching parameterizations. Also displayed are the unfolded
asymmetries (a) solid [dark green] squares, (b) solid [orange] circles, and
(c) solid [red] hyphens, as obtained from the best parameterizations of the
OPE generator. The rms ranges of unfolded asymmetries are visualized as shaded
boxes for the various MC generators.

Figure 2: Relative likelihood distributions of unfolded asymmetries for each
transverse momentum bin for all sets of parameters of each functional form
weighted by the inverse of its $\chi^{2}$. All different MC generators
distributions have been combined in these panels. The distributions of the 3rd
order polynomial parameterization (shaded [light green] area ”Pol3”), power
law behavior (vertically hatched [light orange] area ”Power Law”) and
exponential (horizontally hatched [light red] area ”Exponential”) have been
stacked in these figures. The overall central and rms values are also
displayed.

Figure 3: Neutron transverse single spin asymmetries as a function of the true
transverse momentum. The data points represent the unfolded asymmetries
obtained via the average over all parameterizations and MC generators. The
uncertainty boxes represent the systematic uncertainties due to the
parameterization, functional form, MC generator and unfolding procedure.

Figure 3 displays the functional forms probed for the OPE motivated MC
generator. The regions where a parametrization results in a $\chi^{2}$ below
10 units is also visualized to highlight the range of reasonable
parameterizations. Despite the different transverse momentum distributions of
forward neutrons in the different MC generators, their best asymmetry
distributions are very similar for each set of functional forms. In all
functional forms, a rapidly rising asymmetry is preferred at small $P_{T}$,
while at intermediate transverse momentum (within the second and third data
points) no large variation in the asymmetries is visible. The exponential
function generally prefers the asymptotic value to be reached already at these
transverse momenta. At higher transverse momenta above 0.2 GeV/$c$, the
sensitivity is very limited for all functional forms despite a nonzero
smearing into the observed range. As such, the slightly rising, constant or
even diminishing asymmetries at high transverse momenta can describe the
measured data reasonably well.

In a second step, the spin-dependent data yields that are two-dimensional in
reconstructed transverse momentum and azimuthal angle are unfolded using the
spin-dependent, weighted smearing matrices obtained for each set of
parameters, functional form and MC generator set. For the unfolding itself,
the TSVDUnfold package of root Brun and Rademakers (1997) based on a
regularized singular value decomposition Hocker and Kartvelishvili (1996) was
used. After the unfolding, the asymmetries are calculated from the unfolded
yields as described above. The best parameterization for each functional form
and MC generator is used to obtain the central point of the unfolded
asymmetries and statistical uncertainties. The impact of the variation of
parameters is evaluated by obtaining the root mean square (RMS) of the spread
of unfolded asymmetries which are weighted by the inverse of their respective
$\chi^{2}$ to take the quality of a parameter set into account. These
uncertainties are also displayed in Fig. 3, together with the unfolded
asymmetries using the OPE generator.

The variation of the unfolded asymmetries is displayed in Fig. 3 for each
transverse momentum bin and parameterization, while spreads from the different
MC generators had been combined equally. The central values from these
distributions have been taken as the final asymmetry values while the rms
value is taken as the uncertainty due to the various parameterizations.

In addition to these uncertainties, further systematic uncertainties are
studied by varying the regularization parameter in the TSVDUnfold method as
well as the uncertainties due to the statistical uncertainties on the smearing
matrices themselves. However, most of these values are within the boundaries
of the uncertainties obtained from the variation of parameters and functional
forms. Only those systematic contributions that exceed the aforementioned
uncertainties have been added in quadrature.

##  V Results

The inclusive neutron asymmetries obtained from the average of all
parameterizations and MC generators are displayed in Fig. 3 as a function of
the true transverse momentum. The final results are tabulated in Table 1.

The absolute values of the asymmetries are consistent with an increase with
transverse momentum but show an indication of leveling off at higher
transverse momenta. A simple linear dependence as suggested by Kopeliovich
_et al._ (2011), as well as the central values of transverse momentum
integrated asymmetries at different collision energies Adare  _et al._ (2014);
Fukao  _et al._ (2007), seems not necessarily to be preferred by the data.
However, a simple linear dependence cannot be excluded within uncertainties
either. From the MC reweighting exercise no substantial differences between
the different MC generators have been seen.

Taking into account the indication of very different asymmetries in
ultraperipheral collisions in proton-nucleus collisions Aidala  _et al._
(2018); Mitsuka (2017) and in particular a different sign, it appears that the
UPC contribution to the proton-proton collisions is limited in this $p_{T}$
region. This is expected given the electromagnetic nature of the interaction
being proportional with $Z^{2}$. However, in these inclusive results some
contribution from UPC events may remain, which could alter the transverse
momentum behavior in comparison to the purely hadronic theoretical
calculations.

Table 1: Neutron single spin asymmetries as a function of transverse momentum after unfolding transverse-momentum and azimuthal-angular smearing. $\Delta A_{N}$ corresponds to the statistical uncertainties while the last two columns specify the upper and lower systematic uncertainties $\delta A_{N}$. $\langle P_{T}\rangle$ (GeV/$c$) | $A_{N}$ |  sy$\Delta A_{N}$ | $\delta A_{N}$
---|---|---|---
0.043 | -0.039 |  $\pm$0.003 | +0.014 | -0.014
0.085 | -0.050 |  $\pm$0.002 | +0.013 | -0.013
0.132 | -0.055 |  $\pm$0.002 | +0.022 | -0.014
0.180 | -0.053 |  $\pm$0.001 | +0.017 | -0.017

##  VI Summary

In summary, the PHENIX experiment has measured for the first time the
transverse momentum dependence of very forward neutron single spin asymmetries
in proton-proton collisions at a center of mass energy of 200 GeV. With these
measurements the first reliable tests of the suggested mechanisms producing
such forward neutron asymmetries can be performed. While the uncertainties
from the unfolding are very sizable, a simple linear transverse momentum
dependence as suggested in Kopeliovich  _et al._ (2011) is not inconsistent;
however, the asymmetries appear to level off at higher transverse momenta.
Instead, a much slower rise of the asymmetries or even a turnaround at larger
transverse momenta is favored when considering the best parameterizations. To
understand the mechanisms in even more detail, the correlations with other
detector activity will be useful.

###### Acknowledgements.

We thank the staff of the Collider-Accelerator and Physics Departments at
Brookhaven National Laboratory and the staff of the other PHENIX participating
institutions for their vital contributions. We acknowledge support from the
Office of Nuclear Physics in the Office of Science of the Department of
Energy, the National Science Foundation, Abilene Christian University Research
Council, Research Foundation of SUNY, and Dean of the College of Arts and
Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture,
Sports, Science, and Technology and the Japan Society for the Promotion of
Science (Japan), Conselho Nacional de Desenvolvimento Científico e Tecnológico
and Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Natural
Science Foundation of China (People’s Republic of China), Croatian Science
Foundation and Ministry of Science and Education (Croatia), Ministry of
Education, Youth and Sports (Czech Republic), Centre National de la Recherche
Scientifique, Commissariat à l’Énergie Atomique, and Institut National de
Physique Nucléaire et de Physique des Particules (France), Bundesministerium
für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and
Alexander von Humboldt Stiftung (Germany), J. Bolyai Research Scholarship,
EFOP, the New National Excellence Program (ÚNKP), NKFIH, and OTKA (Hungary),
Department of Atomic Energy and Department of Science and Technology (India),
Israel Science Foundation (Israel), Basic Science Research 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.

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11institutetext: University of Washington, Seattle, Washington, USA

# Users’ Perception of Search Engine Biases and Satisfaction

Bin Han  Chirag Shah  Daniel Saelid

###### Abstract

Search engines could consistently favor certain values over the others, which
is considered as biased due to the built-in infrastructures. Many studies have
been dedicated to detect, control, and mitigate the impacts of the biases from
the perspectives of search engines themselves. In our study, we take the
perspective from end-users to analyze their perceptions of search engine
biases and their satisfaction when the biases are regulated. In the study, we
paired a real search page from search engine Bing with a synthesized page that
has more diversities in the results (i.e. less biased). Both pages show the
top-10 search items given search queries and we asked participants which one
do they prefer and why do they prefer the one selected. Statistical analyses
revealed that overall, participants prefer the original Bing pages and the
locations where the diversities are introduced are also associated with users’
preferences. We found out that users prefer results that are more consistent
and relevant to the search queries. Introducing diversities undermines the
relevance of the search results and impairs users’ satisfaction to some
degree. Additionally, we confirmed that users tend to pay more attention to
the top portion of the results than the bottom ones.

###### Keywords:

fairness search engine bias survey study

##  1 Introduction

Search engines often present results that are biased toward one subtopic,
view, or perspective due to the way they compute relevance and measure user
satisfaction. Among various types of search engine biases, one describes the
case where the search engines embed features that favor certain values over
the others [13, 7]. Many studies have attempted to detect, measure and
mitigate the impacts from search engines biases. All those works aimed to
address the issues from the source of the biases — search engines themselves.

In the previous study we conducted [under review], we took a different path to
inspect the problem from the aspect of end-users. We paired a real search page
and a synthesized page (more varieties in the search results, thus less
biased) and asked participants which one do they prefer. The results showed no
significant differences between the ratios of selecting two pages. However,
what remained unknown to us is that why did participants select the ones they
prefer? What are the reasonings underneath their preferences? Therefore, we
revisited this study and improved our survey design catering to our goals
(more details in Section 3). We would like to evaluate users’ perceptions of
the biases, thus hoping to reveal the reasoning of their preferences.
Additionally, we are interested in studying the effects on users’
satisfactions when the biases are regulated.

##  2 Background

Several prior studies have attempted to disclose and regulate biases, not just
limited in search engines, but also in wilder context of automated systems
such as recommender systems. For example, Collins et al. [4] confirmed the
position bias in recommender systems, which is the tendency of users to
interact with the top-ranked items than the lower-ranked ones, regardless of
their relevance. Ovaisi et al. [11] focused on the selection bias in the
learning-to-rank (LTR) systems, which occurs because “clicked documents are
reflective of what documents have been shown to the user in the first place. ”
They proposed a new approach to account of the selection bias, as well as the
position bias in LTR systems. Another bias, popularity bias, states the
negative influences of historical users’ feedback on the qualities of returned
items from current recommender systems. Boratto et al. [2] designed two
metrics to quantify such popularity bias and proposed a method to reduce the
biased correlation between item relevance and item popularity.

To reduce biases of the search engines, in other words, is to provide fairer
search results. Therefore, our problem is also closely related with fair-
ranking studies, in which the goal is to generate ranking lists with
nondiscriminatory and fair exposures of various defined groups, such as race,
gender, region etc. In our case, the groups are subtopics of the search
results and items in each group share similar values and topics. Chen et al.
[3] investigated the resume search engine and found out the gender-based
unfairness from the usage of demographic information in the ranking algorithm.
Zehlike et al. [14] defined the principles of ranked group fairness and the
fair top-K ranking problems. They proposed the FA*IR algorithm, which
maximizes the utility while satisfying ranked group fairness. In addition to
the mitigation of fairness at the group level, Biega et al. [1] proposed new
measures to capture, quantify, and mitigate unfairness at the individual
subjects level. They proposed a new mechanism — amortized fairness, to address
the position bias in the ranking problems.

Additionally, there are studies in the machine learning community that
investigated human’s perceptions of fairness and biases in algorithms.
Srivastaca et al. [12] conducted experiments to detect the most appropriate
notions of fairness that best captures human’s perception of fairness, given
different societal domains. They found out that simplest definition,
demographic parity, is aligned with most people’s understanding of fairness.
Grgić-Hlača et al. [8] deployed a survey study in the criminal risk prediction
domain to analyze how people people perceive and reason the fairness in the
decisions generated by algorithms. They found out that people’s concerns about
fairness are multi-dimensional and unfairness should not be just limited to
discrimination.

However, fewer studies in the fair-ranking domain have devoted to probe users’
consciousness towards the biases and their behaviors associated with their
awareness. Fewer studies have analyzed how users’ satisfactions are related
with the biases in general. Consequently, inspired by the bias/fairness
perception studies in the machine learning community, our work aims to dive
deeper in this direction.

##  3 Method

In this section, we present the algorithm used to generate the synthesized
search pages and the specifics of the survey design. We also enunciate the two
core questions we want to address from this study and three hypotheses that we
would like to test on. Notice that in sections below, “diversities”,
“varieties” and “differences” are equivalent. Introducing
diversities/varieties/differences could potentially reduce the biases;
“documents”, “items” and “results” are interchangeable, as they all mean the
search engine results.

### The Algorithm to Generate Synthesized Pages

To generate synthesized search pages that are less biased (more diverse in
subtopics), we implemented epsilon-0.3 algorithm (see Table 1), with
statistical parity as the fairness controller. We first group the documents
into $\mathcal{K}$ number of groups. Documents within each group share similar
topics, values, views etc. Therefore, each group can be treated as a subtopic
group. The fairness controller aims to provide a list of documents with equal
or close presence of different subtopic groups: given a search query, we
replace three items from the top-10 list with three lower ranked items,
proportionally to the frequencies of different subtopic groups in the top-10
list. For instance, suppose that there are two subtopic groups (A and B). If
the top-10 list has eight items from group A and two items from group B, we
would replace three out of eight items from group A at top-10 with three lower
ranked documents from group B. The replacement of the documents could happen
in different locations in the top-10 list. Therefore, there are two versions
of the algorithm. Version one, presented in Table 1, replaces three documents
from top-5 in the top-10 list. Version two is exactly the same as the version
one, except for that the replacement happens at bottom-5 in the top-10 list.
Please refer to Figure 1 for details.

Epsilon-0.3 Algorithm — Top-5 Replacement
---
1\. Group top-100 search documents into two subtopic clusters.
2\. Remove top-10 documents from the two clusters.
3\. Calculate cluster 1 (c1) and cluster 2 (c2) frequencies (freq) in top-10
documents.
4\. For three iterations:
if $freq_{c1}==freq_{c2}:$
Randomly select an index in the top-5 and swap with the next highest ranked
document from the cluster, from which the current document was taken.
Remove this document from the cluster list
else if $freq_{c1}>freq_{c2}:$
randomly select an index in the top-5 containing a c1 document, and swap it
with the next highest ranked document from c2. If there are no remaining
documents in c2, swap with a c1 document. Remove the swapped document
from cluster list
else if $freq_{c1}<freq_{c2}:$
randomly select an index in the top-5 containing a c2 document, and swap it
with the next highest ranked document from c1. If there are no remaining
documents in c1, swap with a c2 document. Remove the swapped document
from cluster list
Update frequencies
Remove the index that has been swapped in the top-5
Table 1: Algorithm to generate synthesized pages. The replacement happens in
top-5 from the top-10 list. Figure 1: In the left figure, we replace three
documents (marked in orange) from top-5 in the top-10 list with lower ranked
results. In the right figure, we replace three documents from bottom-5 in the
top-10 list.

We chose the epsilon-0.3 algorithm not only to be consistent with our previous
study, but also based on the fair-ranking work by Gao and Shah [6]. They
tested multiple fairness ranking strategies to probe the relationships among
fairness, diversity, novelty and relevance and found out that epsilon-greedy
algorithms could bring fairer representations of the search results without a
cost on the relevance. In the previous study, we experimented with the
variants of the algorithm — epsilon-0.1 and epsilon-0.2, and found out that
the replacement ratios (0.1 and 0.2) were too low. Therefore, we decided to
work with the epsilon-0.3 algorithm. Additionally, we worked with top-10 list
because popular search engines, such as Google and Bing, usually return 10
items per page as the default setting (though adjustable). Therefore, we
decided to stick with the default number of 10 documents.

### Survey Questions & Hypotheses

The two core study questions we would like to answer are:

  * •

Does introducing more varieties in the search engine results hinder users’
satisfaction?

  * •

What are the reasons of the users’ preferences?

We raised three testable hypotheses to potentially answer the questions:

  * •

H1: People do not care/notice the minute differences between the two search
results: even though we introduced lower ranked results into the top list to
add varieties, the differences might not be drastic enough for some
participants to notice. Or the participants might realize the differences but
they do not care about which one is better.

  * •

H2: The location where the differences present matters. When differences are
at the bottom of the search list, people do not care: intuitively, users might
treat the top-ranked results more seriously than the lower-ranked ones. Even
in top-10 list, the top-5 might receive different attention than the bottom-5.
Therefore, in our survey design, the replacement happens in both locations
(top-5 or bottom-5 in the top-10 list).

  * •

H3: People prefer results with high relevance as opposed to high diversity:
this hypothesis could answer the second question. Introducing lower ranked
search items means adding more diversities into the results, thus weakening
the potential biases of search engines that consistently favor some values
over the others. Unavoidably, however, adding lower ranked results would
sabotage the relevance of the search results, leading to consequences of
potentially lowering users’ satisfactions. Therefore, we want to see whether
they prefer higher relevance (more biased) or higher diversity (less biased).

### Survey Design

The survey starts with a consent form to be signed, which is followed by
several demographic questions (age group, gender and education background).
Then the participants are provided with instructions on how to complete the
survey through a quick demo (as shown in Figure 2). Once they are familiar
with the details, they may proceed to answer the questions. The survey has 20
rounds in total. Each round consists a pair of real Bing search page and a
synthesized page using the algorithm aforementioned, given a specific search
query. Participants have 30 seconds to read the query, compare the items
between two pages, and make a selection. Out of 20 rounds, we randomly select
10 rounds to perform the top-5 in top-10 replacement, while the rest rounds
receive bottom-5 in top-10 replacement.

Figure 2: The interface of the survey. The query shows in the search box at
the top. The paired pages consist of a real Bing search page and a synthesized
one. Participants can select whichever one they prefer and submit.

Based on the experience from the previous study, we thought 20 rounds provide
sufficiently large data for statistical analysis, while not fatiguing the
participants with too much information. Additionally, with some trial runs, we
found out that 30 seconds are enough to participants to compare the two pages
and make a selection. After each round, there is a reflection question (as
shown in Figure 3) on the reasons of the participants’ choice of pages:

  * •

“I did not notice any differences” addresses H1. The differences might not be
palpable enough for the participants.

  * •

“I noticed some differences but did not care. So I randomly picked up one.”
addresses H1. Participants might detect the discrepancies, but they do not
make a difference in users’ satisfaction.

  * •

“I noticed some differences and picked the one that had more results on the
same topic.” & “I noticed some differences and picked the one that had more
variety in the results.” They together address H3. More results on the same
topic means that the documents are more consistent with each other. More
varieties in the results represent the introduced lower ranked results.

Figure 3: Reflection question on the reasons of the participants’ choice of
preferences.

##  4 Results

We launched the survey in MTurk (Amazon Mechanical Turk) by creating a total
of 108 assignment. All the assignments were completed within 4 hours from the
launch time, with the average completion time as 16.4 minutes. With 137
participants completing the survey, we recorded 2,408 responses. After
removing invalid entries, such as users that did not complete the survey or
responses with empty selections, 111 participants with 2,134 responses were
used in the analysis. The basic demographic information in presented in Table
2.

Features | Groups | Count
---|---|---
Age Group | 22-28 | 571 (27%)
29-35 | 681 (32%)
36-49 | 488 (23%)
50-65 | 355 (17%)
Prefer Not To Say | 39 (2%)
Gender | Male | 1212 (57%)
Female | 863 (40%)
Non-binary | 20 (1%)
Prefer Not To Say | 39 (2%)
Education | High School | 158 (7%)
Bachelor | 1264 (59%)
Master | 653 (31%)
PhD (or similar) | 20 (1%)
Prefer Not To Say | 39 (2%)
Table 2: Basic demographic information of participants — age groups, gender,
and education background.

### Selection Ratios

Overall, 53.3% (N=1137) of the responses prefer the real search pages, while
46.7% (N=997) selected the synthesized versions. We ran Chi-Square goodness of
fit test, where the null hypothesis states that the expected frequencies of
selecting both choices are the same. The results turned out to be significant
at 0.01 significance level (p=0.002). In the bottom-5 replacement group
(N=1066), half responses chose the real pages and half chose the synthesized
ones. There is no difference in the selection ratios. However, we observed
significantly different selection ratios in the top-5 replacement group
(N=1068), where 56.6% (N=604) responses preferred the real pages while 43.4%
(N=464) liked the synthesized pages better. Goodness of fit test yield
significant result (p$<$1e-4)

Based on the separate tests in each replacement group, it seems that the
location where the diversities are introduced have an impact on users’
preferences. To further confirm the conjecture, we ran Chi-square test of
independence on two categorical variables: users’ preferences (real page or
synthesized page) and replacement group (top-5 or bottom-5). The result is
significant given p=0.003. It demonstrates that the location is associated
with participants’ preferences.

### Reasoning Analysis

The default four reasons, corresponding to the four choices in order, are “No
Diff”, “Diff Random”, “Diff Same Topic”, and “Diff Variety”. We probed the
reasons for three groups separately – the group that selected the real pages
(called “original” group), the group that selected the synthesized pages with
the top-5 replacement (“Top-5” group), and the group that selected the
synthesized pages with bottom-5 replacement (“Bottom-5” group). We only
presented the analysis of the four default answers here because users’ own
explanations are diverse, which will be analyzed in the discussion section.

The distributions of default answers for each group are exhibited in Table 3.
We noticed that within each group, “Diff Same Topic” dominated all other
answers. Within each group, we ran Chi-square goodness of fit test, in which
the null hypothesis states that the expected frequencies of the default
choices are the same. All three p-values are extremely small, indicating that
the observed frequencies are significantly different from the expected ones.

Groups | No Diff | Diff Random | Diff Same Topic | Diff Variety | p-value
---|---|---|---|---|---
Original | 117 | 222 | 461 | 310 | 2.2e-49
Top-5 | 49 | 87 | 186 | 132 | 7.5e-20
Bottom-5 | 55 | 104 | 218 | 147 | 1.5e-23
Table 3: Distributions of four default choices in each selection group.
p-values are from Chi-square goodness of fit test within each group.

##  5 Discussion

As defined in Section 3, the first question we would like to answer is “Does
introducing more varieties in the search engine results hinder users’
satisfaction?” From the analysis above, we showed that the proportion of
participants preferring the real pages is significantly higher than that of
the participants that selected the synthesized pages. Bringing up lower ranked
results into the top ranked list introduces more varieties and values in the
search results, thus weakening the biases of search engine in favoring certain
values. However, it potentially damages the relevance and consistence of the
results to the queries. Based on the result, it is reasonable to conjecture
that users’ satisfactions are impaired due to the added varieties, even though
the bias is mitigated.

The second question we would like to answer is “What are the reasons of the
users’ choices of preferences?”. We hypothesized that the site where the
varieties are introduced play a role in affecting users’ preferences. And we
indeed observed distinctions between the results from the two replacement
groups. Our results demonstrated that when the differences exhibit at
bottom-5, participants had no compelling tendency of picking up one over the
other. However, when they noticed the differences at top-5, they had a
significant inclination to choose the real Bing page. Our results are
consistent with some previous findings. [5] articulates that “most people use
very short, imprecise search terms and rarely click beyond the first page of
results. They also tend to believe that what comes at the top of the search
results must be the best result (p.13).” Kulshrestha et al. [10] also
mentioned that the top-ranked results are capable of shaping users’ opinions
about the topics, which demonstrates the importance of the search results’
location. In our case, we could interpret it as when the differences are shown
at top-5, participants will pay more attention to pinpoint the differences and
make a selection. The phenomenon was also observed in some users’ explanations
in the reflection questions. Some mentioned that “I like the first 3 results”,
“…at the top that explained …, “preferred the top X list”.

Additionally, from the reasoning analysis section, when participants picked up
the real pages, 40% of the reasons are “Diff Same Topic”. It means that they
did notice some differences between the two pages and they prefer the one with
more homogeneous results. Interestingly, for users that gave their own
explanations, many mentioned that the original pages provide more relevant and
reliable results than the synthesized ones. Introducing diversities by
replacing higher ranked results with lower ranked ones will reduce biases, but
potentially hinder the relevance of the search results, thus sabotaging users’
satisfaction as the aftermath.

However, when we applied the same reasoning analysis on the two replacement
groups, the results do not make logical sense even they are significant. Most
of the participants still selected “Diff Same Topic” as the reason, even
though they picked up the synthesized pages that have more varieties rather
than consistency. It means they believed that the real pages are more diverse
in terms of results. This could be contributed to two reasons: (1) the lower
ranked results are similar to the replaced higher ranked items, such that the
participants did not notice the diversities; (2) the definitions of similarity
and diversity on a topic are not unified and are different from each
participant. Consequently, they may pick up the ones that contain subjectively
similar results from their perspective, even though the pages are objectively
more diverse.

##  6 Conclusion

In our study, we designed a survey to assess users’ perceptions of search
engine biases, with the goal of diagnosing the reasoning underneath their
preferences of the real search pages or the synthesized pages. We also
investigated the effects of bias-mitigation on users’ satisfactions. We
noticed that overall, participants prefer the real search pages over the
synthesized ones with a significant higher ratio. It indicates that adding
more varieties makes the results less biased but less relevant and consistent
to the queries, which hurts users’ satisfactions. In addition, when the
diversities in the synthesized pages are present at the top-5, participants
tend to prefer the real pages. However, when they are at bottom-5, there is no
significant difference between the ratios of selecting two pages. It confirms
our hypothesis as well as some previous studies that the location where the
bias-mitigation happens is critical.

In terms of the future work, two directions could be considered. First, the
survey design could be improved. The reflection question in the first round
might give additional information of what will be asked in later rounds and
could potentially impact users’ selections. In addition, the response options
in the reflection questions are shown in a fixed order, which might generate
order bias [9]. Redesigning the format of reflection questions could
potentially improve the study results. Second, if more variables of interests
could be collected (if applicable) in addition to the demographic features,
mixed-effect regression models could be conducted to account for repeated
measures from the same individuals and the relationships among the various
features and preferences could be probed simultaneously.

## References

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