This is the accepted manuscript made available via CHORUS. The article has been
published as:

Pseudorapidity Dependence of Particle Production andElliptic Flow in Asymmetric Nuclear Collisions of p+Al,
p+Au, d+Au, and ^{3}He+Au at sqrt[s_{NN}]=200 GeV
A. Adare et al. (PHENIX Collaboration)
Phys. Rev. Lett. 121, 222301 — Published 29 November 2018
DOI: 10.1103/PhysRevLett.121.222301

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Pseudorapidity dependence of particle production and elliptic flow in asymmetric√nuclear collisions of p+Al, p+Au, d+Au, and 3 He+Au at sN N = 200 GeV

A. Adare,13 C. Aidala,41 N.N. Ajitanand,57, ∗ Y. Akiba,52, 53, † M. Alfred,23 V. Andrieux,41 K. Aoki,31, 52
4
N. Apadula,28, 58 H. Asano,34, 52 C. Ayuso,41 B. Azmoun,7 V. Babintsev,24 M. Bai,6 N.S. Bandara,40
5
B. Bannier,58 K.N. Barish,8 S. Bathe,5, 53 A. Bazilevsky,7 M. Beaumier,8 S. Beckman,13 R. Belmont,13, 41
6
A. Berdnikov,55 Y. Berdnikov,55 D.S. Blau,33, 44 M. Boer,36 J.S. Bok,46 K. Boyle,53 M.L. Brooks,36
7
J. Bryslawskyj,5, 8 V. Bumazhnov,24 C. Butler,21 S. Campbell,14, 28 V. Canoa Roman,58 R. Cervantes,58
8
C.-H. Chen,53 C.Y. Chi,14 M. Chiu,7 I.J. Choi,25 J.B. Choi,10, ∗ T. Chujo,61 Z. Citron,63 M. Connors,21, 53
9
N. Cronin,42, 58 M. Csanád,17 T. Csörgő,18, 64 T.W. Danley,47 A. Datta,45 M.S. Daugherity,1 G. David,7, 16, 58
10
K. DeBlasio,45 K. Dehmelt,58 A. Denisov,24 A. Deshpande,7, 53, 58 E.J. Desmond,7 A. Dion,58 P.B. Diss,39
11
D. Dixit,58 J.H. Do,65 A. Drees,58 K.A. Drees,6 M. Dumancic,63 J.M. Durham,36 A. Durum,24 T. Elder,21
12
A. Enokizono,52, 54 H. En’yo,52 S. Esumi,61 B. Fadem,42 W. Fan,58 N. Feege,58 D.E. Fields,45 M. Finger,9
13
M. Finger, Jr.,9 S.L. Fokin,33 J.E. Frantz,47 A. Franz,7 A.D. Frawley,20 Y. Fukuda,61 C. Gal,58 P. Gallus,15
14
P. Garg,3, 58 H. Ge,58 F. Giordano,25 A. Glenn,35 Y. Goto,52, 53 N. Grau,2 S.V. Greene,62 M. Grosse Perdekamp,25
15
T. Gunji,12 H. Guragain,21 T. Hachiya,43, 52, 53 J.S. Haggerty,7 K.I. Hahn,19 H. Hamagaki,12 H.F. Hamilton,1
16
S.Y. Han,19, 52 J. Hanks,58 S. Hasegawa,29 T.O.S. Haseler,21 K. Hashimoto,52, 54 X. He,21 T.K. Hemmick,58
17
J.C. Hill,28 K. Hill,13 A. Hodges,21 R.S. Hollis,8 K. Homma,22 B. Hong,32 T. Hoshino,22 N. Hotvedt,28 J. Huang,718
S. Huang,62 K. Imai,29 J. Imrek,16 M. Inaba,61 A. Iordanova,8 D. Isenhower,1 Y. Ito,43 D. Ivanishchev,51
19
B.V. Jacak,58 M. Jezghani,21 Z. Ji,58 J. Jia,7, 57 X. Jiang,36 B.M. Johnson,7, 21 V. Jorjadze,58 D. Jouan,49
20
D.S. Jumper,25 S. Kanda,12 J.H. Kang,65 D. Kapukchyan,8 S. Karthas,58 D. Kawall,40 A.V. Kazantsev,33
21
J.A. Key,45 V. Khachatryan,58 A. Khanzadeev,51 C. Kim,8, 32 D.J. Kim,30 E.-J. Kim,10 G.W. Kim,19 M. Kim,52, 56
22
M.H. Kim,32 B. Kimelman,42 D. Kincses,17 E. Kistenev,7 R. Kitamura,12 J. Klatsky,20 D. Kleinjan,8 P. Kline,58
23
T. Koblesky,13 B. Komkov,51 D. Kotov,51, 55 S. Kudo,61 B. Kurgyis,17 K. Kurita,54 M. Kurosawa,52, 53 Y. Kwon,65
24
R. Lacey,57 J.G. Lajoie,28 E.O. Lallow,42 A. Lebedev,28 S. Lee,65 S.H. Lee,28, 58 M.J. Leitch,36 Y.H. Leung,58
25
N.A. Lewis,41 X. Li,11 X. Li,36 S.H. Lim,36, 65 L. D. Liu,50 M.X. Liu,36 V.-R. Loggins,25 S. Lökös,17, 18 K. Lovasz,16
26
D. Lynch,7 T. Majoros,16 Y.I. Makdisi,6 M. Makek,66 M. Malaev,51 A. Manion,58 V.I. Manko,33 E. Mannel,754
27 H. Masuda,
M. McCumber,36 P.L. McGaughey,36 D. McGlinchey,13, 36 C. McKinney,25 A. Meles,46 M. Mendoza,828
W.J. Metzger,18 A.C. Mignerey,39 D.E. Mihalik,58 A. Milov,63 D.K. Mishra,4 J.T. Mitchell,7 I. Mitrankov,55
29
G. Mitsuka,31, 52, 53 S. Miyasaka,52, 60 S. Mizuno,52, 61 A.K. Mohanty,4 P. Montuenga,25 T. Moon,65 D.P. Morrison,730
S.I. Morrow,62 T.V. Moukhanova,33 T. Murakami,34, 52 J. Murata,52, 54 A. Mwai,57 K. Nagai,60 K. Nagashima,22, 52
31
T. Nagashima,54 J.L. Nagle,13 M.I. Nagy,17 I. Nakagawa,52, 53 H. Nakagomi,52, 61 K. Nakano,52, 60 C. Nattrass,59
32
P.K. Netrakanti,4 T. Niida,61 S. Nishimura,12 R. Nishitani,43 R. Nouicer,7, 53 T. Novák,18, 64 N. Novitzky,30, 58
33
R. Novotny,15 A.S. Nyanin,33 E. O’Brien,7 C.A. Ogilvie,28 J.D. Orjuela Koop,13 J.D. Osborn,41 A. Oskarsson,37
34
G.J. Ottino,45 K. Ozawa,31, 61 R. Pak,7 V. Pantuev,26 V. Papavassiliou,46 J.S. Park,56 S. Park,52, 56, 58 S.F. Pate,46
28
35 M. Patel,
J.-C. Peng,25 W. Peng,62 D.V. Perepelitsa,7, 13 G.D.N. Perera,46 D.Yu. Peressounko,33 C.E. PerezLara,58
36
J. Perry,28 R. Petti,7, 58 M. Phipps,7, 25 C. Pinkenburg,7 R. Pinson,1 R.P. Pisani,7 A. Pun,47 M.L. Purschke,737
P.V. Radzevich,55 J. Rak,30 B.J. Ramson,41 I. Ravinovich,63 K.F. Read,48, 59 D. Reynolds,57 V. Riabov,44, 51
38
Y. Riabov,51, 55 D. Richford,5 T. Rinn,28 S.D. Rolnick,8 M. Rosati,28 Z. Rowan,5 J.G. Rubin,41 J. Runchey,28
39
A.S. Safonov,55 B. Sahlmueller,58 N. Saito,31 T. Sakaguchi,7 H. Sako,29 V. Samsonov,44, 51 M. Sarsour,2140
K. Sato,61 S. Sato,29 B. Schaefer,62 B.K. Schmoll,59 K. Sedgwick,8 R. Seidl,52, 53 A. Sen,28, 59 R. Seto,8 P. Sett,439
41 A. Sexton,
D. Sharma,58 I. Shein,24 T.-A. Shibata,52, 60 K. Shigaki,22 M. Shimomura,28, 43 T. Shioya,61 P. Shukla,47, 25
42
A. Sickles,
C.L. Silva,36 D. Silvermyr,37, 48 B.K. Singh,3 C.P. Singh,3 V. Singh,3 M.J. Skoby,41 M. Slunečka,920
43
K.L. Smith, M. Snowball,36 R.A. Soltz,35 W.E. Sondheim,36 S.P. Sorensen,59 I.V. Sourikova,7 P.W. Stankus,48
44
M. Stepanov,40, ∗ S.P. Stoll,7 T. Sugitate,22 A. Sukhanov,7 T. Sumita,52 J. Sun,58 Z. Sun,16 S. Suzuki,43
45
S. Syed,21 J. Sziklai,64 A. Takeda,43 A. Taketani,52, 53 K. Tanida,29, 53, 56 M.J. Tannenbaum,7 S. Tarafdar,62, 63
46
A. Taranenko,44, 57 G. Tarnai,16 R. Tieulent,21, 38 A. Timilsina,28 T. Todoroki,52, 53, 61 M. Tomášek,15 C.L. Towell,147
R. Towell,1 R.S. Towell,1 I. Tserruya,63 Y. Ueda,22 B. Ujvari,16 H.W. van Hecke,36 S. Vazquez-Carson,13
48
J. Velkovska,62 M. Virius,15 V. Vrba,15, 27 N. Vukman,66 X.R. Wang,46, 53 Z. Wang,5 Y. Watanabe,52, 53
49
Y.S. Watanabe,12, 31 F. Wei,46 A.S. White,41 C.P. Wong,21 C.L. Woody,7 M. Wysocki,48 B. Xia,47 C. Xu,46
50
Q. Xu,62 L. Xue,21 S. Yalcin,58 Y.L. Yamaguchi,12, 53, 58 H. Yamamoto,61 A. Yanovich,24 P. Yin,13 J.H. Yoo,32, 53
3

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I. Yoon,56 H. Yu,46, 50 I.E. Yushmanov,33 W.A. Zajc,14 A. Zelenski,6 S. Zharko,55 S. Zhou,11 and L. Zou8
(PHENIX Collaboration)
1

Abilene Christian University, Abilene, Texas 79699, USA
Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA
3
55
Department of Physics, Banaras Hindu University, Varanasi 221005, India
4
56
Bhabha Atomic Research Centre, Bombay 400 085, India
5
57
Baruch College, City University of New York, New York, New York, 10010 USA
658
Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
759
Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
860
University of California-Riverside, Riverside, California 92521, USA
961Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic
1062
Chonbuk National University, Jeonju, 561-756, Korea
11
63
Science and Technology on Nuclear Data Laboratory, China Institute64
of Atomic Energy, Beijing 102413, People’s Republic of China
1265
Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
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66
University of Colorado, Boulder, Colorado 80309, USA
1467
Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA
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Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic
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69
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
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70
ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary
18
71
Eszterházy Károly University, Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary
1972
Ewha Womans University, Seoul 120-750, Korea
20
73
Florida State University, Tallahassee, Florida 32306, USA
21
74
Georgia State University, Atlanta, Georgia 30303, USA
22
75
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
23
76
Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA
24
77
IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia
25
78
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
26
79
Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia
27
80
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
28
81
Iowa State University, Ames, Iowa 50011, USA
29
82
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4
83
Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan
30
84
Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland
31
85
KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
32
86
Korea University, Seoul, 136-701, Korea
33
87
National Research Center “Kurchatov Institute”, Moscow, 123098 Russia
34
88
Kyoto University, Kyoto 606-8502, Japan
35
89
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
90
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
37
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Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
38
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IPNL, CNRS/IN2P3, Univ Lyon, Universit Lyon 1, F-69622, Villeurbanne, France
39
93
University of Maryland, College Park, Maryland 20742, USA
40
94
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA
41
95
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA4296
Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA
43
97
Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan
44
98
National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia
45
99
University of New Mexico, Albuquerque, New Mexico 87131, USA
46
100
New Mexico State University, Las Cruces, New Mexico 88003, USA
47
101
Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
48
102
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
49
103
IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406, Orsay, France
50
104
Peking University, Beijing 100871, People’s Republic of China
51
105
PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia
52
106
RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
53
107
RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
54
108
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan55
109
Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia
56
110
Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
57
111
Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA
58
112
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
59
113
University of Tennessee, Knoxville, Tennessee 37996, USA
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Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
Tomonaga Center for the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
62
Vanderbilt University, Nashville, Tennessee 37235, USA
63
Weizmann Institute, Rehovot 76100, Israel
64
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
65
Yonsei University, IPAP, Seoul 120-749, Korea
66
Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb, Croatia(Dated: October 12, 2018)√
Asymmetric nuclear collisions of p+Al, p+Au, d+Au, and 3 He+Au at sN N = 200 GeV provide an excellent laboratory for understanding particle production, as well as exploring interactions
among these particles after their initial creation in the collision. We present measurements ofcharged hadron production dNch /dη in all such collision systems over a broad pseudorapidity range
and as a function of collision multiplicity. A simple wounded quark model is remarkably successful
at describing the full data set. We also measure the elliptic flow v2 over a similarly broad pseudorapidity range. These measurements provide key constraints on models of particle emission and theirtranslation into flow.
61

4
Asymmetric nuclear collisions with a light projectile nucleus striking a heavier target nucleus have proven to be an
excellent testing ground for particle production models and the longitudinal dynamics following the initial collision –125 for an early review see Ref. [1]. Many calculations have successfully described the longitudinal (or rapidity) distribution
126 of produced particles in proton-nucleus (p+A) collisions via the fragmentation of color strings and with counting rules
127 based on the number of “wounded” or struck nucleons or quarks in the projectile and target. Recently, a proposal
128 for testing the wounded-quark model [2] was put forth that specifically called for the measurement of dNch /dη over a3
129 broad range of pseudorapidity in p+Au, d+Au, andHe+Au collisions [3]. Fully three-dimensional hydrodynamical
130 models also require input on the longitudinal distribution of initial deposited energy and gradients thereof [4]. Once
131 the initial partons or fluid elements are populated, the models evolve the system dynamically. Measurements of elliptic
132 flow as a function of pseudorapidity provide constraints on the longitudinal dynamics of the evolution.
133
As the incoming hadrons or nuclei break up, the rapidity distribution of liberated partons may be determined by
134 the longitudinal parton distribution functions [5, 6] or via a universal color field breakup for each struck nucleon
135 or quark [7]. For that reason, calculations based on Monte Carlo Glauber models have been developed to calculate
136 the number of struck nucleons and struck quarks (see for example Refs. [8–10]). The PHOBOS collaboration has√
137 previously published charged hadron dNch /dη measurements over |η| < 5.4 in d+Au collisions at
sN N = 200 GeV [11].
√138 PHENIX has also published dNch /dη measurements in high-multiplicity d+Au collisions at
sN N = 200, 62, 39, and
139 19.6 GeV [12]. The wounded-quark model has been constrained by the d+Au data and found to be in reasonable
140 agreement with the centrality dependence, while the wounded-nucleon model cannot describe the data [3]. A crucial
141 test of the wounded-quark model is to see if it is universal across different colliding systems. Additional measurements
142 in light and heavy systems at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can
143 also be tested in this context—see for example different geometry tests in Refs. [13–15].
In Au+Au and Pb+Pb collisions at RHIC and the LHC, the created medium is well described by low viscosity
hydrodynamics [16, 17]. A host of recent experimental observations indicate that hydrodynamics may also be applicable to the asymmetric collisions of small nuclear systems, e.g. p+A, d+Au, 3 He+Au, and perhaps even p+p (fora recent review see Ref. [18]). In heavy ion collisions, the hydrodynamical flow of the medium is characterized via
a Fourier decomposition of the final hadron momentum anisotropy in the direction transverse to the incoming beam
directions [19] as
123
124

X
dN
∝1+
2vn cos [n (φ − ψn )] ,
dφ
n

(1)

where n is the harmonic number, φ is the particle azimuthal angle, ψn is the nth order symmetry axis, and vn is the
145 Fourier coefficient, with v2 referred to as elliptic flow. The pseudorapidity dependence of v2 has been measured in
146 Au+Au and Pb+Pb collisions at RHIC and the LHC, and the elliptic flow is smaller in regions with smaller final
147 hadron dNch /dη – see for example Refs. [20, 21]. The data have been interpreted in terms of hydrodynamics and
148 imply a shear viscosity to entropy density, η/s, that is temperature dependent [22]. Similar measurements in small
149 nuclear collisions of different sizes are a key test for how local rapidity density relates to hydrodynamical evolution
150 into flow.
151
In this Letter, we present a comprehensive set of measurements of dNch /dη and elliptic flow v2 over a broad√
3
He+Au collisions at sN N = 200 GeV. The data sets analyzed
152 pseudorapidity range in p+Al, p+Au, d+Au, and3
153 were recorded in 2014 for
He+Au, 2015 for p+Al and p+Au, and 2016 for d+Au. All data sets were recorded
154 with a minimum-bias trigger that required at least one hit in each of the PHENIX beam-beam counters (BBC).
155 The BBC is composed of two detectors each containing 64 quartz radiators read out with photomultiplier tubes [23].
156 The BBC covers positive and negative pseudorapidity 3.1 < |η| < 3.9. Following the procedure from Ref. [24], the
157 minimum-bias trigger is determined to fire on 88 ± 4%, 88 ± 4%, 84 ± 3%, and 72 ± 4% of the total inelastic cross3
158 section of 2.30, 2.26, 1.76, 0.54 barns for
He+Au, d+Au, p+Au, and p+Al respectively. The dNch /dη analysis has
159 negligible statistical uncertainties and thus a subset of runs with the most stable detector configuration are utilized
160 and the run-to-run variation is used in the determination of systematic uncertainties. For the elliptic flow v2 analysis
161 in high-multiplicity events, also referred to as central events, an additional trigger was used that required the number
162 of fired BBC tubes to be above a set number, roughly corresponding to the 0%–5% highest multiplicity events.
163
The characterization of the different collision systems and centralities follows the procedure detailed in Ref. [24].
164 The multiplicity class is selected by the total charge in the BBC covering negative pseudorapidity, i.e. in the Al- or
165 Au-going direction. The total charge is found to scale with the total number of struck nucleons from the Al or Au
166 nucleus folded with a negative binomial distribution representing the fluctuations in the number of particles produced
167 and measured by the BBC. The 5% most central events have an average number of participating nucleons of 5.1 ±3
168 0.3, 10.7 ± 0.6, 17.8 ± 1.2, and 25.0 ± 1.6 for p+Al, p+Au, d+Au, andHe+Au respectively.
144

5Charged hadrons are reconstructed at midrapidity |η| < 0.35 with a combination of drift chambers and pad chambers [25]. Midrapidity tracks have their momentum reconstructed via their bend in a magnetic field and are efficiently
171 measured for pT > 0.2 GeV/c. At backward −3.0 < η < −1.0 and forward 1.0 < η < 3.0 rapidity, the forward172 silicon-vertex detector (FVTX) measures the traversal of charged tracks in four detector layers as detailed in Ref. [26].
173 FVTX tracks are efficiently measured for pT > 0.3 GeV/c, but with no momentum information, because the silicon
174 strips are oriented lengthwise along the magnetic field bend direction.
175
For the dNch /dη results, the absolute acceptance and efficiency for track reconstruction can be determined with the
176 PHENIX geant-3 Monte Carlo simulation. However, in the last years of data taking, the PHENIX experiment had
177 increasingly significant dead regions and run-to-run variations that became challenging to fully account for. Thus,
178 we determine the acceptance and efficiency for a given running period in a control data set by taking the ratio
179 R(η) of published PHOBOS dNch /dη to the PHENIX raw dNch /dη as a function of pseudorapidity. The control√
180 PHOBOS data sets are Au+Au in 2014 [27], p+p in 2015 [27], and d+Au in 2016 [11] all at
sN N = 200 GeV. This
181 “bootstrapping” procedure is described in detail in Ref. [12]. Sources of systematic uncertainty come from varying
182 the track selection cuts, run-to-run variations, and considering high and low luminosity running periods with different
183 double interaction contributions. We also find good agreement within uncertainties comparing results in the FVTX
184 with an absolute acceptance and efficiency calculation and the “bootstrapped” results.
185
The determination of hadron yields in centrality bins has a known bias effect (see Ref. [24]). In p+p collisions,0
186 inelastic events fire the BBC trigger 55 ± 5% of the time, while in events with a π
or charged hadron at midrapidity
187 that percentage is larger, 79 ± 2%.
This increased trigger efficiency is correlated with a 1.55 times larger BBC
188 multiplicity. This effect results from the diffractive portion of the p+p inelastic cross section disfavoring midrapidity
189 particle production. This bias has been confirmed for midrapidity hadron production down to pT ≈ 0.5 GeV/c [28]190 and for J/ψ measured in the PHENIX muons arms [29], and thus we expect that this bias affects all charged hadrons
191 over the pseudorapidity range studied here. We remove this bias via correction factors that are calculated following
192 the procedure detailed in Ref. [24]. The bias corrections are largest in the smallest system and range from 0.75 ±3
193 0.01 for central 0%–5% p+Al to 0.91 ± 0.01 for central 0%–5%
He+Au. We apply these bias correction factors to
194 all our dNch /dη results.
169

dNch/dη170

45

PHENIX Small Systems sNN=200 GeV
3
He+Au 0-5%
d+Au 0-5%
p+Au 0-5%
p+Al 0-5%
p+p PHOBOS
Wounded Quark Model [Scaled]
3D Hydrodynamics [Scaled]

40
35
30
25
20
15
10
5
0

−3

−2

−1

0

1

2

3

η

FIG. 1. Charged hadron dNch /dη as a function of pseudorapidity in high-multiplicity 0%–5% central 3 He+Au, d+Au, p+Au,√√
and p+Al collisions at sN N = 200 GeV. Also shown are results in inelastic p+p collisions at sN N = 200 GeV as measured
by the PHOBOS Collaboration [27]. Predictions from the wounded-quark [3] and hydrodynamical [4] models are shown. The
calculations have an overall normalization factor (S) to best match the data. These factors are S=0.88, 0.93, 0.85, 0.77 for the
wound quark model for p+Al, p+Au, d+Au, 3 He+Au respectively, and S=0.81, 0.96, 0.75 for the hydrodynamical model for
p+Au, d+Au, 3 He+Au respectively.
195

Figure 1 shows the dNch /dη results for p+Al, p+Au, d+Au, and 3 He+Au at√

sN N = 200 GeV for the 5% highest

6

25
25
20
20
15
15

35

35

dNch/dd35

dNch/dd

PHENIX
30
30

dNch/dd

dNch/dηdNch/dd35
35

p+Au sNN=200 GeV

p+Al sNN=200 GeV

30

25

25

20

20

15

15

10
10

10

10

10

55

5

5

5

00 <3

<2
-2

<1
-1

00

η

11

22

0
3 <3
d

<2
-2

<1
-1

00

η

11

0
3 <3
d

22

He+Au sNN=200 GeV

30

30

0-5%
5-10%
25
10-20%
20-40%
20
40-60% (40-74%, p+Al)
60-88% (60-84%, p+Au)
15
Wounded Quark Model [Scaled]

3d+Au sNN=200 GeV

<2
-2

<1
-1

00

η

11

22

0
3 <3
d

<2
-2

<1
-1

00

η

11

22

3
d

FIG. 2. Charged hadron dNch /dη as a function of pseudorapidity in various multiplicity classes of p+Al, p+Au, d+Au, 3 He+Au√
collisions at sN N = 200 GeV. Predictions from the wounded-quark model [3] are shown.

multiplicity events. Statistical uncertainties are negligible and systematic uncertainties are shown as boxes aroundthe points. The systematic uncertainties are point-to-point correlated and can in principle move the backward, mid,
198 and forward rapidity points separately because they are measured in different detectors. Also shown are the yields√
199 in inelastic p+p collisions at
sN N = 200 GeV as measured by the PHOBOS Collaboration [27]. The full set of
200 multiplicity-selected results for the four asymmetric nuclear collision systems are shown in Fig. 2.
201
The results are compared to predictions from the wounded-quark model. Within the wounded-quark model, each
202 wounded-quark is posited to yield hadrons following a common emission function F (η) [3]. F (η) is constrained by
203 d+Au collision data, and the model then predicts dNch /dη for all collision centralities and systems. The calculations
204 are normalized, with factors listed in the Fig. 1 caption, to best match the data integrated over pseudorapidity,
205 because the exact normalization can be influenced by modest differences in the centrality selection and thus the
206 mean number of wounded quarks. Within the systematic uncertainties on the experimental measurements, the model196

dNch/dη / (Nqp/2) at η=0197

Small Systems sNN=200 GeV
p+p PHENIX
p+p PHOBOS
p+Al PHENIX
p+Au PHENIX
d+Au PHENIX
3
He+Au PHENIX

2.4
2.2
2

1.8
1.6
1.4
1.2
1
0.8
0

5

10

15

20

25

30

35

40
Nqp

FIG. 3. Midrapidity charged hadron dNch /dη per participating quark pair (Nqp /2) as a function of the number of participating
quarks (Nqp ). Results are shown for p+Al, p+Au, d+Au, and 3 He+Au collisions in various multiplicity classes. Also shown
are previously published results in p+p collisions from PHENIX [15] and PHOBOS [27]. The line is the best fit to all the data
to a constant level.

7
provides a good description of the complete data set across collision systems and centrality classes. The results are also
compared in Fig. 1 with a hydrodynamical calculation [4] for 0%–5% central collisions. The calculation includes Monte
209 Carlo Glauber initial conditions with longitudinal entropy distributions [30], 3+1D viscous hydrodynamics [31] with210 η/s = 1/4π and temperature dependent bulk viscosity, followed by statistical hadronization. Again, the calculations
211 are normalized to the data with factors listed in the caption. The agreement in this case is also good within systematic
212 uncertainties, except for a more significant drop in particle yield in the calculation at the most backward rapidity< −2.0.
213 region −3.0 < η∼
214Midrapidity dNch /dη per participating quark pair, Nqp /2, scales as a function of the number of participating quarks
3
215 from d+Au and
He+Au collisions [15]. The previously reported results [15] were not corrected for the modest bias
216 previously discussed. Figure 3 shows the results testing this scaling for all small collision systems, each with the bias
217 correction factors applied. Within the systematic uncertainties, all systems at all centralities follow a common scaling
218 for midrapidity particle production.
219
In d+Au collisions, the elliptic flow v2 was observed to have a similar pseudorapidity dependence as the particle
220 yield dNch /dη [12]. For the other systems we have followed the same procedure for measuring elliptic flow v2 using
221 the event plane method, where the event plane is defined by the Al- or Au-going BBC covering −3.9 < η < −3.1.
222 The results are corrected using ampt [32] and a geant-3 simulation of the detector to correspond to v2 integrated
223 over hadrons at all pT within each pseudorapidity bin. Systematic uncertainties are determined by varying the track
224 selection cuts, collision z-vertex cuts, and ampt input parameters.
207
208

0.07

v2

v2

p+Al sNN=200 GeV 0-5%
PHENIX

p+Au sNN=200 GeV 0-5%

0.07

v2

0.07

0.07 3d+Au sNN=200 GeV 0-5%

0.06

0.06

0.06

0.05
v 2 3D Hydrodynamics

0.05

0.05

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

0.01

0.01

0.01

0.01

0.06

v 2 {EP

He+Au sNN=200 GeV 0-5%}

-3.9<η<-3.1

0.05

dNch/dη [Scaled]

0.04

0

−3

−2

−1

0

1

2

0
3 −3

η

−2

−1

0

1

2

0
3 −3

η

−2

−1

0

1

2

0
3 −3

η

−2

−1

0

1

2

3

η

FIG. 4. Elliptic flow v2 as a function of pseudorapidity in high-multiplicity 0%–5% central p+Al, p+Au, d+Au, and 3 He+Au√
collisions at sN N = 200 GeV. Also shown are predictions from the hydrodynamical model [4]. Lastly, the measured dNch /dηresults are shown scaled to match the v2 at forward rapidity for shape comparison with the elliptic flow coefficients.

Figure 4 shows the elliptic flow v2 as a function of pseudorapidity in 0%–5% central p+Al, p+Au, d+Au, and√He+Au collisions at sN N = 200 GeV. The experimental data have an increasing flow coefficient at forward rapidity
3
227 when going from the smallest system and smallest particle production p+Al to the largest
He+Au. These trends
228 are consistent with arising from the combined influence of initial geometry and particle multiplicity [33]. The v2 also
229 increases towards backward rapidity for each collision system. For the lowest multiplicity systems p+Al and p+Au,< −2.0 that is more pronounced in p+Al. This feature may be due to
230 there is a sharp enhancement in the v2 for η∼
231 the nonflow contribution of short range correlations, because this is the pseudorapidity range that is within one unit
232 of the BBC used for determining the event plane.
233
The data are compared with the same hydrodynamical model [4] that gave a reasonable description of the dNch /dη.
234 There is good qualitative agreement with the system and pseudorapidity dependence of v2 , and good quantitative
235 agreement of its pseudorapidity dependence in p+Au and d+Au. The only feature not qualitatively described is the
236 enhancement at backward rapidity. This enhancement is the strongest in p+Al, weaker but still pronounced in p+Au,
237 and rather weak in d+Au. The strength of this enhancement trends inversely with the dNch /dη, lending additional3
238 evidence that this is due to nonflow influences not incorporated in the hydrodynamical model. In
He+Au collisions,239 the hydrodynamical model overpredicts the forward rapidity (η > 1) v2 by more than 50% and qualitatively has the
240 feature of a weaker forward/backward asymmetry than what is present in the data. Note that the model overpredicts
225

226

3

8
the 3 He+Au dNch /dη by approximately 25% (but is scaled to fit the data in Fig. 1), which may help explain the
242 overpredicted v2 .
243
In Fig. 4, we also scale dNch /dη to match the v2 at forward rapidity to compare the shape of the distributions.
244 Although a larger local particle density dNch /dη is correlated with more elliptic flow, the scaling observed in d+Au
245 appears only approximate when viewed in the context of all collision systems. It is notable that although not shown
246 in Fig. 4, hydrodynamical model calculations [4] also do not exhibit an exact scaling relation v2 ∝ dNch /dη.
247
We have presented a comprehensive set of measurements of particle production dNch /dη and elliptic flow v2 over3
248 a broad pseudorapidity range for a suite of asymmetric nuclear collisions p+Al, p+Au, d+Au, andHe+Au at√249
sN N = 200 GeV. The particle production is remarkably well-described in the context of the wounded-quark model [3].
250 A three-dimensional hydrodynamical model qualitatively describes the particle production and elliptic flow in high251 multiplicity events in all collision systems. However, it over predicts the overall dNch /dη and forward rapidity v23
252 inHe+Au collisions. These data provide an important constraint on models of the longitudinal dynamics in these
253 asymmetric collisions.
254
We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and
255 the staff of the other PHENIX participating institutions for their vital contributions. We thank Adam Bzdak and
256 Piotr Bożek for providing theoretical calculations for the suite of collision systems and centralities from the wounded257 quark model and hydrodynamical model, respectively. We acknowledge support from the Office of Nuclear Physics
258 in the Office of Science of the Department of Energy, the National Science Foundation, Abilene Christian University
259 Research Council, Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University
260 (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion
261 of Science (Japan), Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico and Fundação de Amparo à
262 Pesquisa do Estado de São Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China), Croatian
263 Science Foundation and Ministry of Science and Education (Croatia), Ministry of Education, Youth and Sports (Czech
264 Republic), Centre National de la Recherche Scientifique, Commissariat à l’Énergie Atomique, and Institut National de
265 Physique Nucléaire et de Physique des Particules (France), Bundesministerium für Bildung und Forschung, Deutscher
266 Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), J. Bolyai Research Scholarship,
267 EFOP, the New National Excellence Program (ÚNKP), NKFIH, and OTKA (Hungary), Department of Atomic
268 Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Basic Science Research
269 Program through NRF of the Ministry of Education (Korea), Physics Department, Lahore University of Management
270 Sciences (Pakistan), Ministry of Education and Science, Russian Academy of Sciences, Federal Agency of Atomic
271 Energy (Russia), VR and Wallenberg Foundation (Sweden), the U.S. Civilian Research and Development Foundation
272 for the Independent States of the Former Soviet Union, the Hungarian American Enterprise Scholarship Fund, the
273 US-Hungarian Fulbright Foundation, and the US-Israel Binational Science Foundation.
241∗

Deceased
PHENIX Spokesperson: akiba@rcf.rhic.bnl.gov
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