PHENIX Collaboration

# Nonperturbative-transverse-momentum broadening in dihadron angular
correlations in $\sqrt{s_{{}_{NN}}}=200$ GeV proton-nucleus collisions

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  A. Berdnikov  Saint Petersburg State Polytechnic
University, St. Petersburg, 195251 Russia  Y. Berdnikov  Saint Petersburg
State Polytechnic University, St. Petersburg, 195251 Russia  D.S. Blau
National Research Center “Kurchatov Institute”, Moscow, 123098 Russia
National Research Nuclear University, MEPhI, Moscow Engineering Physics
Institute, Moscow, 115409, Russia  M. Boer  Los Alamos National Laboratory,
Los Alamos, New Mexico 87545, USA  J.S. Bok  New Mexico State University, Las
Cruces, New Mexico 88003, USA  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  Chonbuk National University,
Jeonju, 561-756, 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  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  Debrecen
University, H-4010 Debrecen, Egyetem tér 1, Hungary  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
K. DeBlasio  University of New Mexico, Albuquerque, New Mexico 87131, USA  K.
Dehmelt  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  A. Denisov  IHEP Protvino, State
Research Center of Russian Federation, Institute for High Energy Physics,
Protvino, 142281, Russia  A. Deshpande  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  E.J. Desmond  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  A. Dion  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  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
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  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  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  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
J. Hanks  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  S. Hasegawa  Advanced Science Research
Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-
gun, Ibaraki-ken 319-1195, Japan  T.O.S. Haseler  Georgia State University,
Atlanta, Georgia 30303, USA  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  C. Kim  University of California-Riverside, Riverside,
California 92521, USA  Korea University, Seoul, 02841, Korea  E.-J. Kim
Chonbuk National University, Jeonju, 561-756, Korea  M. Kim  RIKEN Nishina
Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  D. Kincses  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P.
s. 1/A, Hungary  E. Kistenev  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  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  A. Lebedev  Iowa State
University, Ames, Iowa 50011, USA  S. Lee  Yonsei University, IPAP, Seoul
120-749, Korea  S.H. Lee  Iowa State University, Ames, Iowa 50011, USA
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  M.J. Leitch  Los Alamos National Laboratory,
Los Alamos, New Mexico 87545, USA  Y.H. Leung  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
N.A. Lewis  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  X. Li  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  S.H. Lim  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  Yonsei University, IPAP, Seoul 120-749, Korea  M.X. Liu  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  V.-R. Loggins
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  S.
Lökös  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A,
Hungary  Eszterházy Károly University, Károly Róbert Campus, H-3200 Gyöngyös,
Mátrai út 36, Hungary  K. Lovasz  Debrecen University, H-4010 Debrecen,
Egyetem tér 1, Hungary  D. Lynch  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  T. Majoros  Debrecen University,
H-4010 Debrecen, Egyetem tér 1, Hungary  Y.I. Makdisi  Collider-Accelerator
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
M. Makek  Department of Physics, Faculty of Science, University of Zagreb,
Bijenička c. 32 HR-10002 Zagreb, Croatia  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  D.E. Mihalik  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
A. Milov  Weizmann Institute, Rehovot 76100, Israel  D.K. Mishra  Bhabha
Atomic Research Centre, Bombay 400 085, India  J.T. Mitchell  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
I. Mitrankov  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  G. Mitsuka  KEK, High Energy Accelerator Research Organization,
Tsukuba, Ibaraki 305-0801, Japan  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  RIKEN BNL Research Center, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  S. Miyasaka  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro,
Tokyo 152-8551, Japan  S. Mizuno  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  Tomonaga Center for the History of the
Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  P. Montuenga
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  T.
Moon  Yonsei University, IPAP, Seoul 120-749, Korea  D.P. Morrison  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
S.I. Morrow  Vanderbilt University, Nashville, Tennessee 37235, USA  T.
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  RIKEN Nishina
Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  T.
Nagashima  Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro,
Toshima, Tokyo 171-8501, Japan  J.L. Nagle  University of Colorado, Boulder,
Colorado 80309, USA  M.I. Nagy  ELTE, Eötvös Loránd University, H-1117
Budapest, Pázmány P. s. 1/A, Hungary  I. Nakagawa  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  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  T. Niida  Tomonaga Center for the History of
the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan  R. Nishitani
Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan  R.
Nouicer  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  T. Novák  Eszterházy Károly University,
Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary  Institute for
Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian
Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49,
Budapest, Hungary  N. Novitzky  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  A.S. Nyanin
National Research Center “Kurchatov Institute”, Moscow, 123098 Russia  E.
O’Brien  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  C.A. Ogilvie  Iowa State University, Ames, Iowa 50011, USA
J.D. Orjuela Koop  University of Colorado, Boulder, Colorado 80309, USA  J.D.
Osborn  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  A. Oskarsson  Department of Physics, Lund University, Box
118, SE-221 00 Lund, Sweden  G.J. Ottino  University of New Mexico,
Albuquerque, New Mexico 87131, USA  K. Ozawa  KEK, High Energy Accelerator
Research Organization, Tsukuba, Ibaraki 305-0801, Japan  Tomonaga Center for
the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305,
Japan  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  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  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  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.J. Skoby
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040,
USA  M. Slunečka  Charles University, Ovocný trh 5, Praha 1, 116 36, Prague,
Czech Republic  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  S. Suzuki  Nara Women’s University, Kita-uoya Nishi-
machi Nara 630-8506, Japan  J. Sziklai  Institute for Particle and Nuclear
Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences
(Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary  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 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  Z. Wang  Baruch College, City University of New York, New
York, New York, 10010 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  C.L.
Woody  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  C. Xu  New Mexico State University, Las Cruces, New Mexico
88003, USA  Q. Xu  Vanderbilt University, Nashville, Tennessee 37235, USA  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  RIKEN BNL Research Center,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  H. Yamamoto  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A. Yanovich  IHEP
Protvino, State Research Center of Russian Federation, Institute for High
Energy Physics, Protvino, 142281, Russia  J.H. Yoo  Korea University, Seoul,
02841, Korea  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  I. Yoon  Department of Physics and Astronomy,
Seoul National University, Seoul 151-742, Korea  H. Yu  New Mexico State
University, Las Cruces, New Mexico 88003, USA  Peking University, Beijing
100871, People’s Republic of China  I.E. Yushmanov  National Research Center
“Kurchatov Institute”, Moscow, 123098 Russia  W.A. Zajc  Columbia University,
New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533,
USA  A. Zelenski  Collider-Accelerator Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  S. Zharko  Saint Petersburg State
Polytechnic University, St. Petersburg, 195251 Russia  L. Zou  University of
California-Riverside, Riverside, California 92521, USA

###### Abstract

The PHENIX collaboration has measured high-$p_{T}$ dihadron correlations in
$p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV.
The correlations arise from inter- and intra-jet correlations and thus have
sensitivity to nonperturbative effects in both the initial and final states.
The distributions of $p_{\rm out}$, the transverse momentum component of the
associated hadron perpendicular to the trigger hadron, are sensitive to
initial and final state transverse momenta. These distributions are measured
multi-differentially as a function of $x_{E}$, the longitudinal momentum
fraction of the associated hadron with respect to the trigger hadron. The
near-side $p_{\rm out}$ widths, sensitive to fragmentation transverse
momentum, show no significant broadening between $p$$+$Au, $p$$+$Al, and
$p$$+$$p$. The away-side nonperturbative $p_{\rm out}$ widths are found to be
broadened in $p$$+$Au when compared to $p$$+$$p$; however, there is no
significant broadening in $p$$+$Al compared to $p$$+$$p$ collisions. The data
also suggest that the away-side $p_{\rm out}$ broadening is a function of
$N_{\rm coll}$, the number of binary nucleon-nucleon collisions, in the
interaction. The potential implications of these results with regard to
initial and final state transverse momentum broadening and energy loss of
partons in a nucleus, among other nuclear effects, are discussed.

##  I Introduction

High energy collisions of protons with nuclei provide a testing ground for
quantum chromodynamics (QCD). In particular, when large transverse momentum
scales are involved, the collisions can probe the quark and gluon,
collectively referred to as partons, structure of the nucleus. Proton-nucleus
($p$$+$A) collisions have traditionally been used as a control to identify
final-state nuclear effects in high energy nucleus-nucleus collisions where a
strongly interacting quark-gluon plasma (QGP) is formed Adcox  _et al._
(2005). However, measurements in $p$$+$A collisions have revealed many
surprising results that have yet to be completely reconciled with each other;
these have shown that understanding and explaining many different “cold”
nuclear matter effects is already a challenging endeavor Hen  _et al._ (2017);
Chatrchyan  _et al._ (2013); Cronin  _et al._ (1975); Adcox  _et al._ (2002).

For example, in the initial-state, nuclei are known to be more complex than
just a simple linear superposition of nucleons (see e.g. Ref. Hen  _et al._
(2017) for a review). Nuclear parton distribution functions (PDFs) are known
to have several regions where they deviate from simple superpositions of
nucleon PDFs as a function of the longitudinal momentum fraction $x$ that the
parton carries of the nucleon. Understanding how the partonic degrees of
freedom lead to nuclear structure will be a major achievement of QCD; however,
there is still significant effort required in understanding the physical
origin of these measured nuclear modifications. Final-state hadronization from
a nucleus can also be modified similarly to nuclear PDFs in the initial state.
In particular, semi-inclusive deep-inelastic scattering (SIDIS) experiments
have shown that high $z$ hadrons are suppressed in electron-nucleus relative
to electron-deuterium collisions Airapetian  _et al._ (2003), where $z$ is the
longitudinal momentum fraction of the outgoing hadron with respect to the
fragmenting parton. This suppression was found to be dependent on the nuclear
target size Airapetian  _et al._ (2007). In addition, a particle species
dependence was observed, which may reflect differences in the nuclear
modification of quark and/or antiquark fragmentation functions and possible
differences in meson versus baryon production from nuclei Airapetian  _et al._
(2003, 2007).

Several proposed signatures of the QGP have also been measured in $p$$+$A
collisions where the overall system size created in the collision was once
expected to be too small. Collective behavior has been observed across large
pseudorapidity ranges in high multiplicity $p$$+$A collisions Chatrchyan  _et
al._ (2013); Aad  _et al._ (2013); Aaij  _et al._ (2016); Adamczyk  _et al._
(2015); Aidala  _et al._ (2017, 2018a). Additionally, the enhancement of
strangeness in hadron production in high multiplicity $p$$+$A collisions has
recently been measured Adam  _et al._ (2016). Surprisingly, both of these
phenomena have also been observed in high multiplicity $p$$+$$p$ collisions at
Large-Hadron-Collider (LHC) energies Aad  _et al._ (2016a); Adam  _et al._
(2017). However, the suppression of high $p_{T}$ inclusive hadrons or jets in
$p$$+$A collisions with respect to $p$$+$$p$ collisions has not been measured
Adler  _et al._ (2003a); Aad  _et al._ (2015). These results were first used
to establish final-state QGP interactions as the cause of high $p_{T}$ hadron
suppression in nucleus-nucleus collisions Adcox  _et al._ (2002); Chatrchyan
_et al._ (2011). However, the recent addition of collective and strange hadron
measurements but lack of hadron suppression in $p$$+$A collisions has
complicated the idea that a QGP may be formed in smaller collision systems.

Another unexpected physical effect in $p$$+$A collisions is the so-called
“Cronin” effect, which refers to an enhancement in the inclusive hadron
$p_{T}$ spectrum with respect to $p$$+$$p$ collisions at moderate $p_{T}$ of
approximately $2<\mbox{$p_{T}$}<6$ GeV/$c$ which persists over a wide range of
center-of-mass energies Cronin  _et al._ (1975); Adler  _et al._ (2003a); Aad
_et al._ (2016b). This effect has also been observed at moderate $p_{T}$ in
electron-nucleus collisions Airapetian  _et al._ (2003), where a significant
dependence of the enhancement on the longitudinal momentum fraction $z$ of the
hadron was found Airapetian  _et al._ (2007). While this was first proposed to
be due to multiple scattering effects in the nuclear medium, more recent
measurements have shown that hadronization also plays a role Adare  _et al._
(2013). Additional measurements that go beyond single inclusive hadrons may be
able to shed further light on this phenomenon in $p$$+$A collisions. For
example, dijet measurements in the kinematic regime of the Cronin effect have
shown that the initial-state partonic transverse momentum is a function of the
nucleus size Corcoran  _et al._ (1991), which has not been observed at large
jet transverse momentum Adam  _et al._ (2015).

The lack of understanding of the underlying physical sources of these
phenomena motivates measurements in new kinematic regimes with different
observables. Here we present a measurement of dihadron angular correlations in
$p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions at midrapidity collected by the
PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). The unique
capabilities of RHIC allow for a nuclear size dependence to be studied in
$\sqrt{s_{{}_{NN}}}$ = 200 GeV $p$$+$A collisions. High $p_{T}$ two-particle
angular correlations have been theoretically considered as a probe for energy
loss in $p$$+$A and A+A collisions via their transverse momentum broadening
Baier  _et al._ (1997, 2000); Tannenbaum (2017); however, the various
aforementioned effects should also be considered as they will play a role in
both collision systems. The present measurements will contribute to our
understanding of the rich phenomena in hadronic interactions involving nuclei.

##  II Methods

In 2015, the PHENIX experiment Adcox  _et al._ (2003a) at RHIC collected data
from $p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$
GeV. A total minimum bias integrated luminosity of 60, 0.69, and 0.21 pb-1 for
$p$$+$$p$, $p$$+$Al, and $p$$+$Au, respectively, was used for the analysis of
dihadron correlations. From these total integrated luminosities, data quality
assurance and collision vertex position $|z_{\rm vtx}|<30$ cm cuts were
applied. The PHENIX detector measures two-particle angular correlations of
neutral pions and charged hadrons, $\pi^{0}$-h±, with its electromagnetic
calorimeter (EMCal) and drift chamber (DC) and pad chamber (PC) tracking
system. These central arms cover an azimuthal range of $\Delta\phi$
$\approx\pi$ radians and a pseudorapidity range of $|\eta|<0.35$. Detailed
descriptions of the PHENIX central arms can be found in Refs. Adcox  _et al._
(2003b); Aphecetche  _et al._ (2003). In $p$$+$A collisions, the centrality
class is determined with the forward beam-beam counters (BBCs) Ikematsu  _et
al._ (1998), where the centrality percentiles are defined by the multiplicity
measured in the nucleus-going BBC following the procedure in Ref. Adare  _et
al._ (2014).

The EMCal is used to identify high $p_{T}$ neutral pions to construct the
correlation functions. A high-energy-photon trigger is used to identify events
with a high $p_{T}$ photon from a $\mbox{$\pi^{0}$}\rightarrow\gamma\gamma$
decay. Photons are identified using a shower shape cut that removes charged
hadrons as well as most high energy clusters that overlap with another photon.
The neutral pions are reconstructed via their two photon decay, where the
granularity of the EMCal allows $\pi^{0}$ reconstruction up to approximately
20 GeV in this channel. In this analysis neutral pions are collected in the
$p_{T}$ range $5<\mbox{$p_{T}$}<9$ GeV/$c$.

The DC and PC tracking system measures nonidentified charged hadrons in the
event with the triggered high $p_{T}$ photon. Two PCs, located radially behind
the DC, are used to identify and match tracks in the DC with hits in the PCs.
This track matching condition reduces background from secondary tracks due to
conversions or decays. A ring-imaging $\check{\textrm{C}}$erenkov system is
also used to reject electrons from the charged hadron sample. With these
conditions, the DC and PC tracking system is also used to reject tracks in the
EMCal that happen to shower and are thus background for the
$\mbox{$\pi^{0}$}\rightarrow\gamma\gamma$ identification. Nonidentified
charged hadrons are collected between $0.5<\mbox{$p_{T}$}<10$ GeV/$c$ in
correlation with the high $p_{T}$ $\pi^{0}$ to study the correlations in as
large a range as allowed by the data.

The correlations are constructed similarly to previous PHENIX two-particle
correlation analyses, see e.g. Refs. Adler  _et al._ (2006); Adare  _et al._
(2010); Aidala  _et al._ (2018b). Per-trigger yields are constructed for a
given observable, such as $\Delta\phi$, which show the yield of charged
hadrons per-trigger $\pi^{0}$ and are defined by

$\frac{1}{N_{\rm trig}}\frac{dN}{d\mbox{$\Delta\phi$}}=\frac{1}{N_{\rm
trig}}\frac{dN/d\mbox{$\Delta\phi$}_{\rm raw}}{dN/d\mbox{$\Delta\phi$}_{\rm
mixed}\epsilon(\mbox{$p_{T}$})}$ (1)

To account for the PHENIX acceptance, the raw correlations are divided by a
mixed-event background correlation function, $dN/d\mbox{$\Delta\phi$}_{\rm
mixed}$. The background correlation is constructed with neutral pions and
charged hadrons from the same data taking period but different event number;
the events are required to have a similar centrality and z-vertex. To account
for the efficiency of the PHENIX detector, the correlation functions are also
corrected by a charged hadron efficiency defined as $\epsilon(\mbox{$p_{T}$})$
in Eq. 1, which is determined with a single particle Monte Carlo generator as
well as a full GEANT description of the PHENIX apparatus Adler  _et al._
(2003b). After these corrections, the correlations are normalized by the total
number of trigger particles measured to construct the per-trigger yield and
correspond to full azimuthal acceptance within $|\eta|<0.35$.

Figure 1: A schematic diagram showing a dihadron correlation in the transverse
plane. Vector quantities are shown in bold. The red vectors are the two
partons, which are acoplanar due to initial-state partonic $k_{T}$, while the
two black vectors are the measured trigger and associated hadron, slightly
displaced from the partons due to final-state transverse momentum $j_{T}$ from
fragmentation. The quantities $p_{\rm out}$ and $x_{E}$ are shown as blue and
green vectors, respectively.

Correlation functions are typically constructed in terms of the azimuthal
angle $\Delta\phi$ between the trigger and associated particle. Here we choose
to construct the correlations as a function of the momentum space vector
component $p_{\rm out}$ and $x_{E}$, defined as

$\mbox{$p_{\rm out}$}=|{\bf{p}}_{T}^{\rm assoc}|\sin\mbox{$\Delta\phi$}$ (2)

and

$\mbox{$x_{E}$}=-\frac{{\bf{p}}_{T}^{\rm trig}\cdot{\bf{p}}_{T}^{\rm
assoc}}{|{\bf{p}}_{T}^{\rm trig}|^{2}}=-\frac{|{\bf{p}}_{T}^{\rm
assoc}|}{|{\bf{p}}_{T}^{\rm trig}|}\cos\mbox{$\Delta\phi$}.$ (3)

The quantities $p_{\rm out}$ and $x_{E}$ give the transverse momentum
component and longitudinal momentum fraction, respectively, of the associated
hadron with respect to the trigger $\pi^{0}$. These quantities are
schematically diagrammed in Fig. 1, where the Figure shows a two-particle
correlation in the transverse plane and quantities in bold represent vectors.
In this diagram, two hadrons (black vectors) fragment from two high $p_{T}$
partons (red vectors) from a two-to-two partonic scattering. The partons are
originally acoplanar due to their initial-state transverse momenta ($k_{T}$);
the two hadrons may acquire additional acoplanarity due to final-state
transverse momentum ($j_{T}$) during the fragmentation process. In the diagram
the final-state transverse momentum is perpendicular to the parton axis and
denoted as $j_{T_{y}^{\rm trig}}$ and $j_{T_{y}^{\rm assoc}}$, which are
assumed to be Gaussian such that $\sqrt{\langle
j_{T}^{2}\rangle}=\sqrt{2\langle j^{2}_{T_{y}^{\rm
trig}}\rangle}=\sqrt{2\langle j^{2}_{T_{y}^{\rm assoc}}\rangle}$. The quantity
$j_{T}$ could have a $p_{T}^{\rm trig}$ or $p_{T}^{\rm assoc}$ dependence to
it; however, measurements have shown that this dependence is small Acharya
_et al._ . The quantity $p_{\rm out}$ can be nonzero because of the $k_{T}$
and $j_{T}$ transverse momentum contributions, while $x_{E}$ is a proxy for
the momentum fraction $z$ that the final-state hadron carries with respect to
the parton; see Fig. 6 and the associated text. In the figure, $x_{E}$ is
shown multiplied by $p_{T}^{\rm trig}$ to explicitly show the comparison
between $x_{E}$ and $z$. When $p_{\rm out}$ is small, the two-particle
correlation is nearly back-to-back and the acoplanarity is generated by
nonperturbative $k_{T}$ and $j_{T}$ Aidala  _et al._ (2018b); Adare  _et al._
(2017). Additional nonperturbative interactions within the nucleus, as
discussed and referenced in the Introduction, may contribute to this quantity
in $p$$+$A collisions.

Systematic uncertainties are assigned for the charged hadron efficiency and
for the underlying event background subtraction procedure. The systematic
uncertainty on the charged hadron yields is determined to be an overall
normalization uncertainty of 9% on the per-trigger yields. The dominant
contribution is due to the uncertainty that arises from matching tracks in the
PHENIX drift chamber to the outermost pad chamber; however, there are also
contributions from the overall tracking resolution of the detector and the
Monte Carlo determination of the nonidentified charged hadron efficiency. The
underlying event background is statistically subtracted with fits to the away-
side $\Delta\phi$ correlation functions as described in Ref. Adare  _et al._
(2017); these fits determine the percentage of underlying event background
level with respect to the jet yield. The systematic uncertainty is determined
by altering the underlying event region by $\pm 1\sigma$ based on the fit
results. This uncertainty varies from less than 1% at small $p_{\rm out}$ to
several percent at large $p_{\rm out}$ where the underlying event
contribution, and thus background-to-signal, is larger.

##  III Results

Examples of the away-side per-trigger yields as a function of $p_{\rm out}$
are shown in several bins of $x_{E}$ in Fig. 2. The per-trigger yields for
$p$$+$Au and $p$$+$$p$ collisions are shown as open and filled points,
respectively. A transition from nonperturbative behavior in the nearly back-
to-back $p_{\rm out}$ $\approx$0 ($\Delta\phi$ $\approx\pi$) region to
perturbative next-to-leading order behavior at larger $p_{\rm out}$ can be
seen at varying values of $p_{\rm out}$, depending on the $x_{E}$ bin. This
change in shape is highlighted by Gaussian fits to the small $p_{\rm out}$
region, drawn in Fig. 2 as dotted and solid lines for $p$$+$Au and $p$$+$$p$,
respectively. The fit ranges vary depending on the $x_{E}$ bin as the
nonperturbative region is a function of $p_{T}^{\rm assoc}$ and thus $x_{E}$
Aidala  _et al._ (2018b). The fit ranges are chosen to give the best
$\chi^{2}$/NDF, and a systematic uncertainty is assigned based on this choice
as described later; this is the dominant systematic uncertainty on the
Gaussian widths. Generally the fits have a $\chi^{2}$ per NDF of order
$\sim$10 on the $p_{\rm out}$ distributions when fitting only the statistical
uncertainties. When fitting the systematic uncertainties, the fits always have
a $\chi^{2}$ per NDF less than unity. The fit results are nearly identical
when fitting the statistical or systematic uncertainties; therefore,
systematic uncertainties on the Gaussian widths are more conservatively
estimated by adjusting the fit range when fitting to the statistical
uncertainties. The fit ranges are the same for both the $p$$+$$p$ and $p$$+$A
data, and range from $[-0.4,0.4]$ GeV/$c$ in the smallest $x_{E}$ bin to
$[-1.5,1.5]$ GeV/$c$ in the largest $x_{E}$ bin. These fits clearly do not
describe the data at larger values of $p_{\rm out}$ where the data exhibit a
more power-law like behavior. This transition indicates a change from
sensitivity to nonperturbative to perturbative physics effects.

Figure 2: The away-side $p_{\rm out}$ per-trigger yields are shown in both
$p$$+$Au and $p$$+$$p$ collisions for several bins of $x_{E}$. Gaussian fits,
shown as dotted lines for $p$$+$Au and solid lines for $p$$+$$p$, are shown to
the small $p_{\rm out}$ distributions, highlighting the nonperturbative to
perturbative transition. Figure 3: The near-side $p_{\rm out}$ per-trigger
yields are shown in both $p$$+$Au and $p$$+$$p$ collisions for several bins of
$x_{E}$. Gaussian fits, shown as dotted lines for $p$$+$Au and solid lines for
$p$$+$$p$, are performed at small $p_{\rm out}$ where nonperturbative behavior
is dominant in the $\mbox{$\Delta\phi$}\approx$0 region.

Examples of the near-side per-trigger yields as a function of $p_{\rm out}$
are shown in several bins of $x_{E}$ in Fig. 3. The near-side per-trigger
yields show a much narrower distribution than the away-side per-trigger yields
due to the differences between intra-jet correlations and inter-jet
correlations, respectively. In particular, the near-side correlations are only
sensitive to fragmentation transverse momentum, because the $\pi^{0}$ and
hadron are fragmented from the same hard parton. However, the away-side
correlations are sensitive to both initial and final state transverse
momentum. Because the initial-state $k_{T}$ is much larger than final-state
$j_{T}$ (see e.g. Adler  _et al._ (2006); Adare  _et al._ (2010)), this leads
to a broader $p_{\rm out}$ distribution on the away-side than the near-side.
Nonetheless, a nonperturbative Gaussian region can still be identified on the
near side as shown in Fig. 3, similarly to the away side, with a power law
spectrum at larger $p_{\rm out}$ that is not well described by the Gaussian
fit.

To measure the nonperturbative momentum widths, the Gaussian widths are
extracted from the fits to both the near and away side $p_{\rm out}$
distributions. Systematic uncertainties on the Gaussian widths are estimated
by increasing the fit range by 0.2 GeV/$c$ in $p_{\rm out}$ and taking the
absolute value of the difference of the resulting Gaussian width. To study any
modification in $p$$+$A compared to $p$$+$$p$ collisions the squared width
difference is determined between the $p$$+$A and $p$$+$$p$ Gaussian widths.
These differences are shown in Fig. 4 as a function of $x_{E}$ for the near
and away side correlation functions, for both $p$$+$Al and $p$$+$Au
collisions. The near-side width differences in the left column of Fig. 4 show
no significant modification within uncertainties between both $p$$+$Al or
$p$$+$Au and $p$$+$$p$ collisions at all values of $x_{E}$. Similar results
have been seen in dihadron correlations Acharya  _et al._ and fragmentation
function studies with full jet reconstruction Aaboud  _et al._ (2018) in
$p$$+$Pb collisions. However, the away-side width differences in $p$$+$Au and
$p$$+$$p$ collisions show modification as seen in the bottom-right panel of
Fig. 4. There is no significant away-side broadening between $p$$+$Al and
$p$$+$$p$ collisions as seen in the top right panel of Fig. 4 within the
assigned systematic uncertainties.

Figure 4: The Gaussian width differences are shown for the near-side (a) and
away-side (b) between $p$$+$Al and $p$$+$$p$ collisions and for the near-side
(c) and away-side (d) between $p$$+$Au and $p$$+$$p$ collisions as a function
of $x_{E}$.

There is an indication that the away-side squared Gaussian width differences
depend on the nucleus size as indicated in the right column of Fig. 4. To
study this further, the $p_{\rm out}$ per-trigger yields were split into two
centrality bins in the $p$$+$Au data and the same analysis was performed. The
centrality in $p$$+$A collisions is converted to values of $N_{\rm coll}$ with
the method in Ref. Adare  _et al._ (2014), where $N_{\rm coll}$ is defined as
the average number of nucleon-nucleon collisions in a given event class.
Figure 5 shows the squared width differences in $p$$+$A and $p$$+$$p$
collisions as a function of $N_{\rm coll}$ in the two $x_{E}$ bins where a
nonzero Gaussian width difference is observed. The values of these squared
width differences are shown in Tab. 1. The data are fit with linear functions
which are shown on the figure and indicate that the squared width differences
exhibit a positive correlation with $N_{\rm coll}$. The slopes of the fits
were found to be $0.005\pm~{}0.001$ (stat) $\pm 0.003$ (sys) and 0.015
$\pm~{}0.005$ (stat) $\pm~{}0.004$ (sys) for the smaller and larger $x_{E}$
bins, respectively. When the data is fit to a constant of 0, the $\chi^{2}$
per number of degree of freedom becomes approximately 5 for
$0.15<\mbox{$x_{E}$}<0.25$ and approximately 8 for $0.25<\mbox{$x_{E}$}<0.5$.
The measured slopes differ from a slope of 0 with p values of approximately
0.055 and 0.01, for the smaller and larger $x_{E}$ bin respectively, where the
statistical and systematic uncertainties on the slopes were added in
quadrature. This suggests that the interpretation of no transverse momentum
broadening in $p$$+$A compared to $p$$+$$p$ is inconsistent with the data.

Figure 5: The Gaussian width differences between $p$$+$A and $p$$+$$p$ are shown in two $x_{E}$ bins as a function of $N_{\rm coll}$. Linear fits are shown for each $x_{E}$ bin, which exhibit a positive dependence with $N_{\rm coll}$. Table 1:  The values of the Gaussian width differences between $p$$+$A and $p$$+$$p$ and their statistical and systematic uncertainties are shown, corresponding to Fig. 5. Units are $[\rm{GeV}/c]^{2}$ for the width differences and their uncertainties.  System | $N_{\rm coll}$ | $\sigma_{\mbox{$N_{\rm coll}$}}$ | $x_{E}$ | Squared Gaussian width${}_{~{}p+A-p+p}$ | (stat) | (syst)
---|---|---|---|---|---|---
$p$$+$Al | 2.1 | 0.1 | 0.15–0.25 | 0.017 | 0.004 | 0.013
$p$$+$Au | 4.4 | 0.6 | 0.15–0.25 | 0.016 | 0.004 | 0.034
$p$$+$Au | 7.7 | 0.6 | 0.15–0.25 | 0.045 | 0.005 | 0.013
$p$$+$Al | 2.1 | 0.1 | 0.25–0.50 | 0.020 | 0.017 | 0.022
$p$$+$Au | 4.4 | 0.6 | 0.25–0.50 | 0.039 | 0.018 | 0.023
$p$$+$Au | 7.7 | 0.6 | 0.25–0.50 | 0.105 | 0.022 | 0.016

##  IV Discussion

There are a number of different physical processes that could be contributing
to the apparent broadening of the away-side nonperturbative momentum widths in
$p$$+$A compared to $p$$+$$p$ collisions, as discussed in the Introduction.
The apparent lack of broadening on the near-side indicates that additional
nonperturbative radiation during fragmentation in $p$$+$A is small. This may
suggest that the fragmentation of the hard scattered parton into hadrons
occurs outside any nuclear medium that is present; therefore, this
fragmentation is similar between $p$$+$A and $p$$+$$p$ collisions and is
independent of the presence of a nucleus in the kinematic region probed by
this data.

In the last decade, significant emphasis has been placed on the observation of
collective effects in $p$$+$A collisions. The effects of contributions from
$v_{2}$ and $v_{3}$ Fourier harmonics were studied and found to be negligible
in the present analysis; this is because the Gaussian widths are almost
entirely constrained by correlations in the range of $\mbox{$\Delta\phi$}\pm
0.2$ radians around $\mbox{$\Delta\phi$}=\pi$. In this small $\Delta\phi$
range, any modulation from collective dynamics was found to contribute on
average less than 1% to the normalization of the $p_{\rm out}$ correlation
functions. Additionally, the correlations are collected in the midrapidity
$|\eta|<0.35$ region where the $\Delta\eta$ between the high $p_{T}$ trigger
and associated particle is small and thus the jet dynamics will be dominant.
For this reason, any contribution from collective dynamics can be neglected in
these results.

The modification observed in this analysis is found in a similar kinematic
region to where the so-called “Cronin” peak has been observed. In the $x_{E}$
bins where the broadened widths are observed, associated hadrons corresponding
to trigger neutral pions in the range $5<\mbox{$p_{T}^{\rm trig}$}<9$ GeV/$c$
are approximately in the range $1<\mbox{$p_{T}^{\rm assoc}$}<2.5$ GeV/$c$. The
Cronin effect was once attributed to multiple scattering of partons within a
nuclear medium; however, recent measurements revealed a particle ID dependence
and have shown that additional final-state effects must also be present Adare
_et al._ (2013). Additional nonperturbative initial-state partonic $k_{T}$ can
also contribute to the Cronin peak, to which this measurement is sensitive.
Nonetheless, multiple scattering interactions within the nucleus could
manifest themselves as collisional energy loss or elastic scatterings leading
to an angular broadening, both of which could lead to the observed away-side
momentum width broadening in $p$$+$A collisions. Two-particle correlations may
provide additional constraints on the underlying physical mechanism which
leads to this phenomenon. Future measurements with particle identification
will play an important role in identifying the cause of the Cronin peak, as a
particle species dependence has been measured in $d$$+$Au Adare  _et al._
(2013) collisions.

Figure 6: The correlation between $x_{E}$ and $z$ is shown as determined in a
PYTHIA simulation for $\pi^{0}$-hadron correlations in the same kinematic
regime as measured in the data. The correlation may provide insight into the
origins of the inclusive hadron enhancement at moderate $p_{T}$ in $p$$+$A
collisions.

In Ref. Airapetian  _et al._ (2007) a strong dependence on $z$ to the
inclusive charged hadron enhancement in $e$$+$$A$ collisions was found. In
particular, the largest enhancement was found for $0.2<z<0.4$ hadrons. Figure
6 shows the correlation between $x_{E}$ and $z$ for $\pi^{0}$-hadron
correlations in $\sqrt{s}$ = 200 GeV $p$$+$$p$ collisions as determined in a
PYTHIA6 Sjostrand  _et al._ simulation with the default tune. The correlations
are determined in the Monte Carlo simulation in the same kinematic regime as
the data to draw a better comparison between $z$ and $x_{E}$ to this analysis.
Figure 6 shows that $0.25<\mbox{$x_{E}$}<0.5$, where the transverse momentum
broadening is observed to be the largest, corresponds approximately to a range
of $z$ covering $0.07<z<0.2$. This is in a similar region to where Ref.
Airapetian  _et al._ (2007) sees the largest inclusive hadron enhancement in
$e$$+$$A$ collisions. However, it should also be considered that the two
measurements cover a much different $Q^{2}$ range, which may also be relevant
in this comparison.

Nuclear PDFs can also play a role; in particular the nuclear PDFs are known to
vary with the longitudinal momentum fraction of the parton probed Geesaman
_et al._ (1995); Hen  _et al._ (2017). These measurements are in a kinematic
region that may be sensitive to the anti-shadowing region around
$x\approx$0.1. The $p_{\rm out}$ correlation functions are also sensitive to a
small transverse momentum scale, and thus can also probe the transverse-
momentum-dependent parton distribution functions of the nucleus. Dijet
measurements, where the jets have an average $\mbox{$p_{T}$}>4$ GeV/$c$, have
shown that there is a larger $\Delta\phi$ acoplanarity in $p$$+$A compared to
$p$$+$$p$ collisions Corcoran  _et al._ (1991), indicating that there is a
nuclear size dependence to initial-state partonic transverse momentum in the
kinematic regime where Cronin effects may be expected to be relevant. However,
the observation from the present measurement that the broadening depends on
$N_{\rm coll}$ could indicate that the broadening is not simply due to
additional transverse momentum from the nucleus size.

The transverse momentum broadening may also be due to soft radiative energy
loss within the nucleus. Energy loss in cold nuclear matter has been
previously studied with the Drell-Yan process Vasilev  _et al._ (1999).
Transverse momentum broadening has also been measured to be nonzero in SIDIS
interactions Airapetian  _et al._ (2010). While the Drell-Yan measurement is
only sensitive to initial-state partonic energy loss, the SIDIS measurement
and the measurement presented here are sensitive to both initial and final
state energy loss. Global analyses which utilize all of these data may provide
further insight into the origins of the measured transverse momentum
broadening in nuclear Drell-Yan, SIDIS, and $p$$+$A $\rightarrow$ dihadrons
processes. The difference in $p_{\rm out}$ between A+A and $p$$+$$p$
collisions has been used to estimate the energy loss per unit length within
the QGP in Au$+$Au collisions Tannenbaum (2017). Given that there is an
observed difference in the $p_{\rm out}$ widths between $p$$+$A and $p$$+$$p$
collisions this indicates that small energy losses have been measured in these
dihadron correlations. Calculations for energy loss in a nucleus have been
performed for both RHIC and LHC energies in the dijet and direct photon-hadron
channel as well as in $e$$+$$A$ collisions Xing  _et al._ (2012).

##  V Conclusion

In summary, high $p_{T}$ dihadron correlations have been measured in
$\sqrt{s_{{}_{NN}}}=200$ GeV $p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions. The
$p_{\rm out}$ distributions are measured on the near and away side of the
trigger hadron and the distributions are fit with Gaussian functions to
extract the nonperturbative transverse momentum width in each system. The
widths are compared across the various collision systems to search for
modifications present in the nuclear collisions. No near-side modification is
observed within uncertainties in the $p$$+$A collisions, indicating that
intra-jet radiation effects from nuclei are small in these systems. In
contrast, the away-side widths are broadened in $p$$+$Au compared to $p$$+$$p$
at moderate values of $x_{E}$, while no significant modification was observed
in $p$$+$Al compared to $p$$+$$p$. This was observed to be a function of the
centrality or $N_{\rm coll}$ of the $p$$+$A collision, which suggests a path
length dependence to the transverse momentum broadening.

A number of different physical effects may contribute to the measured
transverse momentum broadening in $p$$+$A collisions. In particular,
contributions from long range correlations were systematically studied and
found to be small. The correlations are constructed in a kinematic regime
where “Cronin” effects are known to be large; therefore, multiple initial-
state scatterings or parton recombination effects in the final state may be
contributing to the broadening. The correlations are also sensitive to the
partonic initial-state transverse momentum, and thus may indicate additional
primordial partonic $k_{T}$ in nuclei when compared to a free nucleon.
However, the dependence of the broadening on $N_{\rm coll}$ suggests a path
length dependence to hard scattered partonic energy loss, which may be due to
radiative or elastic interactions with the nuclear remnants. Considering these
different qualitative physics mechanisms, and the many different processes
and/or observables with which they have been measured, will be an important
endeavor in understanding hadronic interactions involving nuclei. Future
measurements, especially at an electron-ion collider, will continue to shed
light on the many physical phenomena that occur in proton-nucleus collisions.

###### 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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