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

Measurements of Elliptic and Triangular Flow in HighMultiplicity ^{3}He+Au Collisions at
sqrt[s_{NN}]=200 GeV
A. Adare et al. (PHENIX Collaboration)
Phys. Rev. Lett. 115, 142301 — Published 28 September 2015
DOI: 10.1103/PhysRevLett.115.142301

Measurements of elliptic and triangular flow in high-multiplicity 3 He+Au collisions at√
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sN N = 200 GeV
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A. Adare,14 S. Afanasiev,33 C. Aidala,15, 42, 46, 47 N.N. Ajitanand,66 Y. Akiba,60, 61 R. Akimoto,13 H. Al-Bataineh,54
J. Alexander,66 M. Alfred,26 H. Al-Ta’ani,54 K.R. Andrews,1 A. Angerami,15 K. Aoki,35, 38, 60 N. Apadula,31, 67
L. Aphecetche,68 E. Appelt,72 Y. Aramaki,13, 60 R. Armendariz,9, 54 S.H. Aronson,8 J. Asai,60, 61 H. Asano,38, 60
E.C. Aschenauer,8 E.T. Atomssa,39, 67 R. Averbeck,67 T.C. Awes,56 B. Azmoun,8 V. Babintsev,27 M. Bai,7
G. Baksay,21 L. Baksay,21 A. Baldisseri,17 N.S. Bandara,46 B. Bannier,67 K.N. Barish,9 P.D. Barnes,42, ∗B. Bassalleck,53 A.T. Basye,1 S. Bathe,6, 9, 61 S. Batsouli,56 V. Baublis,59 C. Baumann,8, 48 A. Bazilevsky,8
M. Beaumier,9 S. Beckman,14 S. Belikov,8, ∗ R. Belmont,47, 72 J. Ben-Benjamin,49 R. Bennett,67 A. Berdnikov,63
Y. Berdnikov,63 J.H. Bhom,76 A.A. Bickley,14 D.S. Blau,37 J.G. Boissevain,42 J.S. Bok,54, 76 H. Borel,17
K. Boyle,61, 67 M.L. Brooks,42 D. Broxmeyer,49 J. Bryslawskyj,6 H. Buesching,8 V. Bumazhnov,27 G. Bunce,8, 61
S. Butsyk,42, 67 C.M. Camacho,42 S. Campbell,15, 31, 67 A. Caringi,49 P. Castera,67 B.S. Chang,76 W.C. Chang,2J.-L. Charvet,17 C.-H. Chen,61, 67 S. Chernichenko,27 C.Y. Chi,15 J. Chiba,35 M. Chiu,8, 28 I.J. Choi,28, 76
J.B. Choi,11 R.K. Choudhury,5 P. Christiansen,44 T. Chujo,71, 72 P. Chung,66 A. Churyn,27 O. Chvala,9V. Cianciolo,56 Z. Citron,67, 74 C.R. Cleven,23 B.A. Cole,15 M.P. Comets,57 Z. Conesa del Valle,39 M. Connors,67
P. Constantin,42 M. Csanád,19 T. Csörgő,75 T. Dahms,67 S. Dairaku,38, 60 I. Danchev,72 D. Danley,55 K. Das,22
A. Datta,46, 53 M.S. Daugherity,1 G. David,8 M.K. Dayananda,23 M.B. Deaton,1 K. DeBlasio,53 K. Dehmelt,21, 67
H. Delagrange,68, ∗ A. Denisov,27 D. d’Enterria,15, 39 A. Deshpande,61, 67 E.J. Desmond,8 K.V. Dharmawardane,54
O. Dietzsch,64 A. Dion,31, 67 P.B. Diss,45 J.H. Do,76 M. Donadelli,64 L. D’Orazio,45 O. Drapier,39 A. Drees,67
K.A. Drees,7 A.K. Dubey,74 J.M. Durham,42, 67 A. Durum,27 D. Dutta,5 V. Dzhordzhadze,9 S. Edwards,7, 22
Y.V. Efremenko,56 J. Egdemir,67 F. Ellinghaus,14 W.S. Emam,9 T. Engelmore,15 A. Enokizono,41, 56, 60, 62
H. En’yo,60, 61 S. Esumi,71 K.O. Eyser,8, 9 B. Fadem,49 N. Feege,67 D.E. Fields,53, 61 M. Finger,10, 33
M. Finger, Jr.,10, 33 F. Fleuret,39 S.L. Fokin,37 Z. Fraenkel,74, ∗ J.E. Frantz,55, 67 A. Franz,8 A.D. Frawley,22
K. Fujiwara,60 Y. Fukao,38, 60 T. Fusayasu,51 S. Gadrat,43 C. Gal,67 P. Gallus,16 P. Garg,4 I. Garishvili,41, 69
H. Ge,67 F. Giordano,28 A. Glenn,14, 41 H. Gong,67 X. Gong,66 M. Gonin,39 J. Gosset,17 Y. Goto,60, 61
R. Granier de Cassagnac,39 N. Grau,3, 15, 31 S.V. Greene,72 G. Grim,42 M. Grosse Perdekamp,28, 61 Y. Gu,67
T. Gunji,13 L. Guo,42 H.-Å. Gustafsson,44, ∗ T. Hachiya,25, 60 A. Hadj Henni,68 C. Haegemann,53 J.S. Haggerty,8
K.I. Hahn,20 H. Hamagaki,13 J. Hamblen,69 H.F. Hamilton,1 R. Han,58 S.Y. Han,20 J. Hanks,15, 67 H. Harada,25
C. Harper,49 E.P. Hartouni,41 K. Haruna,25 S. Hasegawa,32 T.O.S. Haseler,23 K. Hashimoto,60, 62 E. Haslum,44
R. Hayano,13 X. He,23 M. Heffner,41 T.K. Hemmick,67 T. Hester,9 H. Hiejima,28 J.C. Hill,31 R. Hobbs,53
M. Hohlmann,21 R.S. Hollis,9 W. Holzmann,15, 66 K. Homma,25 B. Hong,36 T. Horaguchi,13, 25, 60, 70, 71 Y. Hori,13
D. Hornback,56, 69 T. Hoshino,25 N. Hotvedt,31 J. Huang,8 S. Huang,72 T. Ichihara,60, 61 R. Ichimiya,60
H. Iinuma,35, 38, 60 Y. Ikeda,71 K. Imai,32, 38, 60 J. Imrek,18 M. Inaba,71 Y. Inoue,60, 62 A. Iordanova,9 D. Isenhower,1
L. Isenhower,1 M. Ishihara,60 T. Isobe,13, 60 M. Issah,66, 72 A. Isupov,33 D. Ivanishchev,59 Y. Iwanaga,25
B.V. Jacak,67 M. Jezghani,23 J. Jia,8, 15, 66 X. Jiang,42 J. Jin,15 O. Jinnouchi,61 D. John,69 B.M. Johnson,8T. Jones,1 K.S. Joo,50 D. Jouan,57 D.S. Jumper,1, 28 F. Kajihara,13 S. Kametani,13, 60, 73 N. Kamihara,60, 61
J. Kamin,67 S. Kanda,13 M. Kaneta,61 S. Kaneti,67 B.H. Kang,24 J.H. Kang,76 J.S. Kang,24 H. Kanou,60, 70
J. Kapustinsky,42 K. Karatsu,38, 60 M. Kasai,60, 62 D. Kawall,46, 61 M. Kawashima,60, 62 A.V. Kazantsev,37
T. Kempel,31 J.A. Key,53 V. Khachatryan,67 A. Khanzadeev,59 K.M. Kijima,25 J. Kikuchi,73 A. Kim,20 B.I. Kim,36
C. Kim,36 D.H. Kim,50 D.J. Kim,34, 76 E. Kim,65 E.-J. Kim,11 G.W. Kim,20 M. Kim,65 S.H. Kim,76 Y.-J. Kim,28
Y.K. Kim,24 B. Kimelman,49 E. Kinney,14 K. Kiriluk,14 Á. Kiss,19 E. Kistenev,8 R. Kitamura,13 A. Kiyomichi,60
J. Klatsky,22 J. Klay,41 C. Klein-Boesing,48 D. Kleinjan,9 P. Kline,67 T. Koblesky,14 L. Kochenda,59
V. Kochetkov,27 B. Komkov,59 M. Konno,71 J. Koster,28 D. Kotchetkov,9, 55 D. Kotov,59, 63 A. Kozlov,74 A. Král,16
A. Kravitz,15 J. Kubart,10, 30 G.J. Kunde,42 N. Kurihara,13 K. Kurita,60, 62 M. Kurosawa,60, 61 M.J. Kweon,36
Y. Kwon,69, 76 G.S. Kyle,54 R. Lacey,66 Y.S. Lai,15 J.G. Lajoie,31 D. Layton,28 A. Lebedev,31 D.M. Lee,42 J. Lee,20
K.B. Lee,36 K.S. Lee,36 M.K. Lee,76 S Lee,76 S.H. Lee,67 S.R. Lee,11 T. Lee,65 M.J. Leitch,42 M.A.L. Leite,64
B. Lenzi,64 X. Li,12 P. Lichtenwalner,49 P. Liebing,61 S.H. Lim,76 L.A. Linden Levy,14 T. Liška,16 A. Litvinenko,33
H. Liu,42, 54 M.X. Liu,42 B. Love,72 D. Lynch,8 C.F. Maguire,72 Y.I. Makdisi,7 M. Makek,77 A. Malakhov,33
M.D. Malik,53 A. Manion,67 V.I. Manko,37 E. Mannel,8, 15 Y. Mao,58, 60 L. Mašek,10, 30 H. Masui,71 F. Matathias,15
M. McCumber,14, 42, 67 P.L. McGaughey,42 D. McGlinchey,14, 22 C. McKinney,28 N. Means,67 A. Meles,54

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A. Milov,8, 67, 74 S. Mioduszewski,8 D.K. Mishra,5 M. Mishra,4 J.T. Mitchell,8 M. Mitrovski,66 Y. Miyachi,60, 70
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S. Miyasaka,60, 70 S. Mizuno,60, 71 A.K. Mohanty,5 P. Montuenga,28 H.J. Moon,50 T. Moon,76 Y. Morino,13
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J. Murata,60, 62 A. Mwai,66 S. Nagamiya,35, 60 K. Nagashima,25 Y. Nagata,71 J.L. Nagle,14, ‡ M. Naglis,74
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M.I. Nagy,19, 75 I. Nakagawa,60, 61 H. Nakagomi,60, 71 Y. Nakamiya,25 K.R. Nakamura,38, 60 T. Nakamura,25, 60
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K. Nakano,60, 70 S. Nam,20 C. Nattrass,69 P.K. Netrakanti,5 J. Newby,41 M. Nguyen,67 M. Nihashi,25 T. Niida,71
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S. Nishimura,13 B.E. Norman,42 R. Nouicer,8, 61 T. Novak,75 N. Novitzky,34, 67 A.S. Nyanin,37 C. Oakley,23
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E. O’Brien,8 S.X. Oda,13 C.A. Ogilvie,31 H. Ohnishi,60 M. Oka,71 K. Okada,61 O.O. Omiwade,1 Y. Onuki,60
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J.D. Orjuela Koop,14 J.D. Osborn,47 A. Oskarsson,44 M. Ouchida,25, 60 K. Ozawa,13, 35 R. Pak,8 D. Pal,72
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A.P.T. Palounek,42 V. Pantuev,29, 67 V. Papavassiliou,54 B.H. Park,24 I.H. Park,20 J. Park,65 J.S. Park,65
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S. Park,65 S.K. Park,36 W.J. Park,36 S.F. Pate,54 L. Patel,23 M. Patel,31 H. Pei,31 J.-C. Peng,28 H. Pereira,17
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D.V. Perepelitsa,8 G.D.N. Perera,54 V. Peresedov,33 D.Yu. Peressounko,37 J. Perry,31 R. Petti,8, 67
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C. Pinkenburg,8 R. Pinson,1 R.P. Pisani,8 M. Proissl,67 M.L. Purschke,8 A.K. Purwar,42 H. Qu,23 J. Rak,34, 53
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B.J. Ramson,47 I. Ravinovich,74 K.F. Read,56, 69 S. Rembeczki,21 M. Reuter,67 K. Reygers,48
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D. Reynolds,66 V. Riabov,52, 59 Y. Riabov,59, 63 E. Richardson,45 T. Rinn,31 D. Roach,72 G. Roche,43, ∗67
S.D. Rolnick,9 A. Romana,39, ∗ M. Rosati,31 C.A. Rosen,14 S.S.E. Rosendahl,44 P. Rosnet,43 Z. Rowan,6
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J.G. Rubin,47 P. Rukoyatkin,33 P. Ružička,30 V.L. Rykov,60 B. Sahlmueller,48, 67 N. Saito,35, 38, 60, 61 T. Sakaguchi,869
S. Sakai,71 K. Sakashita,60, 70 H. Sakata,25 H. Sako,32 V. Samsonov,52, 59 S. Sano,13, 73 M. Sarsour,23 S. Sato,32, 35
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A.Yu. Semenov,31 V. Semenov,27, 29 A. Sen,23, 69 R. Seto,9 P. Sett,5 A. Sexton,45 D. Sharma,67, 74 I. Shein,27
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A. Sickles,8, 28, 67 C.L. Silva,31, 42, 64 D. Silvermyr,44, 56 C. Silvestre,17 K.S. Sim,36 B.K. Singh,4 C.P. Singh,44
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M. Slunečka,10, 33 M. Snowball,42 T. Sodre,49 A. Soldatov,27 R.A. Soltz,41 W.E. Sondheim,42
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S.P. Sorensen, I.V. Sourikova,8 F. Staley,17 P.W. Stankus,56 E. Stenlund,44 M. Stepanov,46, ∗ A. Ster,75
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S.P. Stoll,8 T. Sugitate,25 C. Suire,57 A. Sukhanov,8 T. Sumita,60 J. Sun,67 J. Sziklai,75 T. Tabaru,61 S. Takagi,71
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E.M. Takagui,64 A. Takahara,13 A. Taketani,60, 61 R. Tanabe,71 Y. Tanaka,51 S. Taneja,67 K. Tanida,38, 60, 61, 65
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M.J. Tannenbaum,8 S. Tarafdar,4, 74 A. Taranenko,52, 66 P. Tarján,18 E. Tennant,54 H. Themann,67 D. Thomas,179
T.L. Thomas,53 R. Tieulent,23 A. Timilsina,31 T. Todoroki,60, 71 M. Togawa,38, 60, 61 A. Toia,67 J. Tojo,60
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V-N. Tram,39 I. Tserruya,74 Y. Tsuchimoto,25 K. Utsunomiya,13 C. Vale,8, 31 H. Valle,72 H.W. van Hecke,4282
E. Vazquez-Zambrano,15 A. Veicht,15, 28 J. Velkovska,72 R. Vértesi,18, 75 A.A. Vinogradov,37 M. Virius,1683
A. Vossen,28 V. Vrba,16, 30 E. Vznuzdaev,59 M. Wagner,38, 60 D. Walker,67 X.R. Wang,54, 61 D. Watanabe,25
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D. Winter,15 C.L. Woody,8 R.M. Wright,1 M. Wysocki,14, 56 B. Xia,55 W. Xie,61 L. Xue,23 S. Yalcin,67
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Y.L. Yamaguchi,13, 60, 67, 73 K. Yamaura,25 R. Yang,28 A. Yanovich,27 Z. Yasin,9 J. Ying,23 S. Yokkaichi,60, 61
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J.H. Yoo,36 J.S. Yoo,20 I. Yoon,65 Z. You,42, 58 G.R. Young,56 I. Younus,40, 53 H. Yu,58 I.E. Yushmanov,37
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W.A. Zajc,15 O. Zaudtke,48 A. Zelenski,7 C. Zhang,56 S. Zhou,12 J. Zimamyi,75, ∗ L. Zolin,33 and L. Zou989
(PHENIX Collaboration)
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Abilene Christian University, Abilene, Texas 79699, USA
Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
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Department of Physics, Augustana College, Sioux Falls, South Dakota 57197, USA
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Department of Physics, Banaras Hindu University, Varanasi 221005, India
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Bhabha Atomic Research Centre, Bombay 400 085, India
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Baruch College, City University of New York, New York, New York, 10010 USA
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Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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University of California-Riverside, Riverside, California 92521, USA
10Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic
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Chonbuk National University, Jeonju, 561-756, Korea
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Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, P. R. China
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Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
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University of Colorado, Boulder, Colorado 80309, USA
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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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Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France
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Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
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ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary
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Ewha Womans University, Seoul 120-750, Korea
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Florida Institute of Technology, Melbourne, Florida 32901, USA
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Florida State University, Tallahassee, Florida 32306, USA
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Georgia State University, Atlanta, Georgia 30303, USA
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Hanyang University, Seoul 133-792, Korea
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Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
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Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA
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IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia
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University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia
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119Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
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Iowa State University, Ames, Iowa 50011, USA
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Advanced Science Research Center, Japan Atomic Energy Agency, 2-4
122Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan
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Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
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Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland
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KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
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Korea University, Seoul, 136-701, Korea
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Russian Research Center “Kurchatov Institute”, Moscow, 123098 Russia
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Kyoto University, Kyoto 606-8502, Japan
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Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France
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Physics Department, Lahore University of Management Sciences, Lahore 54792, Pakistan
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Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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LPC, Université Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France
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Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
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University of Maryland, College Park, Maryland 20742, USA
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Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA
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Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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Institut für Kernphysik, University of Muenster, D-48149 Muenster, Germany
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Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA
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140Myongji University, Yongin, Kyonggido 449-728, Korea
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Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan52
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National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia
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University of New Mexico, Albuquerque, New Mexico 87131, USA
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New Mexico State University, Las Cruces, New Mexico 88003, USA
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Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
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Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France
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Peking University, Beijing 100871, P. R. China
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PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia
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RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
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RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
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Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia
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Universidade de São Paulo, Instituto de Fı́sica, Caixa Postal 66318, São Paulo CEP05315-970, Brazil
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Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
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Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA
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Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
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SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Université de Nantes) BP 20722-44307, Nantes, France69
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University of Tennessee, Knoxville, Tennessee 37996, USA
70160
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
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Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan72
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Vanderbilt University, Nashville, Tennessee 37235, USA73
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Waseda University, Advanced Research Institute for Science and164
Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan
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Weizmann Institute, Rehovot 76100, Israel
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Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian
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Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary
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Yonsei University, IPAP, Seoul 120-749, Korea
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University of Zagreb, Faculty of Science, Department of Physics, Bijenička 32, HR-10002 Zagreb, Croatia(Dated: September 22, 2015)
We present the first measurement of elliptic (v2 ) and triangular (v3 ) flow in high-multiplicity√
He+Au collisions at sN N = 200 GeV. Two-particle correlations, where the particles have a large
separation in pseudorapidity, are compared in 3 He+Au and in p+p collisions and indicate thatcollective effects dominate the second and third Fourier components for the correlations observed inthe 3 He+Au system. The collective behavior is quantified in terms of elliptic v2 and triangular v3
anisotropy coefficients measured with respect to their corresponding event planes. The v2 values arecomparable to those previously measured in d+Au collisions at the same nucleon-nucleon centerof-mass energy. Comparison with various theoretical predictions are made, including to models
where the hot spots created by the impact of the three 3 He nucleons on the Au nucleus expand
hydrodynamically to generate the triangular flow. The agreement of these models with data may
indicate the formation of low-viscosity quark-gluon plasma even in these small collision systems.
3

171

PACS numbers: 25.75.Dw

5The study of high-energy heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron
Collider has produced abundant evidence for the formation of Quark-Gluon Plasma (QGP). Observation of strong
174 elliptic and triangular flow in these A+A collisions indicates that the QGP has very small viscosity and behaves
175 like a nearly perfect fluid [1–3]. Recently, measurements at the large hadron collider in very high multiplicity events
176 from collisions of p+p and p+Pb have revealed similar particle emission patterns [4–8]. Such features have also been
177 detected in d+Au collisions at RHIC [9–11]. Explanations of the data in terms of the formation of small droplets
178 of QGP which then expand hydrodynamically [12] compete with alternatives involving novel initial-state effects (e.g.
179 glasma models [13]). RHIC is uniquely suited to test these competing theories by its ability to engineer the size and3
180 shape of the initial reaction zone through collisions of p+Au, d+Au, andHe+Au, as proposed in Ref. [14]. In the
181 case when small QGP droplets are formed, the latter two systems should have the strongest elliptic and triangular
182 flow patterns, respectively.
183
The azimuthal anisotropy of produced particles
P can be quantified by the Fourier coefficients vn in the expansion
184 of the particles’ distribution as: dN/dφ ∝ 1 +n=1 2vn cos(n(φ − Ψn )) [15], where n is the order of the harmonic,
185 φ is the azimuthal angle of particles of a given type, and Ψn is the azimuthal angle of the nth-order event plane. In
186 this Letter, the elliptic (v2 ) and triangular (v3 ) flow for inclusive charged hadrons produced at midrapidity |η| < 0.35√
3
187 in high-multiplicity
He+Au collisions at sN N = 200 GeV are measured in the PHENIX experiment with respect
188 to Ψ2 and Ψ3 event planes. The signatures of collective motion beyond known nonflow correlation effects (e.g. jets,
3
189 resonances, etc.) are also examined by comparing long-range correlations between
He+Au and p+p collisions.
190
A full description of the PHENIX experimental setup is given in Ref. [16]. Charged particles are reconstructed in
191 the two PHENIX central-arm tracking systems comprising drift chambers and multi-wire proportional pad chambers
192 (PC) [17]. Each arm covers π/2 in azimuth and |η| < 0.35. The drift-chamber tracks are matched to hits in the
193 outermost PC layer (PC3), reducing the contribution of tracks originating from decays and photon conversions.
194
are measured in different pseudorapidity ranges by the beam-beam counThe observed event-plane angles ΨObsn
195 ters [18] (BBC) and forward-silicon-vertex [19] (FVTX) detectors. The PHENIX experiment has two BBCs, each
196 comprising 64 quartz Čerenkov radiators read out by photomultiplier tubes (PMTs), subtending pseudorapidity
197 (3.0 < |η| < 3.9).
The FVTX [19] detector comprises two identical endcap assemblies, located symmetrically in
198 the north and south directions. Charged particles can be detected with a high efficiency(> 95%) using a cluster of
199 mini-strip hits. The event planes are measured by the BBC in the Au-going (south) direction (BBC-S), which covers
200 −3.9 < η < −3.0, and by the reconstructed clusters in the FVTX in the Au-going (south) endcap (FVTX-S), which
201 covers −3.0 < η < −1.0.
202
The 3 He+Au data for this analysis were obtained in the 2014 run of the PHENIX experiment and include 1.6
203 billion minimum-bias (MB) triggered events and 480 million high-multiplicity (HM) triggered events. The MB trigger
204 is defined as a coincidence between the north and south BBCs requiring one or more photomultiplier tubes firing in
3
205 each, capturing 88±4% of the total inelastic
He+Au cross section. The HM trigger is based on the MB trigger, but
206 additionally requires more than 48 photomultiplier tubes firing in the BBC-S.
P
207
The event centrality class in 3 He+Au collisions is determined as a percentile of the total charge QBBC−S measured
208 in the BBC-S [18, 20–22]. The distribution of BBC-S PMT charge sum is shown in Fig. 1 for both MB and HM
209 triggered events. The distribution for HM events has been scaled down by the relative online trigger prescale factor.
210 For the MB sample, a threshold on the BBC-S charge sum shown in Fig. 1 is applied to select the top 5% central
3211
He+Au collisions. In total, 400 million events have been used for the measurement of v2 and v3 including both HM
212 and MB triggered events having BBC-S charge sum above the threshold.
213
Events with high BBC-S sum charge have been simulated with a Monte Carlo Glauber model [23, 24], following the214 procedure detailed in Ref. [18]. The average number of binary collisions (Ncoll ), participants (Npart ) and initial-state
215 eccentricities (ε2 , ε3 ) were found to be consistent, within uncertainties, between the MB with the 0%–5% central
216 selection, and the HM events being used here. Note that in this Glauber calculation the spatial distribution from each3
217 participant is smeared with a two-dimensional Gaussian, σr = 0.4 fm [18]. The simulation results for central He+Au
218 and d+Au are listed in Table I with the d+Au values from Ref. [18].
172
173

TABLE I. Monte Carlo Glauber characterization results.
System
0%–5% 3 He+Au
0%–5% d+Au

219

Npart
25.0±1.617.3±1.2

Ncoll
26.1±2.0
18.1±1.2ε20.50±0.02
0.54±0.04

ε3
0.28±0.02
0.19±0.01

To estimate the contribution to the flow measurements from elementary processes, such as jets and resonance6

top 5%

105

PHENIX 3He+Au 200 GeV
M.B. Trigger

dN/dQ

104

H.M. Trigger × 0.096

103

102

10

1
0

50

100

150

200

250

300

Charge of BBC(Au-going) (a.u.)

FIG. 1. (Color online) The BBC-S charge distribution in minimum bias 3 He+Au events and in high-multiplicity triggered
events, scaled appropriately. The dashed line indicates the threshold selecting the 0%–5% most central events.

decay, we first examine azimuthal correlations in minimum bias p+p and central 3 He+Au events across a long range
221 in pseudorapidity, with |∆η| ∼ 3.5 between tracks in the PHENIX central arm at a given pT and charge measured in
222 the BBC PMTs. We use the BBCs for these correlation functions because the detector configuration and performance√
223 is uniform over many years, which enables us to combine data for p+p collisions at
s = 200 GeV from running in
224 2005, 2006, 2008, and 2009. This results in 2.7 billion total minimum bias p+p events.
225
Using track-BBC pairs we construct the distribution over relative azimuth, and from that the normalized correlation
226 function:
220

track(p )−PMT

Td(wPMT NSame event
)
d∆φ
R 2π
S(∆φ, pT ) 0 M (∆φ, pT ) d∆φ
C(∆φ, pT ) =R
M (∆φ, pT ) 2π S(∆φ, pT ) d∆φ

S(∆φ, pT ) =

(1)
(2)

0

The weighting wPMT for each pair is taken as the PMT charge. The signal distribution S is over pairs in the same
event; the mixed distribution M is over pairs from different events in the same event centrality and z vertex bin, and229 serves to correct for any nonuniformity in acceptance over ∆φ.
230
Figure 2 shows the correlation functions C(∆φ, pT ) for different pT bins, for HM 3 He+Au collisions using (a)–231 (c) BBC-S and (d)–(f) minimum bias p+p collisions using both BBCs.
We analyze these shapes by fitting each
P4
232 C(∆φ, pT ) to a four-term Fourier cosine expansion, f (∆φ) = 1 +2cn (pT ) cos(n ∆φ). The sum function and
n=1
3
233 each individual cosine component are plotted in Fig. 2 for each distribution. Central He+Au collisions show a clearly
234 visible enhancement of near-side pairs, producing a local maximum in the distribution at ∆φ ∼ 0. In contrast, p+p
235 collisions can be described almost completely by the dipole term cos(∆φ), as expected generically from back-to-back
236 jets and transverse momentum conservation.
As in our d+Au analysis [10], we estimate quantitatively the correlation strength that would be observed in aclass of 3 He+Au collisions purely from elementary processes, such as in p+p collisions. Approximating the 3 He+Au
collisions as superpositions of some number N of p+p collisions, we would then expect the correlation strengths cn
from the superposition to be the same as in p+p, but diluted by a factor of 1/N . We then approximate this dilution
factor as simply the ratio of total charge observed in the BBC-S detector in p+p versus 3 He+Au:
P BBC−S Qp+pelementarycHeAu(pT ) ' cnp+p (pT ) P BBC−S
(3)
n
( Q
)HeAu
227

228

with a numerical value of 1/(20.6 ± 0.4). Figure 3(a) shows the cn ’s from the 3 He+Au correlation functions, and frompp
pp
238 the p+p with the dilution factor applied. The c
2 is found to be positive and the c3 to be negative. This indicates

237

T

C(∆φ,p )

7

1.015
1.010
1.005

(a) pT,track: 0.4-1.0 GeV/c-0.35 < ηtrack < 0.35
-3.9 < η < -3.0, Au-going

3TC(∆φ,p )H.M. He+Au 200 GeV(b)pT,track: 1.0-2.0 GeV/c1.2c3
c 4 p+p 200 GeV

c1
c2

0.9

(e) pT,track: 1.0-2.0 GeV/c

1.010
1.1

1.005

1.0

1.000
0.995

3

H.M. He+Au 200 GeV

0.990
1.015
T

1+Σ 2cncos(n∆ φ)

1.1
1.0

0.995

C(∆φ,p )(d) pT,track: 0.4-1.0 GeV/c

BBC

1.000

1.015

1.2

(c)

p

: 2.0-3.0 GeV/c

T,track

0.9

1.2

p+p 200 GeV(f)p: 2.0-3.0 GeV/c

T,track

1.010
1.1

1.005
1.000

1.0

0.995
3

H.M. He+Au 200 GeV

0.990

-1

0

1

2

∆φ (rad)

3

4

0.9

p+p 200 GeV

PHENIX
-1

0

1

2

3

4

∆φ (rad)FIG. 2. (Color online) The azimuthal correlation functions C(∆φ, pT ), as defined in Eq. 2, for track-BBC pairs with different√
track pT selections in (a)–(c) HM 3 He+Au collisions and (d)–(f) minimum bias p+p collisions both at sN N = 200 GeV. The
track pT bins are (a),(d) 0.4–1.0, (b),(e) 1.0–2.0, and (c),(f) 2.0–3.0 GeV/c. Each correlation function is fit with a four-term
Fourier cosine expansion; the individual components n = 1 to n = 4 are drawn on each panel, together with the fit functionsum.

that the correlation of elementary processes contributes positively to the v2 but negatively to the v3 . The ratios in
Fig. 3(b) show that the relative correlation strength in 3 He+Au from elementary processes grows with pT , as might
241 be expected from jet processes for example, but does not exceed 7% (15%) for c2 (c3 ).
242
We now quantify the strength of collective behavior through the vn coefficients. The vn coefficients for charged3
243 hadrons at midrapidity are measured in central
He+Au events via the event-plane method [25] as vn (pT ) =Particle
Obs
Obs
244 hcos n(φ(pT ) − Ψn )i/Res(Ψn ), where the average is over particles in the same pT bin and events of theObs
245 same centrality. The nth-order event-plane direction Ψn
is determined in each event with the BBC-S or FVTX-S
Obs
246 detectors. The Ψnare corrected for each detector with a standard event-plane flattening technique [25–28] to remove
247 the effect of any small, residual nonuniformities in the detector response. As a cross-check we use event planes from248 both the full FVTX-S covering −3.0 < η < −1.0 and a subsection covering −2.5 < η < −1.5. The choice of the latter
249 is to avoid edge effects and still retain good FVTX-S acceptance.
250
We calculate the resolutions Res(ΨObsn ) for each detector at each n using the standard three-event-plane method [10,251 25], combining two event planes with the nth order event plane determined from central-arm tracks, restricted to low
252 pT (0.2 < pT < 2.0 GeV/c) to minimize contribution from jet fragments. In the case of the n = 2 event plane,
253 the resolution is also estimated using the first-order event plane measured with spectator neutrons in the shower254 maximum detector of the zero-degree calorimeter[28, 29] on the Au-going side (η < −6.5). The values for the
255 resolution obtained in both methods are found to be consistent within uncertainties.
256
The event plane resolutions for each detector and order are shown in Table II. The v2 and v3 measured using the
257 three event planes described above are shown in Fig. 3(c), and are consistent between detectors to within 5%(15%)
258 for v2 (v3 ) over the whole pT range.
259
The main sources of systematic uncertainty for the vn measurements are: (1) track backgrounds from weak decays
3
260 and photon conversions; (2) multiple
He+Au collisions in a bunch crossing (pile-up); (3) biases in event plane
261 determination; (4) the effect of detector alignment and performance on the vn measurement; and (5) elementary
262 process/nonflow correlations. We assign the following values to account for these systematic uncertainties: (1) We
263 estimate the track background contribution by reducing the spatial matching windows in PC3 from 3σ to 2σ, and find
264 a change of less than 2%(5%) fractionally in v2 (v3 ). (2) We expect the vn from pile-up events to be modestly reduced.
265 Conservatively assuming that pile-up events that contaminate the sample at the level of 4%–5% have a negligible
239
240

8

c2×100; c ×1000

PHENIX 3HeAu and pp 200 GeV
0.5

cA2 =cHeAu2

cB2=s×cpp
2

0.4

cA3 =cHeAu
3

cB3=s×c3

pp

3

BBC-S

0.3

(a)

BBC-S

s=Σ Qpp/ Σ QHeAu

cB2/c A2

cB3/c A3(b)v2(Ψ 2, -3.9<η<-3.0)
v2(Ψ 2, -2.5<η<-1.5)
v2(Ψ 2, -3.0<η<-1.0)

v3(Ψ 3, -3.9<η<-3.0) (c)v3(Ψ 3, -2.5<η<-1.5)
v3(Ψ 3, -3.0<η<-1.0)

0.2
0.1

Ratio = cBn/cAn

0.0

0.2

0.0

-0.2
0.25

vn

0.20
0.15
0.10
0.05
0.0

0.5

1.0

1.5

2.0

2.5

3.0

pT (GeV/c)
3
FIG. 3. (Color online) (a) The cn (pT ) coefficients for track-BBC pairs from high multiplicity
He+Au
collisions(filled,denoted
P BBC−S
P BBC−SA(open,/Q“c ”) and cn (pT ) for pairs in minimum bias p+p collisions times the dilution factor
Q
HeAu
p+p

denoted “cB ” ). (b) The ratio cB /cA is shown with statistical error bars. (c) Comparison of extracted values of v2 and v3 formidrapidity tracks in central 3 He+Au using event plane measurements with detectors in different pseudorapidity intervals (seetext).

TABLE II. The resolution of nth-order event-plane angles measured by the BBC-S and FVTX-S detectors.
Subsystem
BBC-S (-3.9 < η < -3.0)
FVTX-S (-2.5 < η < -1.5)
FVTX-S (-3.0 < η < -1.0)

Res(ΨObs
)
2
0.110
0.232
0.274

Res(ΨObs
)
3
0.034
0.052
0.070

vn , this results in a +0
−5 % systematic uncertainty. (3) Event plane effects are estimated from vn measurements using
267 different event plane detectors as shown in Fig. 3(c). They are no more than 5%(15%) for v2 (v3 ). (4) The difference of
268 vn for charged hadrons measured by the east and west DC arms are found to be less than 2%(15%) for v2 (v3 ). (5) The
269 contribution from nonflow correlations at each pT is estimated from Fig. 3(b), reaching a maximum of 7%(15%) for
270 v2 (v3 ). We do not attempt to correct for this contribution and instead treat it as a systematic uncertainty. All of
271 these contributions are summed in quadrature.
272
The final vn results are determined using the event plane measured in the FVTX-S covering -3.0< η <-1.0, and these273 are shown in Fig. 4, with the systematic uncertainties as described above. We observe sizable v2 and v3 anisotropies
3
274 that both rise as a function of pT . It is notable that the v2 (pT ) values for central
He+Au collisions are very similar266

9within uncertainties with those reported earlier in central d+Au collisions [10]. In scenarios where these anisotropies
reflect the initial geometry, this similarity would be expected as the initial eccentricities ε2 for central d+Au and3
277
He+Au are essentially identical, as shown in Table I. The same calculations indicate a much larger ε3 in 3 He+Au
278 compared with d+Au collisions. However, the d+Au data used in [10] were taken in 2008, without a central trigger
279 and before the FVTX was installed, and did not allow extraction of a statistically significant v3 in d+Au.
275

vn

276

0.3

0.25

3

He+Au at 200 GeV, 0-5% Central
PHENIX data v2, v3
SONIC
superSONIC
Glauber+Hydro
IPGlasma+Hydro
AMPT

0.2

v2

0.15

0.1

v3

0.05

0
0

0.5

1

1.5

2

2.5

3
3.5
pT [GeV/c]

FIG. 4. (Color online) Results for v2 (circles) and v3 (squares) as a function of pT for inclusive charged hadrons at midrapidity√
in 0%–5% central 3 He+Au collisions at sN N = 200 GeV; error bars are statistical and shaded bars are systematic uncertainties
as described in the text. Also shown are various theoretical calculations, see text for details and references.

We now compare the experimental data with theory predictions in the literature. Four such predictions shown in
Fig. 4 employ viscous hydrodynamics with η/s at or near the conjectured lower bound 1/4π [30]. The Glauber+Hydro [31]282 (IP-Glasma+Hydro [32]) utilize Glauber (IP-Glasma) initial conditions, and both over predict the magnitude of the v2
283 and v3 data. Improved agreement may be achieved by utilizing a larger value of η/s or by the inclusion of a transition
284 from QGP to a hadronic cascade, which has much larger viscous effects and thus decreases the overall flow. The sonic
285 calculation [14] employs Glauber initial conditions, viscous hydrodynamics, and then at T = 170 MeV a transition
286 to a hadronic cascade. The supersonic calculation [33] additionally includes pre-equilibrium dynamics that boosts
287 the initial velocity fields at the earliest times. The impact of pre-equilibrium is modest on the v2 values and both
288 calculations agree with the data within uncertainties. The effect of pre-equilibrium on v3 is significantly larger as the289 triangular flow takes longer to develop [14]. The supersonic prediction agrees well with the experimental data for
290 pT < 1.5 GeV/c, and then the data trends towards the sonic prediction at higher pT .
291
Lastly, we compare to calculations utilizing the A-Multi-Phase-Transport (ampt) model [34], which incorporates
292 both partonic and hadronic scattering, and has recently been compared with anisotropies in central p+Pb and d+Au
3
293 collisions [35, 36]. ampt results for
He+Au agree reasonably with the experimental v2 and v3 data for pT < 1 GeV
294 and then significantly underpredict the data. Possible underlying causes of the anisotropies within the ampt model
295 are discussed in Ref. [37].
√296
We have presented first results on azimuthal anisotropies v2 and v3 in central 3 He+Au collisions at sN N = 200 GeV.
3297 Calculations including hydrodynamic expansion of the initial hot spots created in He+Au collisions qualitatively de298 scribe the data. Further comparison with different theoretical models should be informative in terms of the contribu299 tions from the initial geometry and each time stage in the medium evolution including pre-equilibrium. Forthcoming
300 results from p+Au collisions at RHIC will provide a full suite of geometries with highly asymmetric collisions to
280

281

10
constrain the origin of the observed anisotropies.
We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and
303 the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from
304 the Office of Nuclear Physics in the Office of Science of the Department of Energy, the National Science Foundation,
305 a sponsored research grant from Renaissance Technologies LLC, Abilene Christian University Research Council,
306 Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry
307 of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan),
308 Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico and Fundação de Amparo à Pesquisa do Estado de309 São Paulo (Brazil), Natural Science Foundation of China (P. R. China), Ministry of Science, Education, and Sports
310 (Croatia), Ministry of Education, Youth and Sports (Czech Republic), Centre National de la Recherche Scientifique,
311 Commissariat à l’Énergie Atomique, and Institut National de Physique Nucléaire et de Physique des Particules
312 (France), Bundesministerium für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander
313 von Humboldt Stiftung (Germany), National Science Fund, OTKA, Károly Róbert University College, and the Ch.
314 Simonyi Fund (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel
315 Science Foundation (Israel), Basic Science Research Program through NRF of the Ministry of Education (Korea),
316 Physics Department, Lahore University of Management Sciences (Pakistan), Ministry of Education and Science,
317 Russian Academy of Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg Foundation (Sweden),
318 the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, the319 Hungarian American Enterprise Scholarship Fund, and the US-Israel Binational Science Foundation.
301
302

∗

Deceased
PHENIX Co-Spokesperson: morrison@bnl.gov‡
322
PHENIX Co-Spokesperson: jamie.nagle@colorado.edu
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