Measurements of azimuthal anisotropy and charged-particle multiplicity in d+Au collisions at \sqrt{s_{_{NN}}}=200, 62.4, 39, and 19.6 GeV
C. Aidala, Y. Akiba, M. Alfred, K. Aoki, N. Apadula, C. Ayuso, V. Babintsev, A. Bagoly, K.N. Barish, S. Bathe, A. Bazilevsky, R. Belmont, A. Berdnikov, Y. Berdnikov, D.S. Blau, M. Boer, J.S. Bok, M.L. Brooks, J. Bryslawskyj, V. Bumazhnov, C. Butler, S. Campbell, V. Canoa Roman, C.Y. Chi, M. Chiu, M. Connors, M. Csanád, T. Csörgő, T.W. Danley, M.S. Daugherity, G. David, K. DeBlasio, K. Dehmelt, A. Denisov, A. Deshpande, E.J. Desmond, J.H. Do, A. Drees, K.A. Drees, M. Dumancic, J.M. Durham, A. Durum, T. Elder, A. Enokizono, S. Esumi, B. Fadem, W. Fan, N. Feege, D.E. Fields, S.L. Fokin, J.E. Frantz, A. Franz, A.D. Frawley, Y. Fukuda, C. Gal, P. Garg, H. Ge, Y. Goto, N. Grau, S.V. Greene, T. Gunji, T. Hachiya, J.S. Haggerty, K.I. Hahn, S.Y. Han, S. Hasegawa, T.O.S. Haseler, X. He, T.K. Hemmick, K. Hill, A. Hodges, K. Homma, B. Hong, T. Hoshino, N. Hotvedt, J. Huang, S. Huang, J. Imrek, M. Inaba, D. Isenhower, Y. Ito, D. Ivanishchev, B.V. Jacak, Z. Ji, B.M. Johnson, V. Jorjadze, D. Jouan, D.S. Jumper, J.H. Kang, D. Kapukchyan, S. Karthas, A.V. Kazantsev, V. Khachatryan, A. Khanzadeev, C. Kim, D.J. Kim, E.-J. Kim, M. Kim, M.H. Kim, D. Kincses, et al. (146 additional authors not shown)
MMeasurements of azimuthal anisotropy and charged-particle multiplicity in d + Aucollisions at √ s NN = 200 , 62.4, 39, and 19.6 GeV C. Aidala, Y. Akiba,
50, 51, ∗ M. Alfred, K. Aoki, N. Apadula, C. Ayuso, V. Babintsev, A. Bagoly, K.N. Barish, S. Bathe,
5, 51
A. Bazilevsky, R. Belmont, A. Berdnikov, Y. Berdnikov, D.S. Blau, M. Boer, J.S. Bok, M.L. Brooks, J. Bryslawskyj,
5, 8
V. Bumazhnov, C. Butler, S. Campbell, V. Canoa Roman, C.Y. Chi, M. Chiu, M. Connors,
20, 51
M. Csan´ad, T. Cs¨org˝o,
17, 61
T.W. Danley, M.S. Daugherity, G. David,
7, 55
K. DeBlasio, K. Dehmelt, A. Denisov, A. Deshpande,
51, 55
E.J. Desmond, J.H. Do, A. Drees, K.A. Drees, M. Dumancic, J.M. Durham, A. Durum, T. Elder, A. Enokizono,
50, 52
S. Esumi, B. Fadem, W. Fan, N. Feege, D.E. Fields, M. Finger, M. Finger, Jr., S.L. Fokin, J.E. Frantz, A. Franz, A.D. Frawley, Y. Fukuda, C. Gal, P. Gallus, P. Garg,
3, 55
H. Ge, Y. Goto,
50, 51
N. Grau, S.V. Greene, T. Gunji, T. Hachiya, J.S. Haggerty, K.I. Hahn, S.Y. Han, S. Hasegawa, T.O.S. Haseler, X. He, T.K. Hemmick, K. Hill, A. Hodges, K. Homma, B. Hong, T. Hoshino, N. Hotvedt, J. Huang, S. Huang, J. Imrek, M. Inaba, D. Isenhower, Y. Ito, D. Ivanishchev, B.V. Jacak, Z. Ji, B.M. Johnson,
7, 20
V. Jorjadze, D. Jouan, D.S. Jumper, J.H. Kang, D. Kapukchyan, S. Karthas, A.V. Kazantsev, V. Khachatryan, A. Khanzadeev, C. Kim,
8, 31
D.J. Kim, E.-J. Kim, M. Kim, M.H. Kim, D. Kincses, E. Kistenev, T. Koblesky, D. Kotov,
49, 53
S. Kudo, K. Kurita, J.G. Lajoie, E.O. Lallow, A. Lebedev, S.H. Lee,
27, 55
M.J. Leitch, Y.H. Leung, N.A. Lewis, X. Li, S.H. Lim,
35, 62
L. D. Liu, M.X. Liu, V.-R. Loggins, S. L¨ok¨os, D. Lynch, T. Majoros, M. Makek, M. Malaev, V.I. Manko, E. Mannel, H. Masuda, M. McCumber, D. McGlinchey,
12, 35
W.J. Metzger, A.C. Mignerey, D.E. Mihalik, A. Milov, D.K. Mishra, J.T. Mitchell, G. Mitsuka, T. Moon, D.P. Morrison, S.I.M. Morrow, T. Murakami,
33, 50
J. Murata,
50, 52
K. Nagai, K. Nagashima, T. Nagashima, J.L. Nagle, M.I. Nagy, I. Nakagawa,
50, 51
H. Nakagomi,
50, 58
K. Nakano,
50, 57
C. Nattrass, R. Nouicer,
7, 51
T. Nov´ak,
17, 61
N. Novitzky, R. Novotny, A.S. Nyanin, E. O’Brien, C.A. Ogilvie, J.D. Orjuela Koop, J.D. Osborn, A. Oskarsson, K. Ozawa,
30, 58
V. Pantuev, V. Papavassiliou, J.S. Park, S. Park,
50, 54, 55
S.F. Pate, M. Patel, W. Peng, D.V. Perepelitsa,
7, 12
G.D.N. Perera, C.E. PerezLara, R. Petti, M. Phipps,
7, 24
C. Pinkenburg, A. Pun, M.L. Purschke, P.V. Radzevich, K.F. Read,
46, 56
V. Riabov,
42, 49
Y. Riabov,
49, 53
D. Richford, T. Rinn, M. Rosati, Z. Rowan, J. Runchey, T. Sakaguchi, H. Sako, V. Samsonov,
42, 49
M. Sarsour, K. Sato, S. Sato, B. Schaefer, B.K. Schmoll, R. Seidl,
50, 51
A. Sen,
27, 56
R. Seto, A. Sexton, D. Sharma, I. Shein, T.-A. Shibata,
50, 57
K. Shigaki, M. Shimomura,
27, 41
C.L. Silva, D. Silvermyr, M.J. Skoby, M. Sluneˇcka, K.L. Smith, R.A. Soltz, S.P. Sorensen, I.V. Sourikova, P.W. Stankus, S.P. Stoll, T. Sugitate, A. Sukhanov, S. Syed, A Takeda, K. Tanida,
28, 51, 54
M.J. Tannenbaum, S. Tarafdar,
59, 60
G. Tarnai, R. Tieulent,
20, 37
A. Timilsina, M. Tom´aˇsek, C.L. Towell, R.S. Towell, I. Tserruya, Y. Ueda, B. Ujvari, H.W. van Hecke, S. Vazquez-Carson, J. Velkovska, M. Virius, V. Vrba,
14, 26
X.R. Wang,
44, 51
Z. Wang, Y. Watanabe,
50, 51
C.P. Wong, C. Xu, Q. Xu, Y.L. Yamaguchi,
51, 55
A. Yanovich, P. Yin, J.H. Yoo, I. Yoon, H. Yu, I.E. Yushmanov, W.A. Zajc, S. Zharko, and L. Zou (PHENIX Collaboration) Abilene Christian University, Abilene, Texas 79699, USA Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA Department of Physics, Banaras Hindu University, Varanasi 221005, India Bhabha Atomic Research Centre, Bombay 400 085, India Baruch College, City University of New York, New York, New York, 10010 USA Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA University of California-Riverside, Riverside, California 92521, USA Charles University, Ovocn´y trh 5, Praha 1, 116 36, Prague, Czech Republic Chonbuk National University, Jeonju, 561-756, Korea Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan University of Colorado, Boulder, Colorado 80309, USA Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic Debrecen University, H-4010 Debrecen, Egyetem t´er 1, Hungary ELTE, E¨otv¨os Lor´and University, H-1117 Budapest, P´azm´any P. s. 1/A, Hungary Eszterh´azy K´aroly University, K´aroly R´obert Campus, H-3200 Gy¨ongy¨os, M´atrai ´ut 36, Hungary Ewha Womans University, Seoul 120-750, Korea Florida State University, Tallahassee, Florida 32306, USA a r X i v : . [ nu c l - e x ] D ec Georgia State University, Atlanta, Georgia 30303, USA Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic Iowa State University, Ames, Iowa 50011, USA Advanced Science Research Center, Japan Atomic Energy Agency, 2-4Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan Helsinki Institute of Physics and University of Jyv¨askyl¨a, P.O.Box 35, FI-40014 Jyv¨askyl¨a, Finland KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan Korea University, Seoul, 136-701, Korea National Research Center “Kurchatov Institute”, Moscow, 123098 Russia Kyoto University, Kyoto 606-8502, Japan Lawrence Livermore National Laboratory, Livermore, California 94550, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden IPNL, CNRS/IN2P3, Univ Lyon, Universit Lyon 1, F-69622, Villeurbanne, France University of Maryland, College Park, Maryland 20742, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia University of New Mexico, Albuquerque, New Mexico 87131, USA New Mexico State University, Las Cruces, New Mexico 88003, USA Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, BP1, F-91406, Orsay, France Peking University, Beijing 100871, People’s Republic of China PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia 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 Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia 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 University of Tennessee, Knoxville, Tennessee 37996, USA Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan Vanderbilt University, Nashville, Tennessee 37235, USA Weizmann Institute, Rehovot 76100, Israel Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, HungarianAcademy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary Yonsei University, IPAP, Seoul 120-749, Korea Department of Physics, Faculty of Science, University of Zagreb, Bijeniˇcka c. 32 HR-10002 Zagreb, Croatia (Dated: December 7, 2017)We present measurements of the elliptic flow ( v ) as a function of transverse momentum ( p T ),pseudorapidity ( η ), and centrality in d +Au collisions at √ s NN = 200, 62.4, 39, and 19.6 GeV.The beam-energy scan of d +Au collisions provides a testing ground for the onset of flow signaturesin small collision systems. We measure a nonzero v signal at all four collision energies, which, atmidrapidity and low p T , is consistent with predictions from viscous hydrodynamic models. Compar-isons with calculations from parton transport models (based on the ampt Monte Carlo generator)show good agreement with the data at midrapidity to forward ( d -going) rapidities and low p T . Atbackward (Au-going) rapidities and p T > . c , the data diverges from ampt calculations of v relative to the initial geometry, indicating the possible dominance of nongeometry related corre-lations, referred to as nonflow. We also present measurements of the charged-particle multiplicity( dN ch /dη ) as a function of η in central d +Au collisions at the same energies. We find that in d +Aucollisions at √ s NN = 200 GeV the v scales with dN ch /dη over all η in the PHENIX acceptance. At √ s NN = 62 .
4, and 39 GeV, v scales with dN ch /dη at midrapidity and forward rapidity, but fallsoff at backward rapidity. This departure from the dN ch /dη scaling may be a further indication ofnonflow effects dominating at backward rapidity. I. INTRODUCTION
Measurements of the azimuthal momentum anisotropyof particles produced in high-energy heavy ion collisions( A + A ) have provided strong evidence for the formationof a strongly coupled Quark-Gluon Plasma (QGP)[1–4].This anisotropy, as measured by the Fourier coefficients, v n , can be understood as arising from initial geometrypropagated to final-state momentum correlations via in-teractions between medium constituents. These inter-actions have been well described by relativistic hydro-dynamics with a low ratio of viscosity to entropy den-sity [5, 6].In 2012, measurements of v in √ s NN = 5.02 TeV p +Pb collisions at the Large Hadron Collider (LHC) [7–9]and √ s NN = 200 GeV d +Au collisions at the Relativis-tic Heavy Ion Collider (RHIC) [10] raised the questionwhether a QGP might be formed even in these smallcollision systems. Further measurements in p +Pb colli-sions revealed that the signal persists for multi-particlecorrelations [11–14], which is additional evidence of col-lective behavior. To test the signal’s connection to theinitial geometry of the collision, PHENIX measured v in p/d/ He+Au collisions and v in He+Au collisionsat √ s NN = 200 GeV [15–18]. The results are consis-tent with the interpretation that the measured v arisesfrom initial geometry. High-multiplicity p + p collisionsat √ s NN = 2.76, 5.02, 7.13, and 13 TeV exhibit simi-lar effects [19–21] and may also be related to the initialgeometry [22].Even in these small collision systems, the data atboth RHIC and the LHC can be described by hydro-dynamic calculations [17, 22]. However, it has also beenshown that calculations using kinetic theories of hadronicand partonic scattering (e.g., a multiphase transport( ampt ) model [23]) can qualitatively describe the v mea-sured in small systems [17, 24, 25]. In both hydrody-namic and kinetic models, initial geometry (coordinatespace anisotropy) is translated to final state momentumspace anisotropy via interactions between medium con-stituents. In contrast, other explanations, including colorrecombination [26] and initial-state effects from glasmadiagrams [27], have also been proposed, where the final-state momentum correlations are due to initial momen-tum correlations rather than a connection to the initialgeometry.Throughout this paper we use a working definition of“flow” as initial geometry propagated to final-state az-imuthal momentum anisotropy, regardless of the mech-anism of propagation (e.g. fluid flow or particle trans-port). All other sources of final-state azimuthal momen-tum anisotropy are referred to as “nonflow”. Examplesof nonflow include jet correlations, resonance decays, andCoulomb interactions. ∗ PHENIX Spokesperson: [email protected]
In 2016, RHIC delivered d +Au collisions at √ s NN = 200, 62.4, 39, and 19.6 GeV in order toinvestigate the onset of collectivity. PHENIX has pre-viously published results on multi-particle correlationsfrom this data set [28], providing evidence for collectivebehavior at all energies. Here we report comprehensivemeasurements of v as a function of p T , η , and centralityin d +Au collisions at √ s NN = 200, 62.4, 39, and 19.6GeV. We also report measurements of the chargedparticle multiplicity ( dN ch /dη ) as a function of η incentral d +Au collisions at the same energies. II. EXPERIMENT AND DATA SET
WestSouth
Side ViewBeam View
PHENIX Detector2012
NorthEast
MuTrMuIDRPC3 RPC1 MuIDRPC3MPC BBC(F)VTXPbSc PbScPbSc PbScPbSc PbGlPbSc PbGlTOF-EPC1 PC1PC3PC2Central MagnetCentralMagnet N o r t h M u o n M a g n e t S ou t h M uon M a gn e t TECPC3BBC(F)VTXMPCBBRICH RICHDC DC ZDC NorthZDC South AerogelTOF-W . m = f t . m = f t MPC(EX) (F)VTX
MPC(EX)
FIG. 1. A schematic view of the PHENIX detector as con-figured in 2016.
The PHENIX detector is described in detail in Ref. [29]and shown schematically in Fig. 1. Global event charac-terization and triggering use two beam-beam counters(BBC)[30] located in the pseudorapidity region 3 . < | η | < .
9, as well as a forward silicon vertex detector(FVTX) [31] covering 1 < | η | <
3. Each BBC com-prises 64 ˇCerenkov counters arrayed around the beampipe 1.44 m from the nominal interaction region. Thecounters comprise 3 cm of quartz coupled to a mesh-dynode photomultiplier tube, where the charge is cal-ibrated to a minimum-ionizing charged particle. The
TABLE I. Summary of the data analyzed by PHENIX fromthe 2016 RHIC d +Au beam energy scan. √ s NN [GeV] (cid:15) MB triggered triggeredevents [10 ] events [10 ]200 88 ±
4% 53 569 (0%–5%)62.4 78 ±
4% 113 214 (0%–10%)39 74 ±
6% 231 171 (0%–20%)19.6 61 ±
8% 33 7 (0%–20%)
FVTX is made up of two annular endcaps, each withfour stations of silicon mini-strip sensors. Each stationcomprises 47 individual silicon sensors, each of which con-tains two columns of mini-strips with 75 µ m pitch in theradial direction and lengths in the φ direction varyingfrom 3.4 mm at the inner radius to 11.5 mm at theouter radius. The negative-rapidity south -side region(Au-going direction) has the BBCS and FVTXS arms,while the positive-rapidity north -side region ( d -going di-rection) has the BBCN and FVTXN arms. Charged-particle tracking is provided by the east and west cen-tral arms at midrapidity, covering | η | < .
35 each withan azimuthal ( φ ) coverage of π/ d +Au inelastic crosssection that the MB trigger fires on, (cid:15) MB , is given in Ta-ble I for both energies. In addition to the MB trigger, ahigh-multiplicity trigger that required >
40 (29) hit tubesin the BBCS for 200 (62.4) GeV was also run, provid-ing a factor of 188 (11) enhancement of high-multiplicityevents. Analyzed events were further required to havea reconstructed collision vertex in the longitudinal direc-tion as reconstructed by the BBC of | z vrtx | <
10 cm. Theresulting number of analyzed events is shown in Table I.At 39 and 19.6 GeV, the FVTX combined with thesouth BBC is used for the MB trigger. This combinationhas a larger trigger efficiency at these lower energies thana BBC coincidence due to the low multiplicities in the re-gion 3 . < η < . φ = 0 .
26 rad,effectively requiring a single track in each of the northand south arms. To reduce background, at least one hittube was required in the south BBC. The efficiency ofthe MB trigger, (cid:15) MB at both energies is given in Table I.Additionally, a high-multiplicity trigger was implementedthat further required >
27 (18) hits in the south BBC for39 (19.6) GeV, providing a factor of 6.0 (1.8) enhance-ment of high-multiplicity events. Analyzed events werealso required to have | z vrtx | <
10 cm, as reconstructedby the FVTX. To reduce beam-gas and beam-pipe back-ground, the total number of reconstructed clusters in the
TABLE II. Summary of the mean number of participants, (cid:104) N part (cid:105) , and eccentricity, (cid:104) ε (cid:105) , for central d +Au collisions at √ s NN = 200, 62.4, 39, and 19.6 GeV. √ s NN [GeV] centrality (cid:104) N part (cid:105) (cid:104) ε (cid:105)
200 0%–5% 17.8 ± ± ± ± ± ± ± ± FVTX, both south and north arms, was required to be <
500 (300) at 39 (19.6) GeV. The resulting number ofanalyzed events is shown in Table I.The collision centrality at all four energies is deter-mined using the total charge in the south (Au-going)BBC, as described in Ref. [32]. Figure 2 shows theBBCS charge distributions from MB triggered data ateach energy along with the limits of the various central-ity bins. It also includes the BBCS charge distributionsfor the high-multiplicity trigger, renormalized to matchthe high-charge region, showing the trigger turn-on ateach energy. To avoid bias in the centrality distribution,analyzed events firing the high-multiplicity trigger arerequired to have centrality 0%–5%, 0%–10%, 0%–20%,0%–20% at √ s NN = 200, 62.4, 39, and 19.6, respectively.These regions correspond to centralities for which thehigh-multiplicity trigger was efficient.Using Monte-Carlo Glauber combined with fluctua-tions modeled by a negative binomial distribution aslaid out in Ref. [32], the mean number of participants, (cid:104) N part (cid:105) , and the mean initial geometry eccentricity, (cid:104) ε (cid:105) ,can be characterized for given centrality bins. Table IIshows the (cid:104) N part (cid:105) and (cid:104) ε (cid:105) values for central collisionsat all four energies. The (cid:104) ε (cid:105) values are consistent at allfour collision energies within uncertainties. The (cid:104) N part (cid:105) values, however, decrease with decreasing energy. Thiscan be attributed to both the decreasing nucleon-nucleoninteraction cross section and the larger centrality bins at39 and 19.6 GeV, which were used to improve the statis-tical precision of the measurements.In the central arms, unidentified charged particle track-ing uses the drift chamber (DC) and pad chamber (PC)layers. We require tracks to have a unique match betweenDC hits and PC hits in the layer immediately surround-ing the DC. Tracks are further required to have a match-ing hit in the third PC layer at R = 4 .
98 m that is within ± σ of the projected track location, where σ character-izes the momentum-dependent widths of the matchingdistributions.In addition to triggering, the FVTX is used for uniden-tified charged particle tracking. The FVTX does notmeasure track momentum, and we therefore are limitedto a momentum integrated measurement. We require re-constructed tracks in the FVTX to have hits in at least 3of the 4 stations with fit quality, χ / d.o.f. <
5. We furtherrequire that the distance of closest approach of the track
BBC Charge South0 10 20 30 40 50 60 7010 BBC Charge South0 10 20 30 40 50 60 70 80 BBC Charge South0 10 20 30 40 50 60 70 8010 BBC Charge South0 20 40 60 80 100 12010 (a) PHENIX d+Au at s NN = 200 GeV (b) PHENIX d+Au at s NN = 62.4 GeV (c) PHENIX d+Au at s NN = 39.0 GeV (d) PHENIX d+Au at s NN = 19.6 GeV Data, Minimum BiasData, High MultiplicityCentrality ClassesGlauber + NBD C oun t s C oun t s C oun t s C oun t s
0 20 40 60 80 100 120
BBC Charge South
0 10 20 30 40 50 60 70
BBC Charge South
0 10 20 30 40 50 60 70 80
BBC Charge SouthBBC Charge South
0 10 20 30 40 50 60 70
FIG. 2. The distributions of total charge in the BBCS for d +Au collisions at √ s NN = 200 (a), 62.4 (b), 39 (c), and 19.6(d) GeV. The data is from MB collisions, and we note that, asdiscussed in the text, the MB trigger definition changes withenergy. The colored bands represent, from right to left, thecentrality categorizations 0%–5%, 5%–10%, 10%–15%, 15%–20%, 20%–30%, 30%–40%, 40%–50%, 50%–60%, and 60%–XX%, where XX is the value of the MB trigger efficiency foreach energy, given in Table I. The thick solid line shows thehigh-multiplicity trigger selection, scaled down to match theMB distribution. to the primary collision vertex, DCA , be within 2.0 cmin both the x and y directions, transverse to the beamaxis. The expected DCA resolution from simulation is ≈ . DCA re-moves background from upstream beam-gas interactions,as well as mis-reconstructed tracks.The luminosity delivered by RHIC for d +Au collisionsat √ s NN = 200 GeV is high enough that approximately6% of events are expected to contain multiple collisions(i.e. pile-up). The fraction of pile-up events is larger incentral events, and is expected to be as large as 20% inthe highest luminosity periods. An algorithm was devel-oped to aid in rejecting these events. For each event, thedistribution of times for each hit tube in the BBCS isdetermined. Then, the fraction, f , of the time distribu-tion for that event which is within a 0.5 ns window ofthe mode of the measured distribution is calculated. Be-cause multiple collisions typically occur at different posi-tions along the beam axis, particles from these collisionstend to leave multiple peaks in the distribution of timesrecorded in the BBCS. Therefore, pile-up events are typ-ically characterized by low values of f . We reject eventswith f < .
95 for centrality 0%–20%. Studies using lowluminosity data and manufactured pile-up events indi-cate that this cut rejects 81% of pile-up events while ac-cepting 93% of single collision events for 0%–5% centralcollisions. Based on the luminosities delivered at 62.4,39, and 19.6 GeV, fewer than 1% of events are expectedto contain multiple collisions, and therefore no cut on f is included. III. ANALYSIS
We first discuss two-particle correlation functions inSec. III A. The analysis of the p T dependence of the sec-ond order flow coefficient, v , is discussed in Sec. III B.The analysis of the η dependence of v is discussedin Sec. III C. The analysis of dN ch /dη is discussed inSec. III D. A. Two-particle correlations
We start by constructing long-range azimuthal corre-lations in d +Au collisions at √ s NN = 200 GeV. The two-particle correlation function is defined as C (∆ φ ) = S (∆ φ ) M (∆ φ ) (cid:82) π M (∆ φ ) (cid:82) π S (∆ φ ) , (1)where ∆ φ is the difference in the azimuthal angles be-tween two tracks, S (∆ φ ) is the signal distribution, con-structed from track pairs in the same event, and M (∆ φ )is the mixed event distribution, constructed from trackpairs from different events in the same centrality and col-lision vertex class. Figure 3 shows C (∆ φ ) for correlations - fD ) fD C ( = 200 GeV 0-5% NN sd+Au CNT -- FVTXS| < 3.35 hD fD cos(n n S - fD ) fD C ( = 200 GeV 0-5% NN sd+Au CNT -- BBCS| < 4.25 hD PHENIX ) fD cos( - fD ) fD C ( = 200 GeV 0-5% NN sd+Au FVTXN -- FVTXS| < 6.00 hD fD cos(2 - fD ) fD C ( = 200 GeV 0-5% NN sd+Au BBCN -- BBCS| < 7.80 hD fD cos(3 FIG. 3. Two-particle ∆ φ correlations in central d +Au collisions at √ s NN = 200 GeV between various detectors. The bluedot-dashed lines, red long-dashed lines, and green dotted lines, correspond to the C , C , and C components, respectively.The black dashed lines correspond to the sum of the C n ’s up to third order. For the correlations in panels (a) and (b), CNTtracks were required to be within 0 . < p T [GeV /c ] < . of tracks between different detectors in central d +Au col-lisions at √ s NN = 200 GeV: (a) between tracks in the cen-tral arms and tracks in the FVTXS, (b) between tracksin the central arms and tubes in the BBCS, (c) betweentracks in the FVTXS and FVTXN, and (d) betweentubes in the BBCS and BBCN. By comparing C (∆ φ )distributions between different sets of detectors we nat-urally change the ∆ η requirement for the pair of tracks.Correlations with a small ∆ η are typically thought tobe dominated by nonflow correlations, particularly fromintrajet correlations near ∆ φ = 0, as well as dijet corre-lations near ∆ φ = π . By increasing the ∆ η gap betweenparticles we naturally reduce the dominance of these non-flow correlations. Figure 3 shows correlation functionswith (a) 0 . < | ∆ η | < .
35, (b) 2 . < | ∆ η | < .
25, (c)2 . < | ∆ η | < .
0, and (d) 6 . < | ∆ η | < . φ = 0and ∆ φ = π . The peak at ∆ φ = π is associated with,for example, dijets. The peak at ∆ φ = 0 does not arisefrom particles within a jet or decays, because we haveimposed a large ∆ η gap. This peak was first observed in A + A collisions and has been termed the long-range near-side ridge. This near-side ridge was one of the key com-ponents in understanding the hydrodynamic descriptionof A + A collisions (See Ref. [33] and references therein).The observation of this structure in high-multiplicity p + p collisions at √ s NN = 7 TeV [20] was one of the first hintsthat collectivity may exist even in small collision systems.We observe a visible near-side ridge up to | ∆ η | > . F (∆ φ ) = 1 + (cid:88) n =1 C n cos n ∆ φ, (2)where C n is the nth order Fourier component. The fullfit and the components are shown as lines in Fig. 3. Thedominant term is the first order C term, and arises fromelementary processes, such as momentum conservation.The second order term, C , is associated with flow. While the longest range correlation shown in Fig. 3(d), with | ∆ η | > .
2, does not show a clear peak at ∆ φ = 0, itdoes include a strong second-order Fourier component, C . [GeV/c] T p v – Global Sys. = {EP} v [PRL 114, 192301 (2015)]{EP} v {2PC} v PHENIX NN s FIG. 4. The v vs p T in 0%–5% central d +Au collisions at √ s NN = 200 GeV using the event-plane method (black filledcircles) and two-particle correlations (red filled diamonds).Also shown are the previously published v vs p T using theevent-plane method (blue filled squares) from PHENIX usingdata collected in 2008 [15]. Using the two-particle correlation (2PC) functions C (∆ φ, p T ), the v as a function of p T , v { P C } , canbe calculated for central arm tracks using v { P C } = (cid:115) C AB (∆ φ, p T ) × C AC (∆ φ, p T ) C BC (∆ φ ) , (3)where the superscript AB refers to correlations betweencentral arm and FVTXS tracks, AC refers to correlationsbetween central arm tracks and BBCS tubes, and BC refers to correlations between FVTXS tracks and BBCStubes. This relation can be understood as arising fromthe assumption of flow factorization, which allows thecorrelation function to be interpreted as e.g. C AB (∆ φ ) = (cid:104) v An v Bn (cid:105) . In that way, Eqn. 3 reduces to v { P C } = (cid:115) (cid:104) v An v Bn (cid:105)(cid:104) v An v Cn (cid:105)(cid:104) v Bn v Cn (cid:105) , (4)where the superscripts A , B , C represent the centralarms, the FVTXS, and the BBCS, respectively.The v { P C } vs p T for 0%–5% d +Au collisions at √ s NN = 200 GeV is shown as the red points in Fig. 4.We also investigate the energy dependence of thenear-side ridge using correlations between tracks in theFVTXN and FVTXS. Figure 5 shows C (∆ φ ) with 2 . < | ∆ η | < . d +Au collisions at √ s NN = 200,62.4, 39, and 19.6 GeV. A visible peak at ∆ φ = 0 is onlyobserved at 200 GeV; however, substantial C compo-nents are extracted at 62.4 and 39 GeV. At 19.6 GeV,no visible C component is extracted. The C (∆ φ ) is in-tegrated over p T and hence dominated by low p T tracks.Therefore, the lack of a visible C component at 19.6 GeVdoes not exclude a nonzero v , particularly at higher p T . B. Analysis of v vs p T using the event-planemethod The standard event-plane method [34] is used to cal-culate v as a function of p T : v ( p T ) = (cid:104) cos 2( φ trk ( p T ) − Ψ FVTXS2 ) (cid:105) R (Ψ FVTXS2 ) , (5)where φ trk is the azimuthal angle of tracks in the cen-tral arms, and Ψ FVTXS2 is the azimuthal angle of thesecond-order event-plane measured by the FVTXS. Theevent plane in the FVTXS is constructed in the usualway of 2 ψ = atan2( Q FVTXS y , Q FVTXS x ), with Q FVTXS = (cid:80) Mi =1 e inφ i , where φ i is the azimuthal angle of some clus-ter in the FVTXS. The underlying physics correlationis the same whether one uses tracks or clusters, but theuse of clusters provides higher event-plane resolution andtherefore greater statistical precision. The resolutionof Ψ FVTXS2 , R (Ψ FVTXS2 ), is calculated using the three-subevent method [34] that correlates measurements inthe FVTXS, BBCS, and central arms. The resolutionis strongly dependent on both the collision energy andcentrality, and is shown in Table III. We note that for39 to 200 GeV we find that R (Ψ FVTXS2 ) increases in themost peripheral centrality bin. This is contrary to ex-pectations, because R (Ψ FVTXS2 ) depends on both the v in the event-plane region and the number of particles,both of which are expected to decrease in more periph-eral events. Nonflow is likely the largest contribution in TABLE III. Resolution of Ψ measured in the BBCS andFVTXS at each energy and centrality. √ s NN [GeV] centrality R (Ψ BBCS2 ) R (Ψ FVTXS2 )200 0%–5% 0.1073 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± the most peripheral collisions, and may result in this in-creased resolution.Due to its better resolution, we use the measurementof Ψ from the FVTXS. However, we can compare the v vs p T measured using the BBCS, which has a largerseparation of | ∆ η | > .
75 relative to the central armtracks compared to | ∆ η | > .
65 with the FVTXS. The v values are found to agree within 2.5% for p T < c , where we expect nonflow effects to be small. For p T > c a larger value of v is observed using theFVTXS compared to the BBCS. This difference is likelydue to differences in the nonflow contributions, which areexpected to be larger at high p T given the smaller ∆ η gapbetween the event plane and the track.At 19.6 GeV, no combination of three-subevents yieldsa real valued event-plane resolution. We expect that thisis due to the low multiplicity at 19.6 GeV combined withthe strong η dependence of v . We therefore extrapolatethe R (Ψ FVTXS2 ) from the results at higher energies. Theevent-plane resolution is expected to follow the form [35] R ( χ ) = √ π χe − χ/ (cid:20) I (cid:18) χ (cid:19) + I (cid:18) χ (cid:19)(cid:21) , (6)where χ = v √ N , N is the multiplicity, and I i are themodified Bessel functions. The measured resolutions at200, 62.4, and 39 GeV are used to extrapolate the resolu-tion at 19.6 GeV under the following three assumptions:1. The v is constant with √ s NN . - fD ) fD C ( = 200 GeV 0-5% NN sd+Au < 3.0 A h FVTXN: 1.0 < < -1.0 B h FVTXS:-3.0 < (a) - fD ) fD C ( = 62.4 GeV 0-5% NN sd+Au (b) ) fD cos(n n S - fD ) fD C ( = 39 GeV 0-10% NN sd+Au (c) ) fD cos( fD cos(2 fD cos(3 - fD ) fD C ( = 19.6 GeV 0-20% NN sd+Au (d) PHENIX
FIG. 5. Two-particle ∆ φ correlations in central d +Au collisions at √ s NN = 200, 62.4, 39, and 19.6 GeV between tracks inthe north and south FVTX detectors. The blue dot-dashed lines, red long-dashed lines, and green dotted lines, correspond tothe C , C , and C components, respectively. The black dashed lines correspond to the sum of the C n ’s up to third order.
2. The v follows the energy dependence given by the ampt model [23], which has been found to reason-ably reproduce the energy dependence of v in smallcollision systems [17, 24].3. The v follows the energy dependence given by ampt for 200–39 GeV, but at 19.6 GeV the v isthe same as at 39 GeV.Using the measured multiplicities, we find that allthree assumptions give results that are in good agree-ment with the measured resolutions at 200–39 GeV. Wetake the average extrapolated resolution from the threecases, and assign the maximum extent of the variation asa systematic uncertainty. This procedure gives a value of R (Ψ FVTXS2 ) = 0 . +0 . − . for 0%–20% central collisionsat √ s NN = 19.6 GeV.During the d +Au data taking in 2016, a 1.0 mrad off-set between the colliding beams and the longitudinal axisof PHENIX was required due to the asymmetric collisionspecies. We negate this effect by applying a counter rota-tion to each central arm track, FVTX cluster, and BBCtube. After applying the counter rotation, we find noappreciable offset between the v ( p T ) measured in theeast ( π/ < φ < π/
2) and west ( − π/ < φ < π/
2) cen-tral arms for central events. However, as we go towardsmore peripheral events, an increasing difference betweenthe east and west central arms is observed. This may bedue to a decrease in the flow v signal relative to back-ground uncorrelated to the beam axis. When calculatingΨ FVTXS2 , we use the standard Q vector approach [34].To account for any remaining beam offset or backgroundeffects, we apply a centrality and collision energy depen-dent offset to the y component of the 2nd order Q vector,∆ Q y , such that the difference between the east and westcentral arms is removed.The dominant sources of systematic uncertainty in themeasurement of v ( p T ) are: (1) Track background fromphoton conversions and weak decays. We estimate theeffect of these tracks by comparing the v measured witha tighter cut on the matching window required for hits inthe 3rd layer of the PC. We find that this increases the v by up to 2%, independent of centrality and energy. (2)Contamination from event pile-up. The effect of pile-upat 200 GeV is estimated by varying the pile-up rejectionbetween 0 . < f < .
98. This has a negligible effecton the v , and we assign a 1% uncertainty at 200 GeV.(3) Uncertainty on ∆ Q y . As a conservative estimate,we vary the ∆ Q y values by ±
50% and compare the re-sulting v ( p T ) values. An uncertainty of < v ( p T ) values mea-sured independently using the FVTXS and BBCS eventplanes. As discussed above, this difference for p T < c is found to be 2.5% independent of centrality andenergy. (5) The difference between the event-plane andtwo-particle-correlation methods. As shown in Fig. 4,there is good agreement between the two methods in cen-tral collisions, however there is some difference for moreperipheral collisions. We include this difference as an ad-ditional systematic uncertainty. (6) Uncertainty in theevent-plane resolution as given in Table III. As discussedabove, the resolution at 19.6 GeV is extrapolated fromthe measured results at 200–39 GeV and a systematic un-certainty is assigned based on varying the assumptions ofthe extrapolation. The uncertainties are summarized inTable IV, categorized by type . PHENIX considers threecategories of systematic uncertainties:1. Type A : point-to-point uncorrelated;2.
Type B : point-to-point correlated;3.
Type C : global scale uncertainties.On all plots, type A uncertainties are represented asvertical error bars, type B uncertainties by filled boxes,and type C uncertainties are quoted on the plot or in thelegend.In previous PHENIX publications on flow in small sys-tems [16, 17], an estimation of the nonflow contributionsto the measured v has been included in the systematicuncertainties. The estimation used the ratio of the C measured in p + p collisions, scaled by the relative charge TABLE IV. Systematic uncertainties on measurements of v vs p T . Source Type √ s NN [GeV]200 62.4 39 19.6Track Background B 2.0% 2.0% 2.0% 2.0%Event Pile-up B 1.0% < < < < < < < +35% − in the BBCS, to the C measured in p/d/ He+Au. InRef. [15], nonflow was estimated to contribute positivelybetween ∼
5% at p T = 1 GeV/ c and ∼
10% at p T = 4GeV/ c to the observed v signal. This estimation as-sumes that correlations in p + p collisions come from non-flow alone, which may be an overestimate given recentresults in p + p collisions at the LHC. In this analysis welack a suitable p + p reference at all four energies and,therefore, do not make any estimation of the nonflowcontributions to the measured v in this paper.Figure 4 shows the v vs p T in 0%–5% central d +Aucollisions at √ s NN = 200 GeV measured with the event-plane method compared to the two-particle correlationmethod described above. The two methods are consis-tent with each other. The two-particle method alwaysgives the RMS average of v , i.e. (cid:112) (cid:104) v (cid:105) . By contrast,the event-plane method is an estimator of (cid:104) v α (cid:105) /α [35],where 1 < α <
2. For sufficiently high-multiplicities,e.g. in central A + A , α approaches 1 and the event-planemethod is an estimator of (cid:104) v (cid:105) . As the multiplicity de-creases, α approaches 2 and the event-plane method isequivalent to the two-particle method. The consistencybetween the two methods here demonstrates we are in theregime where the multiplicity is low enough that the twomethods are equivalent. It is important to remember,then, that all event-plane method results have the samedependence on the fluctuations of the v distribution asthe 2-particle method.Also shown in Fig. 4 is the previously published mea-surement of v ( p T ) in 0%–5% central d +Au collisionsat √ s NN = 200 from PHENIX using data collected in2008 [15]. The results are in good agreement for p T < c . We note that the result presented here uses adifferent detector to measure the event plane than thatused in Ref. [15]. This is a dominant source of systematicuncertainty in the measurement and is therefore largelyuncorrelated between the two. Further, at high p T , non-flow effects play a larger role (as discussed later in thispaper), and are dependent on the ∆ η gap between theregion in which the event plane is measured and the re-gion in which the v is measured. The increasing nonflowat high p T , which is not estimated in the measurementpresented here, potentially explains the modest differencebetween the two measurements. C. Analysis of v vs η using the event-plane method The measurement of the η dependence of v uses thesame event-plane method as discussed in Sec. III B. How-ever, in order to cover the maximum extent in η , tracksin both the FVTXN and FVTXS are included alongsidetracks measured in the central arms. This necessitatesusing the event plane measured in the BBCS (Ψ BBCS2 ),rather than the FVTXS. The resolutions of Ψ
BBCS2 ateach energy are given in Table III. - - - h C o rr ec t i on F ac t o r = 200 GeV 0-5% NN sd+Au FIG. 6. The correction factor on v ( η ) as a function of η . To calculate the p T -integrated v ( η ) we must correctfor the detector acceptance and efficiency. This correc-tion is estimated using the ( ampt ) model [23], coupled toa full geant -3 model [36] of the PHENIX detector. The“true” v is calculated in ampt relative to the parton par-ticipant plane, Ψ Parton Plane2 . The same events are thenrun through geant -3 and the v is recalculated usingreconstructed tracks, relative to the same Ψ Parton Plane2 .The resulting correction factor ( ε corr ( η )) for d +Au at √ s NN = 200 GeV is shown in Fig. 6, and is found torange from 2%–30%. The correction factors at 62.4 and39 GeV are similar, but show systematic increases at for-ward rapidity. The uncertainty on the correction factoris estimated by investigating the following effects:1. The correction’s dependence on the true v .02. The correction’s dependence on the true p T distri-bution.3. The correction’s dependence on the simulation-to-data matching.We investigate the correction’s dependence on the true v by varying the parton-parton interaction cross sectionin ampt from 1.5 mb to 3.0 mb. This causes a changein the true v of ∼ ± p T distribution, the shapeof the input p T distribution is modified such that themean p T changes by ± ± ± ± .
4% system-atic uncertainty is assigned on the correction factor. Thisleads to a systematic uncertainty on the measured v ( η )of < η .The resulting, p T -integrated, v ( η ) is calculated using v ( η ) = (cid:104) cos 2( φ trk ( η ) − Ψ BBCS2 ) (cid:105) R (Ψ BBCS2 ) ε corr ( η ) , (7)where φ trk is the azimuthal angle of tracks in the FVTXor central arms, Ψ BBCS2 is the second-order azimuthalevent plane measured by the BBCS, R (Ψ BBCS2 ) is theresolution of Ψ
BBCS2 , and ε corr ( η ) is the detector accep-tance and efficiency correction factor.The other dominant sources of systematic uncertaintyare similar to those detailed for the v ( p T ) measurementabove. (1) Track background in the FVTX is investigatedby tightening the DCA track cut. We assign a 2% un-certainty on v ( η ) based on this study. (2) The same 1%systematic uncertainty due to event pile-up is assignedbased upon the investigation detailed in Sec. III B. (3)Remaining effects due to the 1.0 mrad beam angle areinvestigated by looking at the difference in the v ( η ) asmeasured by the east and west central arms. We esti-mate a systematic uncertainty on v ( η ) assuming a uni-form distribution as σ = (cid:112) (cid:104) v west2 ( η ) (cid:105) − (cid:104) v east2 ( η ) (cid:105) / √ v ( p T ), wecross check the result, which in this case uses the BBCSevent plane, with v ( η ) measured using the FVTXS eventplane. This allows us to test the agreement at mid andforward rapidities, but not at backward rapidity becausetracks cannot be measured in the same region in whichthe event plane is measured. We find a larger differencebetween the event-plane results in the forward region andassign a 6.5% uncertainty based on the difference. (5) Asystematic uncertainty is assigned based on the uncer-tainty in the calculated event-plane resolution, as givenin Table III. A summary of the systematic uncertainties,and their assigned type, is shown in Table V. TABLE V. Systematic uncertainties on measurements of v vs η . Source Type √ s NN [GeV]200 62.4 39Track Background B 2.0% 2.0% 2.0%Event Pile-up B 1.0% < < D. Analysis of dN ch /dη vs η We begin by measuring the ratio of dN ch /dη in central d +Au collisions at √ s NN = 62.4, 39, and 19.6 GeV rel-ative to 0%–5% central d +Au collisions at √ s NN = 200GeV. The ratio of the raw track distributions are calcu-lated using the analysis cuts described in Sec. II. Vari-ations in the detector performance over time, and as afunction of the azimuthal angle, are tested by selectingten different time periods during the data taking at eachenergy, as well as four distinct regions in φ . The RMSof the ratios for each combination of time period and φ range are taken as a systematic uncertainty. - - h r a t i o h / d c h d N = 200 GeV NN s = 62.4 GeV / 0-5% d+Au NN s 0-5% d+Au = 200 GeV NN s = 39 GeV / 0-5% d+Au NN s 0-10% d+Au = 200 GeV NN s = 19.6 GeV / 0-5% d+Au NN s 0-20% d+Au PHENIX
FIG. 7. Ratio of dN ch /dη vs η in central d +Au collisionsat √ s NN = 62.4, 39, and 19.6 GeV relative to 0%–5% central d +Au collisions at √ s NN = 200 GeV. Systematic uncertain-ties are shown as filled boxes surrounding each point. When calculating the dN ch /dη ratios, it is also impor-tant to consider the change in acceptance and efficiency( A × ε ) between collision energies, particularly due tochanges in the mean p T ( (cid:104) p T (cid:105) ). We calculate the changein A × ε by simulating ampt events at each collisionenergy, run through a full geant -3 description of thePHENIX detector. The ratio of the resulting A × ε dis-tributions for each energy are then calculated as a correc-tion to the ratios in raw data. The sensitivity of the A × ε [GeV/c] T p v = 200 GeV 0-5% NN sd+Au | < 0.35 h | (a)0.3% – Global Sys. = {EP} v [GeV/c] T p v = 62.4 GeV 0-5% NN sd+Au (b)1.8% – Global Sys. = {EP} AMPT v 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 [GeV/c] T p v = 39 GeV 0-10% NN sd+Au (c)3.6% – Global Sys. =
PHENIX [GeV/c] T p v = 19.6 GeV 0-20% NN sd+Au (d)) |<3 h Y Res(Extrapolated -48%+35%Global Sys. = - - - h v = 200 GeV 0-5% NN sd+Au – Global Sys. = (e){EP} v - - - h v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (f){Parton Plane} AMPT v {EP} AMPT v 3 - - - h v = 39 GeV 0-10% NN sd+Au – Global Sys. = (g)
PHENIX
FIG. 8. The value of v as a function of p T in central d +Au collisions at √ s NN = 200 (a), 62.4 (b), 39 (c), and 19.6 (d) GeV. v as a function of η in central d +Au collisions at √ s NN = 200 (e), 62.4 (f), and 39 (g) GeV. The lower [green] curves showcalculations from the ampt model [23] where the v is calculated relative to the parton plane. The upper [blue] curves showcalculations from the ampt model, where the v is calculated using the event-plane method, as described in the text. ratio to the true p T distribution is tested by varying therelative (cid:104) p T (cid:105) between energies by ± A × ε ratio of 10%, which we as-sign as a systematic uncertainty. The corrected dN ch /dη ratios are shown in Fig. 7.To calculate the absolutely normalized dN ch /dη ateach energy, we fix the dN ch /dη in 0%–20% d +Au colli-sions at √ s NN = 200 GeV to the result previously mea-sured by PHOBOS [37]. The PHOBOS result is in excel-lent agreement with the previously published dN ch /dη atmidrapidity measured by PHENIX [38]. This method al-lows us to reduce the overall systematic uncertainties thatarise from calculating an absolutely normalized A × ε . Tocalculate the dN ch /dη in 0%–5% central d +Au collisionsat √ s NN = 200 GeV, we also need the ratio of dN ch /dη in0%–5% / 0%–20% central d +Au collisions at 200 GeV.This ratio is calculated in the same manner describedabove. The systematic uncertainties on the PHOBOSmeasurement are propagated directly to the dN ch /dη in0%–5% central d +Au collisions at 200 GeV. IV. RESULTS AND DISCUSSION
The v ( p T ) in central d +Au collisions at √ s NN = 200,62.4, 39, and 19.6 GeV is shown in Fig. 8(a)–(d). The v ( p T ) in centrality bins are shown in Appendix V. Apositive v signal that increases with increasing p T is ob-served in all centrality bins at all four energies.The v ( η ) in central d +Au collisions at √ s NN = 200,62.4, and 39 GeV is shown in Fig. 8(e)–(g). At all threeenergies we observe a v that decreases with increasing η between 0 < η <
3. At 200 GeV, the v at backwardrapidity is similar or greater to that measured at η = 0.This is reminiscent of the asymmetric dN ch /dη measuredin d +Au collisions [37]. At 62 GeV the v at backward ra-pidity starts to decrease for η <
0. This trend is strongerat 39 GeV, where the v distribution falls to zero for η = − .
8. This decrease at backward rapidity may bedue to nonflow contributions in regions near where theevent plane is measured ( − . < η < − . A. Comparison of v results with ampt calculations The ( ampt ) model [23] combines string melting andthen both partonic and hadronic scattering. It has pre-viously been compared to measurements of flow in smallcollision systems [16, 17, 24, 25], and found to be in goodagreement with p/d/ He+Au collisions at √ s NN = 200GeV for p T < c . Following Ref. [39], we use ampt Version 2.26, which is additionally modified to utilize theHulth´en wavefunction description of the deuteron andblack disk nucleon-nucleon interactions with the Monte-Carlo Glauber component. Further details are discussedin Appendix V. In addition, within ampt one can runwith only partonic scattering (i.e. no hadronic scat-tering) or with only hadronic scattering (i.e. no par-tonic scattering), and the results are also shown in Ap-pendix V. In all cases, the charged particle multiplicityin the region − . < η < − .
1. Central collisions
Figure 8 shows the v calculated relative to theΨ plane calculated from initial partons, labeled v { Parton Plane } . By calculating v relative to theparton plane, we can isolate the v that is truly coupledto the initial geometry, or what we refer to as flow. At 200and 62.4 GeV, ampt provides a reasonable description ofthe data for p T < c and under-predicts the datafor p T > c . At 39 and 19.6 GeV ampt under-predicts the data at all but the lowest p T . We furtherfind good agreement between v ( η ) and v { Parton Plane } at mid and forward rapidities at all three collision ener-gies. At backward rapidity we find good agreement at200 GeV, but ampt does not show the same fall-off asseen in the data at 62.4 and 39 GeV.Because ampt is a full event generator, we can not onlydetermine v { Parton Plane } , but also mimic in detail theexperimental measurement using only the final-state par-ticles. We use the same event-plane method as used inthe data analysis, matching the nominal pseudorapidityranges of the detectors rather than a full geant -3 sim-ulation of the detector response. This result, labeled as v { EP } , includes not only flow, but also nonflow corre-lations as modeled within ampt . The results are shownin Fig. 8. As a function of p T , the v { EP } calculationsare similar to v { Parton Plane } for p T < . c .For p T > . c the event-plane results produce a We note that Ref. [39] includes ampt calculations of v ( p T ) rela-tive to the initial nucleon positions for b < d +Au collisionsat the energies measured here. The results are broadly similarto those shown here. larger v signal, which is in better agreement with thedata. This difference highlights the contributions fromnonflow that, in ampt , increase with increasing p T anddecreasing collision energy.When looking at v ( η ), shown in Fig. 8, we find thatthe ampt event-plane results are in good agreement withthe measured data for η > η of the v { EP } compared to the v { Parton Plane } , indicating aroughly 15% increase in the v with the addition of non-flow. Both calculations are in agreement with the datawithin uncertainties. At 62.4 and 39 GeV we see a largerincrease in the event-plane result versus the parton planeresult compared to the 200 GeV. What is particularlyinteresting is that ampt shows a decrease in the event-plane result for η < − η ≈ − .
5. While this decrease doesn’t occur at the same η , and is only in qualitative agreement with the data,it points out that within ampt this feature only ariseswhen you combine flow and nonflow. When using theevent-plane method at these low energies, ampt predictsa larger deviation between the true flow signal and the ex-perimentally observed flow signal as the ∆ η between theregion in which the tracks are measured and the region inwhich the event plane is measured decreases. We furthercaution that, while ampt qualitatively agrees with ourmeasurements over a broad range in collision energy andparticle kinematics, we can not use it to definitively sep-arate flow from nonflow, but rather to give some insightand possible intuition for interpreting the experimentalresults in regions where we are currently unable to per-form the separation experimentally.Using ampt , we can also study whether our mea-sured v ( η ) is likely to arise solely from nonflow contri-butions. By setting the partonic and hadronic interac-tion cross sections to zero within ampt , we eliminate allinteractions that translate initial-state geometry to final-state momentum correlations. This is shown explicitly inFig. 9, where v { Parton Plane } = 0 at all η . However,even with all partonic and hadronic scattering turned off,nonflow correlations can still give rise to a v { EP } sig-nal. This is shown by the upper [purple] curves in Fig. 9.Note, that in this mode the event plane angle arises onlyfrom nonflow correlations, and has no connection to theinitial geometry (i.e. the parton plane). In this casethe resolution of the event plane is roughly a factor of 3lower than with partonic and hadronic interactions. Atall three energies, v { EP } < .
01 for η > ampt with partonic and hadronic scattering switched off. Thisregion is far removed (∆ η > .
1) from the region in whichthe event plane is constructed and is therefore unlikelyto contain correlations from jets or particle decays. Inthe region η <
0, however, an increasing v { EP } is ob-served. This indicates, as expected, that the smaller the∆ η gap the larger the effects of nonflow. In all cases,the measured v ( η ) for η > v { EP } from ampt with nonflow correlations only. This extends3 - - - h v = 200 GeV 0-5% NN sd+Au – Global Sys. = (a){EP} v - - - h v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (b){Parton Plane} AMPT v No Scattering{EP} AMPT v - - - h v = 39 GeV 0-10% NN sd+Au – Global Sys. = (c)
PHENIX
FIG. 9. The value of v as a function of η in central d +Au collisions at √ s NN = 200, 62.4, and 39 GeV compared to calculationsfrom the ampt model [23] in which both the partonic and hadronic scatterings have been turned off. The upper [purple] curvesshow calculations from the ampt model using the event-plane method as described in the text. The lower [green] curves ( v = 0in all cases) show calculations from ampt where v is calculated relative to the parton plane. to η < v { EP } from nonflow correlations only lendsfurther confidence that the low p T and η > v { EP } signal at η < v { EP } signal at η < ampt .
2. Centrality dependence
We now return to the centrality dependence of v ( p T ).From the comparison of v ( p T ) in central collisions wecan separate the p T spectra into two regions: (1) p T < c where ampt parton and event plane results areroughly similar. (2) p T > c where the eventplane results, which include nonflow contributions, yielda larger v than that calculated with the parton plane.We choose two particular p T bins, 0 . < p T < . . < p T < .
5, and investigate the centrality dependenceof the v at √ s NN = 200, 62.4, and 39 GeV in compar-ison with the results from ampt , as shown in Fig. 10.Note that while the event plane resolution uncertainty isa global scale uncertainty when plotting v as a functionof p T , when plotting v as a function of centrality it be-comes a type B systematic uncertainty and is added inquadrature with the other type B systematic uncertain-ties in Fig. 10.Starting with the low p T v , ampt shows similar re- sults between the parton and event planes, indicatingwithin ampt that the flow dominates in this p T region.The ampt results also predict a decrease in the v resultstowards more peripheral collisions, as expected from thedecrease in the mean ellipticity of the initial geometryand lower particle multiplicity. This is contrary to thetrends in the data where the values of v increase in themost peripheral collisions. This increase is more pro-nounced in the lower-energy data and it may indicatethat nonflow contributions are larger in the data than inAMPT. The v values measured in the centrality rangeup to 20% are in good agreement with the predictionsfrom AMPT.At high p T , ampt predicts a significantly larger v cal-culated relative to the event plane compared to the par-ton plane, indicating significant contributions from non-flow correlations. At 39 and 62.4 GeV, we observe a v that increases with more peripheral collisions. At 62.4GeV, ampt well reproduces this increasing behavior. At200 GeV, however ampt over-predicts the observed in-crease, while under-predicting the increase at 39 GeV. B. Comparison of v results with hydrodynamiccalculations Shown in Fig. 11 are predictions from the sonic andsuper sonic models for v ( p T ) at midrapidity [39]. The sonic model [41] uses Monte-Carlo Glauber initial con-ditions to determine the energy density distribution. Forthese calculations, b < b < ε values are consistent with those given in Table II. The4 centrality v [GeV/c] < 0.8) T (0.6 < p{EP} v = 200 GeV NN sd+Au (a) centrality v {Parton Plane} AMPT v = 62.4 GeV NN sd+Au (c) centrality v PHENIX = 39 GeV NN sd+Au (e) centrality v [GeV/c] < 2.5) T (2.0 < p{EP} v = 200 GeV NN sd+Au (b) centrality v {EP} AMPT v = 62.4 GeV NN sd+Au (d) centrality v PHENIX = 39 GeV NN sd+Au (f) FIG. 10. The value of v as a function of centrality (a,c,e) at 0 . < p T [GeV /c ] < . . < p T [GeV /c ] < . d +Au collisions at √ s NN = (a,b) 200, (c,d) 62.4, and (e,f) 39 GeV. The upper [blue] curves show calculations from the ampt model [23] where the v is calculated using the event plane method as described in the text. The lower [green] curves show ampt calculations where the v is calculated relative to the parton plane. initial energy density is tuned such that the dN ch /dη atmidrapidity matches the values given in Table VI. TheGlauber initial conditions are followed by viscous hy-drodynamics with η/s = 1 / π , and at T = 170 MeVthe transition to a hadron cascade. The super sonic model [42] additionally includes pre-equilibrium dynam-ics. At 200 and 62.4 GeV, both calculations are in ex-cellent agreement with the data, with super sonic pro-viding a slightly better description for p T > c .At 39 and 19.6 GeV, both calculations under-predict thedata for p T > . c . This difference may be dueto the increasing contributions of nonflow present in the data at high p T and lower collision energies, which is notaccounted for in these calculations. Without a reliableestimate of the nonflow contribution, the data is unableto distinguish between sonic and super sonic .Figure 11(e) includes hydrodynamic predictions of the η dependence of v in d +Au collisions at √ s NN = 200GeV from Bozek and Broniowski [40]. These calcula-tions utilize MC Glauber initial conditions, evolved withevent-by-event 3+1D viscous hydrodynamics, followed bystatistical hadronization at freeze-out. The calculationsare in good agreement with the data for η > − − < η < − [GeV/c] T p v = 200 GeV 0-5% NN sd+Au | < 0.35 h | (a)0.3% – Global Sys. = {EP} v [GeV/c] T p v = 62.4 GeV 0-5% NN sd+Au (b)1.8% – Global Sys. = SONIC v superSONIC v 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 [GeV/c] T p v = 39 GeV 0-10% NN sd+Au (c)3.6% – Global Sys. =
PHENIX [GeV/c] T p v = 19.6 GeV 0-20% NN sd+Au (d)) |<3 h Y Res(Extrapolated (d)-48%+35%Global Sys. = - - - h v = 200 GeV 0-5% NN sd+Au – Global Sys. = (e){EP} v - - - h v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (f)[Phys. Lett. B747, 135 (2015)]P. Bozek, W. Broniowski SONIC v superSONIC v 3 - - - h v = 39 GeV 0-10% NN sd+Au – Global Sys. =
PHENIX (g)
FIG. 11. The value of v as a function of p T in central d +Au collisions at √ s NN = (a) 200, (b) 62.4, (c) 39, and (d) 19.6 GeV. v as a function of η in central d +Au collisions at √ s NN = (e) 200, (f) 62.4, and (g) 39 GeV. At midrapidity, the [lower] purpleand upper [orange] curves show theoretical calculations from sonic and super sonic [39], respectively. The dashed [red] curvein panel (e) shows hydrodynamic predictions from Ref. [40].TABLE VI. The charged particle multiplicity ( dN ch /dη ) atmidrapidity for central d +Au collisions at √ s NN = 200, 62.4,39, and 19.6 GeV. √ s NN [GeV] centrality data ampt (super) sonic
200 0%–5% 20.3 ± ± ± ±
239 0%–10% 9.3 ± ± ± ± C. Comparison of dN ch /dη results with ampt calculations The measurements of dN ch /dη vs η in central d +Aucollisions at √ s NN = 200, 62.4, 39, and 19.6 GeV areshown in Fig. 12. At all four energies, the dN ch /dη atbackward rapidity is larger than that at forward rapidity,and the overall dN ch /dη decreases at all η with decreas-ing energy. Also shown in Fig. 12 are calculations from ampt in the same centrality classes, as well as a predic-tion from Bozek and Broniowski [40] for 0%–5% central d +Au collisions at √ s NN = 200 GeV. At 200 GeV, ampt agrees with the data well at mid and forward rapidities, while over-predicting the data at backward rapidity. Thecalculation from Bozek and Broniowski agrees with thedata at mid to forward rapidity, while under-predictingthe data at backward rapidities. It is worth noting thatcalculations from Bozek and Broniowski are substantiallylower than the ampt calculations for η < −
1. This ispotentially due to the centrality determination in ampt (and data), which selects on multiplicity in the region − . < η < − .
1, which may naturally cause an autocor-relation with the dN ch /dη in the region − < η < −
1. Atthe lower three energies, ampt matches the data well atforward psuedorapidity only and over-predicts the dataat midrapidity.We next turn to investigating whether there is a scalingof v ∝ dN ch /dη . Figure 13(a)–(c) shows the measured v ( η ) overlaid with the dN ch /dη , where the dN ch /dη isarbitrarily scaled at each energy to match the v at for-ward rapidity. We have chosen to match the dN ch /dη tothe v at η >
0, as we expect the v in this region tohave the lowest contribution from nonflow, as discussedin Sec. IV A. The required scaling factor increases withdecreasing energy, with scaling factors of 0.0020, 0.0025,and 0.0030 at 200, 62.4, and 39 GeV, respectively.Figure 13(d)–(f) shows the v { Parton Plane } from ampt overlaid with the scaled dN ch /dη , also from ampt ,6 - - h h / d c h d N = 200 GeV 0-5% NN sd+Au (a) PHENIX (Run 16)[PRC 93, 024901 (2016)]PHENIX (Run 8)AMPT[Phys. Lett. B747, 135 (2015)]P. Bozek, W. Broniowski - - h h / d c h d N = 62.4 GeV 0-5% NN sd+Au (b) 2 - - h h / d c h d N = 39 GeV 0-10% NN sd+Au (c) - - h h / d c h d N = 19.6 GeV 0-20% NN sd+Au (d) FIG. 12. The dN ch /dη vs η in central d +Au collisions at √ s NN = (a) 200, (b) 62.4, (c) 39, and (d) 19.6 GeV. The solid[green] curves are the ampt calculations in similar centrality bins. The dashed [red] curve in panel (a) is a hydrodynamicprediction from Ref. [40] for 0%–5% central d +Au collisions at √ s NN = 200 GeV. - - - h = 200 GeV 0-5% NN sd+Au PHENIX (a) – ({EP} v 0.0020 · h /d ch dN - - - h = 62.4 GeV 0-5% NN sd+Au (b) – ({EP} v 0.0025 · h /d ch dN - - - h = 39 GeV 0-10% NN sd+Au (c) – ({EP} v 0.0030 · h /d ch dN - - - h = 200 GeV 0-5% NN sd+Au PHENIX (d) {Parton Plane} AMPT v 0.0020 · h /d ch AMPT dN Bozek v 0.0020 · h /d ch Bozek dN - - - h = 62.4 GeV 0-5% NN sd+Au (e) {Parton Plane} AMPT v 0.0025 · h /d ch AMPT dN - - - h = 39 GeV 0-10% NN sd+Au (f) {Parton Plane} AMPT v 0.0030 · h /d ch AMPT dN
FIG. 13. The v vs η and dN ch /dη vs η , scaled to match the v in 1 . < η < .
0, for central d +Au collisions at √ s NN =(a) 200, (b) 62.4, and (c) 39 GeV. The dashed-double-dot and solid [green] curves in panels (d)–(f) show the results from ampt using the same scaling factors determined from the data. The dash and dash-dot [red] curves in panel (d) show thehydrodynamic predictions from Ref. [40] in 0%–5% central d +Au collisions at √ s NN = 200 GeV, again using the same scalingfactor determined from the data. v and dN ch /dη from Bozek and Broniowski, where dN ch /dη is scaled by the same factor of 0.0020.Starting with the 200 GeV results in Fig. 13(a)&(d),we find that when using a constant scaling factor across η , the scaled dN ch /dη and v ( η ) agree well within un-certainties. The increase in the v from forward to back-ward rapidity is matched by the increase in the dN ch /dη .In comparison, the ampt shows an approximate scalingonly at forward rapidity, although a better match is foundwhen using a scaling factor of 0.0022, rather than 0.0020.The scaled dN ch /dη breaks from the v { Parton Plane } for η <
1, indicating that within ampt there is no directscaling of the dN ch /dη and v { Parton Plane } . Similarly,the calculations by Bozek and Broniowski show an ap-proximate scaling at forward rapidity, and a modest scalebreaking at backward rapidities.At 62.4 and 39 GeV, we find that the scaled dN ch /dη and v ( η ) agree within uncertainties at mid and forwardrapidities. At backward rapidity however, the scaled dN ch /dη is significantly larger than the v for the samescaling factor. It is notable that ampt v does not scalewith dN ch /dη at backward rapidity at any energy. Asdiscussed in Sec. IV A, ampt calculations indicate thatthere could be an anti-correlation effect at backward ra-pidity that decreases the observed v relative to the true v when using the event-plane method. Further inves-tigations into potential nonflow anti-correlations in theevent-plane method with a small ∆ η gap would be usefulto shed more light on these possible conclusions. V. SUMMARY AND CONCLUSIONS
PHENIX has presented new measurements of the sec-ond order flow coefficient v in bins of centrality in d +Aucollisions at √ s NN = 200, 62.4, 39, and 19.6 GeV as afunction of p T and η . We find that at mid to forward ra-pidities and low p T , v appears to be dominated by flow,where we define flow as the translation of initial geome-try to final-state momentum anisotropy via interactionsbetween medium constituents. In contrast, at backwardrapidity and high p T , nonflow becomes an increasinglysignificant contribution.It would be interesting to compare the v results mea-sured in the d +Au beam energy scan with those mea-sured in p + p and p +Pb collisions at the LHC. The mul-tiplicity ranges probed in the d +Au beam energy scanare comparable to those in p + p collisions at the LHC,which range from dN ch /dη ≈ dN ch /dη >
80 in very high-multiplicity events [43]. Com-paring the different systems at similar multiplicities, butvastly different collision energies and initial geometries,may give further insight into the underlying mechanismgenerating the v signal. We further present measure-ments of dN ch /dη vs η at all four energies. At 200 GeV,we find that a constant scale factor yields agreement be- tween the measured v vs η and the shape of dN ch /dη .At 62.4 and 39 GeV, the shapes of v and dN ch /dη matchwell at mid and forward rapidity, however the dN ch /dη increases at backward rapidity while the v decreases.This presents a different picture than that observed at200 GeV, and may be due to anti-correlations present inthe event-plane method when the ∆ η gap becomes small.These results provide further evidence that the v measured in small systems arises from initial geometrycoupled to interactions between medium constituents,whether described by parton scattering or hydrodynam-ics. In d +Au collisions at √ s NN = 200 GeV, theseflow effects dominate and they continue to play a sig-nificant, though less dominant role all the way down to √ s NN = 19.6 GeV. ACKNOWLEDGMENTS
We thank the staff of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the staff of the other PHENIX participating in-stitutions for their vital contributions. We acknowledgesupport from the Office of Nuclear Physics in the Officeof Science of the Department of Energy, the National Sci-ence Foundation, Abilene Christian University ResearchCouncil, Research Foundation of SUNY, and Dean ofthe College of Arts and Sciences, Vanderbilt University(U.S.A), Ministry of Education, Culture, Sports, Science,and Technology and the Japan Society for the Promotionof Science (Japan), Conselho Nacional de Desenvolvi-mento Cient´ıfico e Tecnol´ogico and Funda¸c˜ao de Amparo`a Pesquisa do Estado de S˜ao Paulo (Brazil), Natural Sci-ence Foundation of China (People’s Republic of China),Croatian Science Foundation and Ministry of Scienceand Education (Croatia), Ministry of Education, Youthand Sports (Czech Republic), Centre National de laRecherche Scientifique, Commissariat `a l’´Energie Atom-ique, and Institut National de Physique Nucl´eaire et dePhysique des Particules (France), Bundesministerium f¨urBildung und Forschung, Deutscher Akademischer Aus-tausch Dienst, and Alexander von Humboldt Stiftung(Germany), J. Bolyai Research Scholarship, EFOP, theNew National Excellence Program ( ´UNKP), NKFIH, andOTKA (Hungary), Department of Atomic Energy andDepartment of Science and Technology (India), IsraelScience Foundation (Israel), Basic Science Research Pro-gram through NRF of the Ministry of Education (Korea),Physics Department, Lahore University of ManagementSciences (Pakistan), Ministry of Education and Science,Russian Academy of Sciences, Federal Agency of AtomicEnergy (Russia), VR and Wallenberg Foundation (Swe-den), the U.S. Civilian Research and Development Foun-dation for the Independent States of the Former SovietUnion, the Hungarian American Enterprise ScholarshipFund, the US-Hungarian Fulbright Foundation, and theUS-Israel Binational Science Foundation.8
APPENDIX A: CENTRALITY DEPENDENCE OF v ( p T ) The v ( p T ) in centrality bins for d +Au collisions at √ s NN = 200, 62.4, and 39 GeV are shown in Figs. 14,15, and 16, respectively.9 [GeV/c] T p v {EP} v = 200 GeV 0-5% NN sd+Au PHENIX – Global Sys. = (a) [GeV/c] T p v {Parton Plane} AMPT v {EP} AMPT v – Global Sys. = (b) [GeV/c] T p v – Global Sys. = (c) [GeV/c] T p v – Global Sys. = (d) [GeV/c] T p v – Global Sys. = (e) [GeV/c] T p v – Global Sys. = (f)
FIG. 14. For d +Au collisions at √ s NN = 200 GeV, the value of v as a function of p T in (a) 0%–5%, (b) 5%–10%,(c) 10%–20%, (d) 20%–40%, (e) 40%–60%, and (f) 60%–88%. The upper [blue] curves show calculations from the ampt model [23], where the v is calculated using the event-plane method, as described in the text. The lower [green] curves show ampt calculations, where the v is calculated relative to the parton plane. [GeV/c] T p v {EP} v = 62.4 GeV 0-5% NN sd+Au PHENIX – Global Sys. = (a) [GeV/c] T p v {Parton Plane} AMPT v {EP} AMPT v – Global Sys. = (b) [GeV/c] T p v – Global Sys. = (c) [GeV/c] T p v – Global Sys. = (d) [GeV/c] T p v – Global Sys. = (e) [GeV/c] T p v – Global Sys. = (f)
FIG. 15. For d +Au collisions at √ s NN = 62.4 GeV, descriptions of the symbols and curves are the same as in Fig. 14. [GeV/c] T p v {EP} v = 39 GeV 0-10% NN sd+Au PHENIX – Global Sys. = (a) [GeV/c] T p v {Parton Plane} AMPT v {EP} AMPT v – Global Sys. = (b) [GeV/c] T p v – Global Sys. = (c) [GeV/c] T p v – Global Sys. = (d) [GeV/c] T p v – Global Sys. = (e)
FIG. 16. For d +Au collisions at √ s NN = 39 GeV, descriptions of the symbols and curves are the same as in Fig. 14. TABLE VII. Nondefault parameter values used when running ampt .Parameter ValueISOFT 4PARJ(41) 2.2PARJ(42) 0.5Parton screening mass 6 . d . d APPENDIX B:
AMPT
DETAILS
The ampt calculations shown in this work are gen-erated following Ref. [39]. We use ampt
Version 2.26,which is additionally modified to utilize the Hulth´enwavefunction description of the deuteron and blackdisk nucleon-nucleon interactions with the Monte-CarloGlauber component. The input ampt parameters whichare tuned outside the default values are shown in Ta-ble VII. Unlike Ref. [39], which uses a parton interactioncross section of 1.50 mb, we use a parton interaction crosssection of σ parton = 0 .
75 mb, as we find it provides a bet-ter description of the centrality binned data.In addition to the full ampt calculations with bothpartonic and hadronic scattering shown in Figs. 8 and 14–16, we provide calculations for the following three cases: • N.S. – Both partonic scattering and hadronic scat-tering turned off (i.e. no scattering) • P.S. – Partonic scattering only • H.S. – Hadronic scattering onlyTo turn off hadronic scattering we turn off the hadroncascade (NTMAX = 3). In order to turn off partonicscattering we set the parton interaction cross section to0 mb. Figures 17 and 18 show the results for central d +Au collisions.Figure 17 shows the results from ampt for v as a func-tion of p T and pseudorapidity using the parton planemethod, which yields a pure flow result with respectto initial geometry. Focusing on the p T dependence inFig. 17 (upper panels), the hadronic scattering only sce-nario results in larger v compared to the partonic scat-tering only scenario at low p T < c and then a com-parable v for higher p T . Note that these contributionscannot simply be summed to achieve the result with bothpartonic and hadronic scattering because the space-timeinput for the hadronic scattering stage changes depend-ing on whether there is or is no partonic scattering stage.The significantly larger v in the hadronic scattering onlyscenario at low- p T is most clearly seen in Fig. 17 (lowerpanels) because the v as a function of pseudorapidity isintegrated over all p T . At high- p T , the partonic-scattering-only scenariohas a more comparable contribution to the hadronic-scattering-only scenario, with it being slightly smallerat 200 GeV and slightly larger at 39 GeV. Because the ampt model employs a formation time for partons suchthat higher p T partons start scattering earlier in time, itmakes sense that this contributes more significantly. Itis notable that in Ref. [39], it was shown that the partonscattering began to dominate for p T > . c . Thisdifference is likely due to the larger parton interactioncross section of 1.50 mb used in Ref. [39]. As the colli-sion energy decreases, the partonic scattering contributesmore to the overall v signal. As discussed in Sec. IV A,the no scattering case has v { Parton Plane } = 0 by def-inition, as it no longer has the ability to translate initialgeometry to momentum anisotropy.Figure 18 shows results calculated using the event-plane method ( v { EP } ), i.e. simulating the experimentalmethod of extracting v . The general statement abovethat hadronic scattering dominates at low- p T while par-tonic scattering contributes mainly at higher p T remainstrue down to √ s NN = 39 GeV. However, as discussedin Sec. IV A, the case with both partonic and hadronicscattering turned off now shows a nonzero v { EP } sig-nal. This v { EP } result without scattering indicates thatnonflow is small at low- p T but grows with increasing p T .For collision energies of 39 GeV and above, the v { EP } result without scattering is inconsistent with the mea-sured results as a function of both p T and η . However, at √ s NN = 19.6 GeV, the v { EP } results in all four cases arenearly consistent. This appears to indicate that, within ampt , the v { EP } measurement is dominated by non-flow contributions and does not reflect the true flow evenat low p T .1 [GeV/c] T p v = 200 GeV 0-5% NN sd+Au | < 0.35 h , | – h 0.3% – Global Sys. =
PHENIX (a){EP} v [GeV/c] T p v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (b){Parton Plane} AMPT v H. S.{Parton Plane} AMPT v 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 [GeV/c] T p v = 39 GeV 0-10% NN sd+Au – Global Sys. = (c) P. S.{Parton Plane} AMPT v N. S.{Parton Plane} AMPT v [GeV/c] T p v = 19.6 GeV 0-20% NN sd+Au ) |<3 h Y Res(Extrapolated -48%+35%Global Sys. = (d) - - - h v = 200 GeV 0-5% NN sd+Au – Global Sys. = (e){EP} v {Parton Plane} AMPT v - - - h v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (f) N. S.{Parton Plane} AMPT v P. S.{Parton Plane} AMPT v H. S.{Parton Plane} AMPT v 3 - - - h v = 39 GeV 0-10% NN sd+Au – Global Sys. = (g)
PHENIX
FIG. 17. (a, b, c, d) the value of v vs p T in central d +Au collisions at √ s NN = 200, 62.4, 39, and19.6 GeV. (e, f, g) the valueof v vs η in central d +Au collisions at √ s NN = 200, 62.4, and 39 GeV. The curves are calculations from ampt underdifferentconditions. With ordering of curves from top to bottom (a, b, c, d) at p T = 0 . η = 0, the uppermost [red]curve is ampt with both partonic and hadronic scattering; the upper-middle [yellow] curve is ampt with hadronic scatteringonly (H.S.); the lower-middle [cyan] curve is ampt with partonic scattering only (P.S.); and the lowest [purple] curve is ampt with no scattering (N.S.). For all ampt curves, the v is calculated relative to the initial parton plane. [GeV/c] T p v = 200 GeV 0-5% NN sd+Au | < 0.35 h , | – h 0.3% – Global Sys. =
PHENIX (a){EP} v [GeV/c] T p v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (b){EP} AMPT v H. S.{EP} AMPT v 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 [GeV/c] T p v = 39 GeV 0-10% NN sd+Au – Global Sys. = (c) P. S.{EP} AMPT v N. S.{EP} AMPT v [GeV/c] T p v = 19.6 GeV 0-20% NN sd+Au ) |<3 h Y Res(Extrapolated -48%+35%Global Sys. = (d) - - - h v = 200 GeV 0-5% NN sd+Au – Global Sys. = (e){EP} v {EP} AMPT v - - - h v = 62.4 GeV 0-5% NN sd+Au – Global Sys. = (f) N. S.{EP} AMPT v P. S.{EP} AMPT v H. S.{EP} AMPT v 3 - - - h v = 39 GeV 0-10% NN sd+Au – Global Sys. = (g)
PHENIX
FIG. 18. The description of all symbols and curves are the same as in Fig. 17, except that forall ampt curves the v is calculatedrelativeto the final-state event plane. [1] I. Arsene et al. (BRAHMS Collaboration), “Quark gluonplasma and color glass condensate at RHIC? The Per-spective from the BRAHMS experiment,” Nucl. Phys. A , 1 (2005).[2] K. Adcox et al. (PHENIX Collaboration), “Formation ofdense partonic matter in relativistic nucleus-nucleus colli-sions at RHIC: Experimental evaluation by the PHENIXcollaboration,” Nucl. Phys. A , 184 (2005).[3] B. B. Back et al. (PHOBOS Collaboration), “The PHO-BOS perspective on discoveries at RHIC,” Nucl. Phys. A , 28 (2005).[4] J. Adams et al. (STAR Collaboration), “Experimentaland theoretical challenges in the search for the quarkgluon plasma: The STAR Collaboration’s critical assess-ment of the evidence from RHIC collisions,” Nucl. Phys.A , 102 (2005).[5] P. Romatschke, “New Developments in Relativistic Vis-cous Hydrodynamics,” Int. J. Mod. Phys. E , 1 (2010).[6] U. Heinz and R. Snellings, “Collective flow and viscosityin relativistic heavy-ion collisions,” Ann. Rev. Nucl. Part.Sci. , 123 (2013).[7] G. Aad et al. (ATLAS Collaboration), “Observation ofAssociated Near-Side and Away-Side Long-Range Corre-lations in √ s NN =5.02 TeV Proton-Lead Collisions withthe ATLAS Detector,” Phys. Rev. Lett. , 182302(2013).[8] B. Abelev et al. (ALICE Collaboration), “Long-range an-gular correlations on the near and away side in p -Pb col-lisions at √ s NN = 5 .
02 TeV,” Phys. Lett. B , 29(2013).[9] S. Chatrchyan et al. (CMS Collaboration), “Observationof long-range near-side angular correlations in proton-lead collisions at the LHC,” Phys. Lett. B , 795(2013).[10] A. Adare et al. (PHENIX Collaboration), “QuadrupoleAnisotropy in Dihadron Azimuthal Correlations in Cen-tral d +Au Collisions at √ s NN =200 GeV,” Phys. Rev.Lett. , 212301 (2013).[11] G. Aad et al. (ATLAS Collaboration), “Measurementwith the ATLAS detector of multi-particle azimuthal cor-relations in p +Pb collisions at √ s NN =5.02 TeV,” Phys.Lett. B , 60 (2013).[12] S. Chatrchyan et al. (CMS Collaboration), “Multiplicityand transverse momentum dependence of two- and four-particle correlations in p Pb and PbPb collisions,” Phys.Lett. B , 213 (2013).[13] B. Bezverkhny Abelev et al. (ALICE Collaboration),“Multiparticle azimuthal correlations in p -Pb and Pb-Pbcollisions at the CERN Large Hadron Collider,” Phys.Rev. C , 054901 (2014).[14] V. Khachatryan et al. (CMS Collaboration), “Evidencefor Collective Multiparticle Correlations in p -Pb Colli-sions,” Phys. Rev. Lett. , 012301 (2015).[15] A. Adare et al. (PHENIX Collaboration), “Measure-ment of long-range angular correlation and quadrupoleanisotropy of pions and (anti)protons in central d +Aucollisions at √ s NN =200 GeV,” Phys. Rev. Lett. ,192301 (2015).[16] A. Adare et al. (PHENIX Collaboration), “Measure-ments of elliptic and triangular flow in high-multiplicity He+Au collisions at √ s NN = 200 GeV,” Phys. Rev. Lett. , 142301 (2015).[17] C. Aidala et al. (PHENIX Collaboration), “Measure-ment of long-range angular correlations and azimuthalanisotropies in high-multiplicity p +Au collisions at √ s NN = 200 GeV,” Phys. Rev. C , 034910 (2017).[18] J. L. Nagle, A. Adare, S. Beckman, T. Koblesky, J. Or-juela Koop, D. McGlinchey, P. Romatschke, J. Carlson,J. E. Lynn, and M. McCumber, “Exploiting Intrinsic Tri-angular Geometry in Relativistic He +Au Collisions toDisentangle Medium Properties,” Phys. Rev. Lett. ,112301 (2014).[19] G. Aad et al. (ATLAS Collaboration), “Observation ofLong-Range Elliptic Azimuthal Anisotropies in √ s =13and 2.76 TeV pp Collisions with the ATLAS Detector,”Phys. Rev. Lett. , 172301 (2016).[20] V. Khachatryan et al. (CMS Collaboration), “Observa-tion of Long-Range Near-Side Angular Correlations inProton-Proton Collisions at the LHC,” J. High EnergyPhys.
09 (2010) et al. (CMS Collaboration), “Evidencefor collectivity in pp collisions at the LHC,” Phys. Lett.B , 193 (2017).[22] R. D. Weller and P. Romatschke, “One fluid to rule themall: viscous hydrodynamic description of event-by-eventcentral p+p, p+Pb and Pb+Pb collisions at √ s = 5 . , 064901 (2005).[24] P. Bozek, A. Bzdak, and G.-L. Ma, “Rapidity depen-dence of elliptic and triangular flow in protonnucleus col-lisions from collective dynamics,” Phys. Lett. B , 301(2015).[25] J. D. Orjuela Koop, A. Adare, D. McGlinchey, and J. L.Nagle, “Azimuthal anisotropy relative to the participantplane from a multiphase transport model in central p +Au, d +Au , and He+Au collisions at √ s NN = 200 GeV,”Phys. Rev. C , 054903 (2015).[26] A. Ortiz Velasquez, P. Christiansen, E. Chautle Flores,I. A. Maldonado Cervantes, and G. Pais, “Color Recon-nection and Flowlike Patterns in pp Collisions,” Phys.Rev. Lett. , 042001 (2013).[27] K. Dusling and R. Venugopalan, “Azimuthal collimationof long range rapidity correlations by strong color fieldsin high multiplicity hadron-hadron collisions,” Phys. Rev.Lett. , 262001 (2012).[28] C. Aidala et al. (PHENIX Collaboration), “Measure-ments of multiparticle correlations in d +Au collisionsat 200, 62.4, 39, and 19.6 GeV and p +Au collisionsat 200 GeV and implications for collective behavior,”arXiv:1707.06108.[29] K. Adcox et al. (PHENIX Collaboration), “PHENIX de-tector overview,” Nucl. Instrum. Methods Phys. Res.,Sec. A , 469 (2003).[30] M. Allen et al. (PHENIX Collaboration), “PHENIX in-ner detectors,” Nucl. Instrum. Methods Phys. Res., Sec.A , 549 (2003).[31] C. Aidala et al. (PHENIX Collaboration), “The PHENIXForward Silicon Vertex Detector,” Nucl. Instrum. Meth-ods Phys. Res., Sec. A , 44 (2014).[32] A. Adare et al. (PHENIX Collaboration), “Centrality categorization for R p ( d )+ A in high-energy collisions,”Phys. Rev. C , 034902 (2014).[33] P. Sorensen, B. Bolliet, A. Mocsy, Y. Pandit, andN. Pruthi, “The Rise and Fall of the Ridge in HeavyIon Collisions,” Phys. Lett. B , 71 (2011).[34] A. M. Poskanzer and S. A. Voloshin, “Methods for ana-lyzing anisotropic flow in relativistic nuclear collisions,”Phys. Rev. C , 1671 (1998).[35] J.-Y. Ollitrault, A. M. Poskanzer, and S. A. Voloshin,“Effect of flow fluctuations and nonflow on elliptic flowmethods,” Phys. Rev. C et al. (PHOBOS Collaboration), “Scalingof charged particle production in d +Au collisions at √ s NN = 200 GeV,” Phys. Rev. C , 031901 (2005).[38] A. Adare et al. (PHENIX Collaboration), “Transverseenergy production and charged-particle multiplicity atmidrapidity in various systems from √ s NN = 7 . , 024901 (2016).[39] J. D. Orjuela Koop, R. Belmont, P. Yin, and J. L. Nagle,“Exploring the Beam Energy Dependence of Flow-LikeSignatures in Small System d +Au Collisions,” Phys. Rev.C , 044910 (2016).[40] P. Bozek and W. Broniowski, “Collective flow in ultra-relativistic He-Au collisions,” Phys. Lett. B , 308(2014).[41] M. Habich, J. L. Nagle, and P. Romatschke, “Particlespectra and HBT radii for simulated central nuclear col-lisions of C + C, Al + Al, Cu + Cu, Au + Au, and Pb+ Pb from √ s = 62 .
4- 2760 GeV,” Eur. Phys. J. C ,15 (2015).[42] P. Romatschke, “Light-Heavy Ion Collisions: A windowinto pre-equilibrium QCD dynamics?” Eur. Phys. J. C , 305 (2015).[43] J. Adam et al. (ALICE Collaboration), “Charged-particle multiplicities in proton-proton collisions at √ s =0 .77