Measurement of transverse-single-spin asymmetries for midrapidity and forward-rapidity production of hadrons in polarized p+p collisions at s √ = 200 and 62.4 GeV
A. Adare, S. Afanasiev, C. Aidala, N.N. Ajitanand, Y. Akiba, H. Al-Bataineh, J. Alexander, A. Angerami, K. Aoki, N. Apadula, L. Aphecetche, Y. Aramaki, J. Asai, E.T. Atomssa, R. Averbeck, T.C. Awes, B. Azmoun, V. Babintsev, M. Bai, G. Baksay, L. Baksay, A. Baldisseri, K.N. Barish, P.D. Barnes, B. Bassalleck, A.T. Basye, S. Bathe, S. Batsouli, V. Baublis, C. Baumann, A. Bazilevsky, S. Belikov, R. Belmont, R. Bennett, A. Berdnikov, Y. Berdnikov, J.H. Bhom, A.A. Bickley, D.S. Blau, J.G. Boissevain, J.S. Bok, H. Borel, K. Boyle, M.L. Brooks, H. Buesching, V. Bumazhnov, G. Bunce, S. Butsyk, C.M. Camacho, S. Campbell, A. Caringi, B.S. Chang, W.C. Chang, J.-L. Charvet, C.-H. Chen, S. Chernichenko, C.Y. Chi, M. Chiu, I.J. Choi, J.B. Choi, R.K. Choudhury, P. Christiansen, T. Chujo, P. Chung, A. Churyn, O. Chvala, V. Cianciolo, Z. Citron, B.A. Cole, Z. Conesa del Valle, M. Connors, P. Constantin, M. Csanád, T. Csörgő, T. Dahms, S. Dairaku, I. Danchev, K. Das, A. Datta, G. David, M.K. Dayananda, A. Denisov, D. d'Enterria, A. Deshpande, E.J. Desmond, K.V. Dharmawardane, O. Dietzsch, A. Dion, M. Donadelli, O. Drapier, A. Drees, K.A. Drees, A.K. Dubey, J.M. Durham, A. Durum, D. Dutta, V. Dzhordzhadze, L. D'Orazio, S. Edwards, Y.V. Efremenko, et al. (351 additional authors not shown)
aa r X i v : . [ h e p - e x ] D ec Measurement of transverse-single-spin asymmetries for midrapidity andforward-rapidity production of hadrons in polarized p + p collisions at √ s = 200 and62.4 GeV A. Adare, S. Afanasiev, C. Aidala,
44, 45
N.N. Ajitanand, Y. Akiba,
57, 58
H. Al-Bataineh, J. Alexander, A. Angerami, K. Aoki,
36, 57
N. Apadula, L. Aphecetche, Y. Aramaki,
13, 57
J. Asai, E.T. Atomssa, R. Averbeck, T.C. Awes, B. Azmoun, V. Babintsev, M. Bai, G. Baksay, L. Baksay, A. Baldisseri, K.N. Barish, P.D. Barnes, ∗ B. Bassalleck, A.T. Basye, S. Bathe,
6, 9, 58
S. Batsouli, V. Baublis, C. Baumann, A. Bazilevsky, S. Belikov, ∗ R. Belmont, R. Bennett, A. Berdnikov, Y. Berdnikov, J.H. Bhom, A.A. Bickley, D.S. Blau, J.G. Boissevain, J.S. Bok, H. Borel, K. Boyle, M.L. Brooks, H. Buesching, V. Bumazhnov, G. Bunce,
8, 58
S. Butsyk, C.M. Camacho, S. Campbell, A. Caringi, B.S. Chang, W.C. Chang, J.-L. Charvet, C.-H. Chen, S. Chernichenko, C.Y. Chi, M. Chiu,
8, 26
I.J. Choi, J.B. Choi, R.K. Choudhury, P. Christiansen, T. Chujo, P. Chung, A. Churyn, O. Chvala, V. Cianciolo, Z. Citron, B.A. Cole, Z. Conesa del Valle, M. Connors, P. Constantin, M. Csan´ad, T. Cs¨org˝o, T. Dahms, S. Dairaku,
36, 57
I. Danchev, K. Das, A. Datta, G. David, M.K. Dayananda, A. Denisov, D. d’Enterria, A. Deshpande,
58, 64
E.J. Desmond, K.V. Dharmawardane, O. Dietzsch, A. Dion,
29, 64
M. Donadelli, O. Drapier, A. Drees, K.A. Drees, A.K. Dubey, J.M. Durham,
40, 64
A. Durum, D. Dutta, V. Dzhordzhadze, L. D’Orazio, S. Edwards, Y.V. Efremenko, F. Ellinghaus, T. Engelmore, A. Enokizono,
39, 53
H. En’yo,
57, 58
S. Esumi, K.O. Eyser, B. Fadem, N. Feege, D.E. Fields,
50, 58
M. Finger, M. Finger, Jr., F. Fleuret, S.L. Fokin, Z. Fraenkel, ∗ J.E. Frantz,
52, 64
A. Franz, A.D. Frawley, K. Fujiwara, Y. Fukao,
36, 57
T. Fusayasu, I. Garishvili, A. Glenn,
14, 39
H. Gong, M. Gonin, J. Gosset, Y. Goto,
57, 58
R. Granier de Cassagnac, N. Grau,
3, 15
S.V. Greene, G. Grim, M. Grosse Perdekamp,
26, 58
T. Gunji, H.-˚A. Gustafsson, ∗ A. Hadj Henni, J.S. Haggerty, K.I. Hahn, H. Hamagaki, J. Hamblen, R. Han, J. Hanks, E.P. Hartouni, K. Haruna, E. Haslum, R. Hayano, X. He, M. Heffner, T.K. Hemmick, T. Hester, J.C. Hill, M. Hohlmann, W. Holzmann,
15, 63
K. Homma, B. Hong, T. Horaguchi,
13, 24, 57, 67
D. Hornback, S. Huang, T. Ichihara,
57, 58
R. Ichimiya, H. Iinuma,
36, 57
Y. Ikeda, K. Imai,
30, 36, 57
J. Imrek, M. Inaba, D. Isenhower, M. Ishihara, T. Isobe,
13, 57
M. Issah,
63, 69
A. Isupov, D. Ivanischev, Y. Iwanaga, B.V. Jacak, J. Jia,
8, 15, 63
X. Jiang, J. Jin, B.M. Johnson, T. Jones, K.S. Joo, D. Jouan, D.S. Jumper, F. Kajihara, S. Kametani, N. Kamihara, J. Kamin, J.H. Kang, J. Kapustinsky, K. Karatsu,
36, 57
M. Kasai,
57, 59
D. Kawall,
44, 58
M. Kawashima,
A.V. Kazantsev, T. Kempel, A. Khanzadeev, K.M. Kijima, J. Kikuchi, A. Kim, B.I. Kim, D.H. Kim, D.J. Kim,
32, 73
E. Kim, E.-J. Kim, S.H. Kim, Y.-J. Kim, E. Kinney, K. Kiriluk, ´A. Kiss, E. Kistenev, J. Klay, C. Klein-Boesing, D. Kleinjan, L. Kochenda, B. Komkov, M. Konno, J. Koster, A. Kozlov, A. Kr´al, A. Kravitz, G.J. Kunde, K. Kurita,
57, 59
M. Kurosawa, M.J. Kweon, Y. Kwon,
66, 73
G.S. Kyle, R. Lacey, Y.S. Lai, J.G. Lajoie, D. Layton, A. Lebedev, D.M. Lee, J. Lee, K.B. Lee, K.S. Lee, T. Lee, M.J. Leitch, M.A.L. Leite, B. Lenzi, X. Li, P. Lichtenwalner, P. Liebing, L.A. Linden Levy, T. Liˇska, A. Litvinenko, H. Liu,
40, 51
M.X. Liu, B. Love, D. Lynch, C.F. Maguire, Y.I. Makdisi, A. Malakhov, M.D. Malik, V.I. Manko, E. Mannel, Y. Mao,
55, 57
L. Maˇsek,
10, 28
H. Masui, F. Matathias, M. McCumber, P.L. McGaughey, D. McGlinchey,
14, 22
N. Means, B. Meredith, Y. Miake, T. Mibe, A.C. Mignerey, P. Mikeˇs, K. Miki,
57, 68
A. Milov, M. Mishra, J.T. Mitchell, A.K. Mohanty, H.J. Moon, Y. Morino, A. Morreale, D.P. Morrison, † T.V. Moukhanova, D. Mukhopadhyay, T. Murakami, J. Murata,
57, 59
S. Nagamiya, J.L. Nagle, ‡ M. Naglis, M.I. Nagy,
19, 72
I. Nakagawa,
Y. Nakamiya, K.R. Nakamura,
36, 57
T. Nakamura,
24, 57
K. Nakano,
57, 67
S. Nam, J. Newby, M. Nguyen, M. Nihashi, T. Niida, R. Nouicer, A.S. Nyanin, C. Oakley, E. O’Brien, S.X. Oda, C.A. Ogilvie, M. Oka, K. Okada, Y. Onuki, A. Oskarsson, M. Ouchida,
24, 57
K. Ozawa, R. Pak, A.P.T. Palounek, V. Pantuev,
27, 64
V. Papavassiliou, I.H. Park, J. Park, S.K. Park, W.J. Park, S.F. Pate, H. Pei, J.-C. Peng, H. Pereira, V. Peresedov, D.Yu. Peressounko, R. Petti, C. Pinkenburg, R.P. Pisani, M. Proissl, M.L. Purschke, A.K. Purwar, H. Qu, J. Rak,
32, 50
A. Rakotozafindrabe, I. Ravinovich, K.F. Read,
53, 66
S. Rembeczki, K. Reygers, V. Riabov, Y. Riabov, E. Richardson, D. Roach, G. Roche, S.D. Rolnick, M. Rosati, C.A. Rosen, S.S.E. Rosendahl, P. Rosnet, P. Rukoyatkin, P. Ruˇziˇcka, V.L. Rykov, B. Sahlmueller,
46, 64
N. Saito,
33, 36, 57, 58
T. Sakaguchi, S. Sakai, K. Sakashita,
57, 67
V. Samsonov, S. Sano,
13, 70
T. Sato, S. Sawada, K. Sedgwick, J. Seele, R. Seidl,
26, 58
A.Yu. Semenov, V. Semenov,
25, 27
R. Seto, D. Sharma, I. Shein, T.-A. Shibata,
57, 67
K. Shigaki, M. Shimomura, K. Shoji,
36, 57
P. Shukla, A. Sickles, C.L. Silva,
29, 61
D. Silvermyr, C. Silvestre, K.S. Sim, B.K. Singh, C.P. Singh, V. Singh, M. Sluneˇcka, A. Soldatov, R.A. Soltz, W.E. Sondheim, S.P. Sorensen, I.V. Sourikova, F. Staley, P.W. Stankus, E. Stenlund, M. Stepanov, A. Ster, S.P. Stoll, T. Sugitate, C. Suire, A. Sukhanov, J. Sziklai, E.M. Takagui, A. Taketani,
57, 58
R. Tanabe, Y. Tanaka, S. Taneja, K. Tanida,
36, 57, 58, 62
M.J. Tannenbaum, S. Tarafdar, A. Taranenko, P. Tarj´an, H. Themann, D. Thomas, T.L. Thomas, M. Togawa,
36, 57, 58
A. Toia, L. Tom´aˇsek, Y. Tomita, H. Torii,
24, 57
R.S. Towell, V-N. Tram, I. Tserruya, Y. Tsuchimoto, C. Vale,
8, 29
H. Valle, H.W. van Hecke, E. Vazquez-Zambrano, A. Veicht, J. Velkovska, R. V´ertesi,
18, 72
A.A. Vinogradov, M. Virius, A. Vossen, V. Vrba, E. Vznuzdaev, X.R. Wang, D. Watanabe, K. Watanabe, Y. Watanabe,
57, 58
F. Wei, R. Wei, J. Wessels, S.N. White, D. Winter, C.L. Woody, R.M. Wright, M. Wysocki, W. Xie, Y.L. Yamaguchi,
13, 57, 70
K. Yamaura, R. Yang, A. Yanovich, J. Ying, S. Yokkaichi,
57, 58
Z. You, G.R. Young, I. Younus,
38, 50
I.E. Yushmanov, W.A. Zajc, O. Zaudtke, C. Zhang, S. Zhou, and L. Zolin (PHENIX Collaboration) Abilene Christian University, Abilene, Texas 79699, USA Institute of Physics, Academia Sinica, Taipei 11529, Taiwan Department of Physics, Augustana College, 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 Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, P. R. China 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 Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France 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 Ewha Womans University, Seoul 120-750, Korea Florida Institute of Technology, Melbourne, Florida 32901, USA Florida State University, Tallahassee, Florida 32306, USA Georgia State University, Atlanta, Georgia 30303, USA Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan 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 Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia 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 Russian Research Center “Kurchatov Institute”, Moscow, 123098 Russia Kyoto University, Kyoto 606-8502, Japan Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France Physics Department, Lahore University of Management Sciences, Lahore, Pakistan Lawrence Livermore National Laboratory, Livermore, California 94550, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA LPC, Universit´e Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden University of Maryland, College Park, Maryland 20742, USA Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA Institut fur Kernphysik, University of Muenster, D-48149 Muenster, Germany Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA Myongji University, Yongin, Kyonggido 449-728, Korea Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan 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, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France Peking University, Beijing 100871, P. R. 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 Universidade de S˜ao Paulo, Instituto de F´ısica, Caixa Postal 66318, S˜ao Paulo CEP05315-970, Brazil Seoul National University, Seoul, Korea Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes) BP 20722 - 44307, Nantes, France University of Tennessee, Knoxville, Tennessee 37996, USA Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan Vanderbilt University, Nashville, Tennessee 37235, USA Waseda University, Advanced Research Institute for Science andEngineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan 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 (Dated: June 26, 2018)Measurements of transverse-single-spin asymmetries ( A N ) in p + p collisions at √ s = 62 . A N is measuredfor neutral pion and eta mesons reconstructed from diphoton decay, and, at forward rapidities,neutral pions are measured using both diphotons and electromagnetic clusters. The neutral-pionmeasurement of A N at midrapidity is consistent with zero with uncertainties a factor of 20 smallerthan previous publications, which will lead to improved constraints on the gluon Sivers function.At higher rapidities, where the valence quark distributions are probed, the data exhibit sizableasymmetries. In comparison with previous measurements in this kinematic region, the new dataextend the kinematic coverage in √ s and p T , and it is found that the asymmetries depend onlyweakly on √ s . The origin of the forward A N is presently not understood quantitatively. Theextended reach to higher p T probes the transition between transverse momentum dependent effectsat low p T and multi-parton dynamics at high p T . PACS numbers:
I. INTRODUCTION
The proton is a fundamental and stable bound state ofquantum chromodynamics. Collinear perturbative quan-tum chromodynamics (pQCD) at leading twist in the op-erator product expansion successfully describes the quarkand gluon substructure of the proton observed in highenergy scattering experiments [1]. The parton distribu-tion functions, f i ( x, Q ), constitute the number densi-ties of partons of flavor i in the proton. They dependon the partonic momentum fraction, x , and on the mo- ∗ Deceased † PHENIX Co-Spokesperson: [email protected] ‡ PHENIX Co-Spokesperson: [email protected] mentum transfer scale, Q . Two similar sets of distri-bution functions parametrize the spin dependent partondistributions in protons polarized either longitudinally ortransversely with respect to the proton momentum direc-tion [2]. The longitudinally polarized structure has beensuccessfully described using pQCD at leading twist [3].Initially, transverse-single-spin asymmetries or the an-alyzing power ( A N ) of hadrons h produced in the trans-versely polarized p ↑ + p → h + X reaction were expectedto be small [4], but experiments instead measured largeasymmetries of up to A N ≈ √ s over the past three decades, from 4.9 to 200 GeV [5–10], Recent results from the Relativistic Heavy Ion Col-lider (RHIC) show that large asymmetries persist evenup to √ s = 200 GeV [11–13]. Unlike at the low to inter-mediate energies, the measured unpolarized cross sectionat high energies is well reproduced by pQCD calcula-tions [11, 13], indicating that unpolarized collisions canbe described by the standard collinear factorized theory,while transversely polarized collisions cannot.To better describe the large A N measurements, thetheoretical framework has been extended to includetransverse momentum dependent (TMD) distributionsand multi-parton dynamics (higher twist effects). Be-cause the intrinsic partonic transverse momentum scaleis set by the mass of the proton, these effects dominatefor hadrons with low momenta transverse to the beamaxis, p T < ∼ c . At least two TMD effects have beenproposed to explain the observed nonzero asymmetries.The first of these, known as the Sivers effect, corre-lates the proton spin with the partonic transverse mo-mentum k T [14]. It has been measured in semi-inclusivedeep inelastic scattering (SIDIS) experiments with sensi-tivity mainly to the quarks [15, 16]. Previous results in p + p collisions [17] have been used to constrain the gluonSivers function [18]. Recently, this function has receivedintense theoretical attention based on questions of uni-versality and an expected sign change of A N in SIDIScompared to Drell-Yan production [19, 20].A second transverse momentum dependent effect,known as the Collins effect, describes the coupling of atransverse quark polarization (transversity) and a trans-verse spin dependent fragmentation from a struck quarkinto a hadron [21]. The spin dependent fragmenta-tion part has been measured in e + + e − annihilation forcharged pions [22, 23] and serves as input for Collinsasymmetries in proton scattering to access the transver-sity distribution [24–26]. The full integral over all par-tonic momenta 0 ≤ x ≤ δ Σ,which is calculable in lattice QCD [27, 28]. This will bea fundamental test of the theory.At large transverse momenta the collinear higher twisteffects are thought to become more important in the cre-ation of transverse spin asymmetries [29, 30]. For Drell-Yan production it has been shown that both initial stateTMD and multi-parton dynamics provide equivalent de-scriptions of transverse asymmetries in an overlap regionat intermediate transverse momenta [31]. With increas-ing p T the asymmetries are expected to fall off and van-ish in the strictly collinear regime, which has not beenobserved experimentally yet. It is best probed at highcenter-of-mass energies, where the range of transversemomenta is wider.This paper reports on measurements of A N at √ s =62 . √ s = 62 . √ s = 200 GeV) with integrated luminosi-ties of 42 nb − and 4.3 pb − , respectively. Results arepresented for neutral mesons in a midrapidity region( | η | < .
35) as well as for π mesons and inclusive electro-magnetic clusters at forward/backward pseudorapidities(3 . < | η | < . II. EXPERIMENTAL SETUPA. PHENIX Midrapidity and Global Detectors
The PHENIX midrapidity spectrometer is used to de-tect neutral pions and η mesons via their decay intotwo photons. The spectrometer covers a pseudorapidityrange of | η | < .
35 and is split into two approximatelyback-to-back arms each covering ∆ ϕ = π/ η × ∆ ϕ ≈ . × .
01. Events are selectedusing an EMCal based high tower energy trigger in coin-cidence with a minimum bias trigger. The trigger, digiti-zation electronics, and details of the hardware have beendiscussed previously [32]. The trigger efficiency starts atabout 5% for neutral pions with p T ≈ c and risesto and saturates at about 90% at p T > . c . Amulti-wire proportional chamber with pad readout [33]is situated in front of the calorimeter face, and is used toveto charged particles.The minimum bias trigger was defined as the coinci-dence of signals from two Beam Beam Counters (BBC)covering the full azimuthal angle and the pseudorapid-ity range 3 . < | η | < . B. Muon Piston Calorimeter
The PHENIX Muon Piston Calorimeter (MPC) is anelectromagnetic calorimeter which was designed to mea-sure photons and neutral mesons at forward-rapidity.The detector comprises two separate devices placed alongthe beamline to the North and to the South of the nom-inal interaction point, labeled N-MPC and S-MPC. TheS-MPC was first installed in 2006 and the N-MPC fol-lowed a year later. Therefore, the analysis of the 2006data set ( √ s =62.4 GeV) uses only the S-MPC while the2008 data set ( √ s =200 GeV) includes both detectors.Both MPCs are located in cavities of the steel pis-ton which is part of the PHENIX muon detector magnetyoke. The diameter of each cavity limits the detector’souter diameter to 45 cm, while the beampipe requiresan inner diameter of no less than 8 cm (N-MPC) or Energy (au)
10 20 30 40 50 60 70 80 C oun t s Data: InclusiveData: With CutsFitGaussianPower Law
FIG. 1: (color online) Uncalibrated energy spectra with andwithout cuts to isolate minimum ionizing particles (MIP)in the MPC. These cuts include: neighboring tower en-ergy deposits and track-matching cuts using the upstreamBBCs ˇCerenkov counters. The spectrum with the cut is fitwith a power law and a Gaussian. The Gaussian peak po-sition is taken as the most probable MIP energy deposit, E ≈
234 MeV.
10 cm (S-MPC). The MPCs are placed ±
220 cm from thenominal interaction point and are composed of 192 (S-MPC) or 220 (N-MPC) towers stacked to form an annu-lus around the beampipe. The detector acceptance cov-ers the full azimuthal angle and a pseudorapidity rangeof − . < η < − . . < η < . scintillating crys-tal wrapped with Tyvek R (cid:13) , aluminized mylar andMonoKote R (cid:13) , with a Hamamatsu S8664-55 avalanchephotodiode for read-out. Each crystal measures2.2 × ×
18 cm , corresponding to a depth of 21.2 radi-ation lengths and 0.844 nuclear interaction lengths. In-dependently of the minimum bias trigger, the MPC isequipped with its own high energy cluster trigger. Thetrigger and digitization electronics are identical to thoseof the EMCal and are discussed in detail in [32]. Forthe presented data, the trigger efficiency starts at 5% forphoton energies E ≈
30 GeV and reaches a plateau at90% above
E >
50 GeV.A test-beam measurement, carried out at the MesonTest Beam Facility at the Fermi National Accelerator now the MT6 area at the Fermilab Test Beam Facility Laboratory confirmed the calorimeter’s linear energy re-sponse and measured the electromagnetic shower shapes.These shower shapes were then used to tune a geant in situ usinga two-step process. First, minimum ionizing particlesare used. Yields of charged tracks in the calorimeterare enhanced by requiring a correlated hit in the BBCthat is located in front of the MPC. Additionally, thetower multiplicity of the cluster is required to be smallcompared to a typical electromagnetic shower to increasethe hadronic contributions. A sample minimum ionizingparticle peak is shown in Fig. 1 with an expected meanenergy of 234 MeV. The initial MIP calibration is thenused as the seed in an iterative and converging procedurefor individual towers that is based on the π peak in theinvariant mass distribution. Time dependencies in thetower gains are tracked and corrected for by a monitoringsystem of LEDs, whose intensities are monitored by PINdiodes. Finally, the overall calibration is verified and theenergy resolution is determined by comparing the massesof the π and η peaks in the two-cluster invariant massdistributions between data and a Monte-Carlo simula-tion. A set of representative two-cluster invariant masspeaks is shown in Fig. 2. The relative energy resolution( δE/E ) of the calorimeter is found to be 13%/ √ E ⊕ ) (GeV/c invariant M C oun t s × Trigger: Minimum Bias(11 < E < 17 GeV)NorthSouth ) (GeV/c invariant M C oun t s Trigger: MPC(40 < E < 80 GeV)
FIG. 2: (color online) Two-cluster invariant mass distribu-tions from the 2008 data set at √ s =200 GeV for both theNorth and South MPC detectors. The left panel shows π peak from minimum bias triggered data set at low energywhile the right side shows the η meson peak from the MPCtriggered data set at high two-cluster energies E . A compari-son of the peak position and widths from data and simulationare used to determine the energy scale uncertainty. C. Polarized Proton Beams
RHIC accelerates and stores polarized proton beamsat energies up to 255 GeV in two independent rings. Thebeams collide at several interaction points along the ring.Each ring can be filled with up to 120 bunches with differ-ent transverse polarization directions. These directionsalternate to reduce systematic effects from slow varia-tions in luminosity or detector acceptances and efficien-cies. Additionally, the patterns are chosen from four pre-defined basic patterns to reduce time dependent correla-tions and detector effects.Previous publications describe in detail the necessaryaccelerator instrumentation for producing the collidingpolarized beams [36]. The polarization is measured witha set of polarimeters external to the PHENIX experi-ment using elastic scattering from a hydrogen gas jet ora Carbon fiber target. For the determination of the ab-solute polarization of both proton beams, the hydrogenjet polarimeter with a known polarization of the atomicjet is used [37]. Due to the low density of the gas jeta polarization measurement with good accuracy requiresmany hours of data taking. Therefore, the relative polar-ization is measured several times per fill with high preci-sion by fast p +C polarimeters for each of the two storagerings [38]. These relative measurements are then normal-ized using results from the jet polarimeter.While both of the RHIC beams are polarized dur-ing the measurement of the single spin asymmetries pre-sented in this paper, summation over the bunches of onebeam effectively averages the polarization to zero. Thisprocedure is applied to one of the two beams at a timeand can therefore be used as a cross check of two uncor-related measurements of the asymmetry. The directionof the polarized beam is commonly referred to as for-ward in the following; backward is in the direction ofthe unpolarized beam. Table I summarizes the beam po-larizations for the different data sets and center-of-massenergies, with ~p = (0 , , p z ) pointing North, according tothe PHENIX coordinate system. TABLE I: Polarizations for RHIC proton beams in 2006 and2008. The polarization uncertainty is a global scale uncer-tainty of the measured asymmetries A N and is not includedin any of the figures or data tables.Year √ s (GeV) Beam direction P beam ~p = (0 , , p z ) (49.0 ± ~p = (0 , , − p z ) (49.0 ± ~p = (0 , , p z ) (48.0 ± ~p = (0 , , − p z ) (41.0 ± The stable polarization direction around the accelera-tor is vertical ( P ↑ = (0 , P,
0) or P ↓ = (0 , − P, ϕ = 0 . ± . stat ± . syst rad.For the rest of the measurements, all other polarizationvectors are found to be consistent with the vertical di-rection within statistical uncertainties [39]. The polar-ization directions are accounted for in the determinationof the relevant asymmetries. In addition, the 2006 and2008 polarization direction measurements have been in- dependently verified using the analysis techniques fromSec. III A. III. ANALYSISA. Transverse-Single-Spin Asymmetries
The A N that can generally arise in polarized scatter-ing experiments are described in the framework of polar-ization analyzing tensors which gives information aboutfully polarized initial and final states of the scatteringprocess. The polarization can be aligned along three di-mensions in the scattering frame, i.e., longitudinal in theprojectile direction ~L , sideways in the scattering (or pro-duction) plane ~S , or normal to the scattering plane ~N ,where ~S = ~N × ~L . In the following, the left side refers tothe direction of ~S in this right-handed system, the rightside to the opposite direction. For A N , we are only con-sidering a normal polarization for the projectile. Targetand final states are unpolarized. The normal space quan-tization can create a transverse asymmetry within thescattering plane. A rotation into the laboratory frame(where the beam polarization P is prepared) then trans-forms this pure left-right asymmetry into an azimuthal( ϕ ) modulation of the cross section dσ ( ϕ ) ∝ A N · P · cos ϕ .The transverse asymmetry A N can be determined frompoint-like detectors as: A N = 1 P · ϕ dσ ( ϕ ) − dσ ( ϕ + π ) dσ ( ϕ ) + dσ ( ϕ + π ) . (1)The same result can be achieved with a detector in justone hemisphere by a rotation of the polarization vector P ↑ → P ↓ : dσ ↑ ( ϕ ) = dσ ↓ ( ϕ + π ) dσ ↓ ( ϕ ) = dσ ↑ ( ϕ + π ) . Integrating the cross sections over the detector accep-tance, beam luminosities, and the duration of the mea-surement, A N is experimentally extracted from the geo-metric means of the particle yields: ǫ ( ϕ ) = A N · P · cos ϕ = q N ↑ L · N ↓ R − q N ↓ L · N ↑ R q N ↑ L · N ↓ R + q N ↓ L · N ↑ R , (2)where N L , N R refer to particle yields in detector seg-ments ∆ ϕ of the left ( ϕ ) and right ( ϕ + π ) hemispheres.An alternate estimator is used to study systematic effects ǫ ( ϕ ) = A N · P · cos ϕ = N ↑ − R · N ↓ N ↑ + R · N ↓ , (3)with R being the ratio of luminosities between the twospin states ↑ and ↓ . This luminosity is determined usingthe polarization-sorted counts from the minimum biastrigger. The asymmetries in this analysis are calculatedin 8 or 16 bins in the azimuth, unless noted otherwise,and then fit to the cosine modulation (with and withoutan additional free phase ϕ for consistency checks). Sys-tematic uncertainties are estimated by comparing asym-metries from Eqs. 2 and 3, which may be due to differentassumptions in the integration of the cross sections. B. A π N at √ s = 62 . GeV and High x F Measurements at √ s = 62 . . × MPCtriggered events. The π → γ + γ decay is reconstructedfrom pairs of clusters in the detector with a selection onthe photon shower shape. Clusters which have their cen-tral tower marked as either noisy or inactive are removedfrom the analysis. The π contribution is selected fromthe cluster pairs by requiring a minimum pair energy, E pair > α of the two cluster energies E and E , α = (cid:12)(cid:12)(cid:12)(cid:12) E − E E + E (cid:12)(cid:12)(cid:12)(cid:12) . (4)The two cluster invariant mass distributions look qual-itatively similar to those from √ s = 200 GeV shown inFig. 2. The shape of the distributions has been studiedin simulations based on the pythia event generator [40]Tune A [41] with a full detector simulation (similar toSec. II.B). The background is dominated by combinato-rial effects from reconstructing two clusters from differentparent sources. The background yield is determined bymixing uncorrelated clusters from different events andnormalizing to the invariant mass distribution above the π peak, but below any contribution from the η peak.From the integral of the resulting π peak one can deter-mine the π yields. The final asymmetries are calculatedaccording to Eq. 2 from the geometrical means of the π yields. The systematic uncertainties to these asymme-tries are estimated using Eq. 3.Figure 3 shows A N at √ s = 62 . x F = 2 · p z / √ s , with p z being the longitudinal compo-nent of the momentum along the direction of the polar-ized proton beam. While there is a significant, nonzeroasymmetry rising with x F > x F < p T dependence of A N , up to a range that is largelylimited by kinematics due to the low 62.4 GeV center-of-mass energy. No strong p T dependence is observed.Figure 5 compares the x F -dependence of neutral pion A N of this publication with the world data set [10, 11]at center-of-mass energies from √ s = 19 . x F dependence. F x -0.6 -0.4 -0.2 0 0.2 0.4 0.6 N A -0.04-0.0200.020.040.060.080.10.12 =62.4GeVs + X, π → p+p |<3.8 η , 3.5<| π PHENIX |<3.5 η , 3.1<| π PHENIX
FIG. 3: (color online) Neutral pion A N at √ s = 62 . x F in two different pseudorapidity ranges (3 . < | η | < . . < | η | < .
8) with statistical and systematicuncertainties. Appendix Table III gives the data in plain text.An additional uncertainty from the beam polarization (seeTable I) is not included. T p N A >0 F =62.4GeV, xs + X, π → p+p FIG. 4: Neutral pion A N at √ s = 62 . p T Appendix Table IV gives the plaintext data. An additional uncertainty from the beam polar-ization (see Table I) is not included.
The asymmetries appear to be independent of the center-of-mass energy, including at high energies where the ap-plicability of pQCD is well established at √ s = 200 GeVat p T > c .Figure 6 shows the pion isospin dependence of A N at √ s = 62 . π PHENIX data and charged pion data from theBRAHMS collaboration [10]. The BRAHMS measure-ments of charged pions were carried out with two detectorsettings covering different subranges in pseudorapiditywhich compare well to the acceptance of the MPC. While F x N A =62.4 GeVs<3.8 η π PHENIX =19.4 GeVs π E704 =200 GeVs>=3.3, η < π STAR =200 GeVs>=3.7, η < π STAR + X π → p+p FIG. 5: (color online) Comparison of neutral pion A N as func-tion of x F from √ s = 19 . π + and π asymmetries are positive, those of π − are ofopposite sign. The amplitudes of the charged pion asym-metries are of similar size, with the π − perhaps slightlylarger, whereas both are significantly larger than the neu-tral pion asymmetry. F x N A -0.5-0.4-0.3-0.2-0.100.10.20.3 <3.8 η , 3.1< π PHENIX =3.6 η , + π BRAHMS =3.9 η , + π BRAHMS =3.6 η , - π BRAHMS =3.9 η , - π BRAHMS =62.4GeVs + X, π → p+p FIG. 6: (color online) Isospin comparison of pion A N asa function of x F at √ s = 62 . C. A clusterN at √ s = 200 GeV and High x F At energies below E π < ∼
20 GeV the MPC is ableto resolve the π → γ + γ decay. However, with in-creasing energy, the opening angle between the two pho-tons becomes so small that their electromagnetic clustersfully merge in the detector. This limits the x F range at √ s = 200 GeV to below 0.2 for π ’s reconstructed via thetwo-gamma decay mode. To overcome this limitation thedata analysis is done for inclusive clusters.The data set at √ s = 200 GeV includes 1 . × eventsrecorded with a high energy cluster trigger. Clusters inthe analysis are required to have fired the correspondingtrigger, i.e., N-MPC or S-MPC, and to satisfy a time offlight cut. Clusters whose central tower is either markednoisy or inactive are removed from the analysis. The con-tributions from hadrons to the cluster yields are reducedby selecting for photonic shower shapes. To minimize ef-fects from energy leakage at the detector edges, a radialfiducial cut is applied. The transverse asymmetries aredetermined with Eq. 2 and systematic uncertainties areestimated using the difference from Eq. 3.The cluster composition is estimated using MonteCarlo simulations. Again, a full detector simulation isbased on input from pythia k = 2)and all other particles originating from high energy scat-tering processes ( k = 1) with a minimum p T of 2 GeV.The normalization factors are determined by comparingthe simulated cross sections with RHIC measurementsat √ s = 200 GeV [42–45]. The composition analysis dif-ferentiates between electromagnetic clusters originatingfrom photonic decays of π and η mesons, direct photons,and energy deposited by charged hadrons ( h ± ). Contri-butions from other sources, e.g. fragmentation photonsand ω meson decays, are combined in the “other γ ” cat-egory.Figure 7 summarizes the cluster composition as func-tion of p T with large x F > .
4; Table II lists the corre-sponding values in detail. In the context of this pythia study, over the studied kinematic range contributionsfrom decay photons of π mesons are the dominant sourceof clusters in the MPC. With increasing p T there is a siz-able increase in contributions from direct and other pho-tons. The relative uncertainty of the composition fromthis study at p T > c is less than 20% and signifi-cantly smaller at lower p T .Figure 8 summarizes the x F -dependence of the clus-ter A N for two different pseudorapidity ranges similar toFig. 3. Systematic uncertainties again are evaluated bycomparison of results from Eqs. 2 and 3. Within statisti-cal uncertainties the asymmetries in the backward direc-tion x F < A N rises almost linearly with x F .The asymmetries are of similar size compared to earlierresults at different center-of-mass energies as shown inFig. 5.Figure 9 presents A N , as a function of transverse mo-mentum p T for values of | x F | > . A N is largestin forward kinematics (compare Fig. 8). The asymme-try rises smoothly and then seems to saturate above p T > c . A significant decrease of the asymme-try as expected from higher twist calculations is not ob-served [31]. Again, negative x F asymmetries are found tobe consistent with zero within statistical uncertainties. (GeV/c) T p F r a c t i ona l c l u s t e r c o m po s i t i on γ other +/- h η γ direct π FIG. 7: Cluster composition from p + p Monte Carlo eventgenerator studies at √ s = 200 GeV with a full detector sim-ulation. The kinematic cuts and p T ranges are the same asused in the data analysis and directly comparable to Fig. 9,in particular x F > . F x -0.6 -0.4 -0.2 0 0.2 0.4 0.6 N A -0.04-0.0200.020.040.060.080.10.12 =200GeVs Cluster + X, → p+p |<3.8 η η FIG. 8: (color online) The A N of electromagnetic clusters at √ s = 200 GeV as function of x F and in two different pseu-dorapidity ranges. Appendix Table VI gives the data in plaintext. An additional uncertainty from the beam polarization(see Table I) is not included. Figure 10 shows A N as a function of p T for differentranges of x F . These ranges are chosen to match that of anearlier measurement of π asymmetries from the STARexperiment [11]. The two measurements in general dis-play a good agreement. At large x F and high p T there isperhaps a hint that the inclusive cluster asymmetries aresmaller, but with present statistics the difference is notyet significant. We note that the STAR measurement isfor identified π ’s and the PHENIX measurement is forclusters with a mixed composition. As mentioned previ-ously, these clusters are dominantly from π ’s, but alsoinclude contributions from the decays of η and other neu-tral mesons, as well as a contribution from direct photons (GeV/c) T p N A -0.02-0.0100.010.020.030.040.050.060.070.08 =200GeVs Cluster + X, → p+p > 0.4 F x < -0.4 F x FIG. 9: (color online) The A N of electromagnetic clustersat √ s = 200 GeV at large | x F | > . p T . Appendix Table VII gives thedata in plain text. An additional uncertainty from the beampolarization (see Table I) is not included. < 0.3 F (a) 0.25 < x =200 GeVs Cluster + X → p+p + X (STAR) π → p+p < 0.35 F (b) 0.3 < x < 0.4 F (c) 0.35 < x < 0.47 F (d) 0.4 < x < 0.56 F (e) 0.47 < x < 0.85 F (f) 0.56 < x N A (GeV/c) T p FIG. 10: (color online) Comparison of A N of electromagneticclusters and π mesons [11] at √ s = 200 GeV as function of p T in different ranges of x F . Appendix Table VIII gives thedata in plain text. An additional uncertainty from the beampolarization (see Table I) is not included. which is increasing with x F and p T .0 D. A π ,ηN at √ s =200 GeV and Small x F The data selection and asymmetry analysis in themidrapidity spectrometer closely follows the procedureof previous analyses [17]. The data set includes 6.9 × events triggered by the high p T photon trigger. Pho-ton clusters are selected using photonic shower shape cutsin the electromagnetic calorimeter, the time of flight be-tween the collision point and the calorimeter, a minimumdeposited energy of 200 MeV, and a charged particle vetofrom tracking in front of the calorimeter. Cluster pairsare then chosen with an energy asymmetry (Eq. 4) of lessthan 0.8 (0.7) for π ( η ) identification, and by requiringthat the photon with the higher energy fired the trigger.The yields are taken as the number of cluster pairs in a ±
25 MeV/ c window around the mean of the π peak inthe invariant mass distribution ( ±
70 MeV/ c around themean of the η mass). The width of the π peak decreasesfrom 12 to 9 MeV/ c as p T increases from 1 to 12 GeV/ c (35 to 25 MeV/ c for the η ). The background fractionsin the signal windows depend on p T and range from 29%to 4% under the π peak and 75% to 41% for the η peakas p T increases.To remove a possible background asymmetry, theweighted asymmetry between a low and high mass re-gion around the signal peak is determined and subtractedfrom the signal region. These regions are defined from47 to 97 and from 177 to 227 MeV/ c for the π , andfrom 300 to 400 and from 700 to 800 MeV/ c for the η meson. The signal asymmetry A signal N can be calculatedusing yields from the peak region N incl and from the in-terpolated background yields N bg : A signal N = A incl N − rA bg N − r , (5)with the background fraction r = N bg /N incl under eitherthe π or η signal. The background asymmetries are allconsistent with zero.Due to the limited azimuthal acceptance of the midra-pidity spectrometer the asymmetries are only measuredfrom integrated yields in the whole detector hemispheresto the left and right of the polarization direction. Toaccount for the cosine modulation of the particle produc-tion, the asymmetries need to be corrected by an averagefactor f = 1 / h cos ϕ i taken over the detector acceptance.The asymmetries are calculated from Eq. 2, and the cor-responding systematic uncertainties are estimated fromdifferences with Eq. 3.Both the inclusive and background asymmetries are de-termined for each RHIC fill to test for possible variationswith time. The mean values are then used for the cal-culation of the final asymmetries for π and η mesons asfunction of p T , see Fig. 11 and Tables IX and X. The fig-ure shows the asymmetries for the whole detector accep-tance ( | η | < .
35) and for two samples selecting slightlyforward/backward going particles (0 . < | η | < . -0.1-0.0500.050.1 + X π → (a) p+p + X η → (b) p+p < 0.35 η -0.35 < > 0 F | < 0.35, x η F | < 0.35, x η N A (GeV/c) T p =200 GeVsp+p FIG. 11: (color online) The A N measured at midrapidity( | η | < . p T for π (a) and η (b) mesons (seeTables IX and X). Triangles are slightly forward/backward go-ing sub-samples of the full data set (circles). These are shiftedin p T for better visibility. An additional uncertainty from thebeam polarization (see Table I) is not included. data set. These very precise results are all consistentwith zero over the observed p T range. IV. DISCUSSION
The A N of neutral pions and inclusive charged hadronshave previously been measured with the PHENIX midra-pidity spectrometer [17]. Those asymmetries have beenfound to be consistent with zero and have been usedto constrain the gluon Sivers function [18] despite theirlimited statistical precision. The new results shown inFig. 11 exceed the former precision by a factor of 20 forthe π transverse asymmetries while extending the p T reach to above 10 GeV/ c . Also, this paper reports on A N of η mesons at x F ≈ √ s and p T . Altogether, no significantdeviation from zero can be seen in the results within the1statistical uncertainties in the covered transverse momen-tum range. Any difference in the two meson asymmetrieswould likely be dominated by fragmentation effects. Ei-ther these are small or suppressed by the contributingtransversity distribution in the covered kinematic range.In the forward direction, nonvanishing meson asym-metries persist all the way up to √ s = 200 GeV, asshown in Figs. 3 and 8. While there is no asymmetryin the backward direction ( x F < A N scales almostlinearly with positive x F > .
2. This behavior is similarto previous experimental results, as summarized in Fig. 5,where no strong center-of-mass energy dependence of theasymmetry is observed. The kinematic coverage of theexperiments is not exactly the same and may account forthe small differences in the data, but it is striking howwell the data match between measurements taken overcenter-of-mass collision energies that vary by more thanan order of magnitude, from √ s = 19.4 to 200 GeV. If thesame mechanisms are responsible across this entire colli-sion energy range, then these mechanisms seem to havea weak dependence over the interaction scale Q spannedby the world’s data.At forward rapidity x F is linearly proportional to thepolarized parton momentum fraction x : x F ≡ p L / √ s ≈ h z i p jet / √ s ≈ h z i x , (6)where h z i is the mean momentum fraction of the hadronfrom the jet fragmentation. This suggests the possibil-ity that these asymmetries are largely created by someintrinsic function of x that is only weakly dependent onthe collision energy.Further, from a comparison of the asymmetries of thepion isospin triplet at √ s = 62 . pythia eventgenerator studies show that the production of π − are al-most equally from unfavored u and favored d quark frag-mentation, while π + are almost exclusively from favored u quark fragmentation. At the same time, about three infour π stem from u quarks, with the other fourth com-ing from d quarks. Because the Sivers effect comes fromthe initial state quarks, the data can not be explainedby these initial state effects alone, under the assumptionthat the ratio of the u and d quark Sivers functions (es-pecially at high x ) are the same as those extracted fromSIDIS [47], According to these assumptions, one shouldnaively expect a small Sivers effect asymmetry for the π + , which has roughly equivalent and canceling contri-butions from u and d quarks. Instead a large asymmetryis observed for the π + .Collinear higher twist calculations predict that A N de-creases with increasing transverse momentum once p T is of the same order as the partonic momentum scale Q and both are much larger than Λ QCD [31]. Wherethis turnover of the initially rising A N happens is largelyunknown, though. The cluster asymmetries in Fig. 9have an extended p T -range compared to previous mea-surements of π mesons [11], but the data still do not allow for a conclusive answer for the onset of this drop ofthe asymmetry up to p T > c .The electromagnetic cluster contributions at √ s =200 GeV are dominated by π decays, as demonstratedin Fig. 7. With rising p T , the fraction of direct and otherphotons increases while the contribution from η mesonsdoes not change significantly. A comparison of the clusterasymmetries with those of π mesons from STAR [11] inFig. 10 is largely consistent at small x F and statisticallylimited at x F > .
47, where the direct photon contribu-tion to the inclusive clusters becomes more important.Transverse asymmetries of direct photons are of specialinterest in the future because they directly relate to theSivers effect and its process dependence [48].The data presented in this paper provide crucial in-put to the long-standing question of the source of A N inhadronic collisions. The extended statistics of A N mea-surements for π and η at midrapidity, the cluster A N at 200 GeV, the complete isospin triplet of asymmetriesat 62.4 GeV, and the extended range over beam colli-sion energies, all quantitatively test the various theoriesseeking to explain these asymmetries. In particular, thehigh statistics midrapidity data strongly constrain thepresence of a gluon Sivers effect at midrapidity. ThePHENIX data on π transverse asymmetries, along withthe world data, do not allow for a strong evolution with Q in the combined effects from whatever causes theseasymmetries. Finally, the mix of favored versus unfa-vored fragmentation for the three different pion states,and how these contribute to the asymmetries, also placeconstraints on the strengths of the contributing effects. ACKNOWLEDGMENTS
We thank the staff of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the staff of the other PHENIX participatinginstitutions for their vital contributions. We acknowl-edge support from the Office of Nuclear Physics in theOffice of Science of the Department of Energy, the Na-tional Science Foundation, a sponsored research grantfrom Renaissance Technologies LLC, Abilene ChristianUniversity Research Council, Head of Department ofPhysics, University of Illinois at Urbana Champaign, Re-search Foundation of SUNY, and Dean of the College ofArts and Sciences, Vanderbilt University (U.S.A), Min-istry of Education, Culture, Sports, Science, and Tech-nology, the Japan Society for the Promotion of Science,and Head Investigator, Graduate School of Science, Hi-roshima University (Japan), Conselho Nacional de De-senvolvimento Cient´ıfico e Tecnol´ogico and Funda¸c˜ao deAmparo `a Pesquisa do Estado de S˜ao Paulo (Brazil), Nat-ural Science Foundation of China (P. R. China), Min-istry of Education, Youth and Sports (Czech Repub-lic), Centre National de la Recherche Scientifique, Com-missariat `a l’´Energie Atomique, and Institut Nationalde Physique Nucl´eaire et de Physique des Particules2(France), Bundesministerium f¨ur Bildung und Forschung,Deutscher Akademischer Austausch Dienst, and Alexan-der von Humboldt Stiftung (Germany), Hungarian Na-tional Science Fund, OTKA (Hungary), Department ofAtomic Energy and Department of Science and Technol-ogy (India), Israel Science Foundation (Israel), NationalResearch Foundation and WCU program of the Min-istry Education Science and Technology (Korea), PhysicsDepartment, Lahore University of Management Sciences(Pakistan), Ministry of Education and Science, RussianAcademy of Sciences, Federal Agency of Atomic En-ergy, and Program Coordinator, Russian Research Cen-ter, Kurchatov Institute (Russia), VR and WallenbergFoundation (Sweden), the U.S. Civilian Research andDevelopment Foundation for the Independent States ofthe Former Soviet Union, the US-Hungarian FulbrightFoundation for Educational Exchange, and the US-IsraelBinational Science Foundation.
APPENDIX
Data tables of measured A N with statistical and sys-tematic uncertainties and cluster composition for clusterasymmetries at forward pseudorapidities. TABLE II: Fractional composition of electromagnetic clustersin the MPC at √ s = 200 GeV for x F > .
4, as shown in Fig. 7. h x F i h p T i π η direct γ h + , − other γ TABLE III: The A N at √ s = 62 . x F for two pseudorapidity ranges, as shown in Fig. 3. h| x F |i h p T i A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < . < | η | < . − . ± . ± . − . ± . ± . . < | η | < . . ± . ± . . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . A N as a function of p T at √ s = 62 . h p T i h| x F |i A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < . < η < . . ± . ± . − . ± . ± . . < η < . . ± . ± . − . ± . ± . . < η < . . ± . ± . − . ± . ± . . < η < . . ± . ± . − . ± . ± . A N at √ s = 62 . x F , as shown in Figs. 5 and 6. h| x F |i h p T i A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . . < | η | < . . ± . ± . − . ± . ± . A N at √ s = 200 GeV as function of p T at forward/backward rapidities in two different pseudorapidity ranges,as shown in Fig. 8. h| x F |i h p T i (GeV/ c ) A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± TABLE VII: The A N at √ s = 200 GeV in forward/backward rapidities ( | x F | > . h| x F |i p T (GeV/ c ) A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± . < | η | < . ± ± ± ± A N as function of p T and x F at forward/backward rapidities, as shown in Fig. 10. h| x F |i h p T i (GeV/ c ) A N ± σ stat ± σ syst ( x F > A N ± σ stat ± σ syst ( x F < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE IX: The A N of π mesons at √ s = 200 GeV at midrapidity as function of p T , as shown in Fig. 11. The data in slightlyforward and backward kinematics (0 . < | η | < .
35) are subsets of the full data set ( | η | < . h p T i (GeV/ c ) A N ± σ stat ± σ syst A N ± σ stat ± σ syst A N ± σ stat ± σ syst ( | η | < .
35) (0 . < | η | < . , x F >
0) (0 . < | η | < . , x F < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A N of η mesons at √ s = 200 GeV at midrapidity as function of p T , as shown in Fig. 11. The data in slightlyforward and backward kinematics (0 . < | η | < .
35) are subsets of the full data set ( | η | < . h p T i (GeV/ c ) A N ± σ stat ± σ syst A N ± σ stat ± σ syst A N ± σ stat ± σ syst ( | η | < .
35) (0 . < | η | < . , x F >
0) (0 . < | η | < . , x F < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± [1] H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky,et al., Phys. Rev. D , 074024 (2010).[2] J. C. Ralston and D. E. Soper, Nucl. Phys. B , 109(1979).[3] D. de Florian, R. Sassot, M. Stratmann, and W. Vogel-sang, Phys. Rev. D , 034030 (2009).[4] G. L. Kane, J. Pumplin, and W. Repko, Phys. Rev. Lett. , 1689 (1978).[5] R. D. Klem, J. E. Bowers, H. W. Courant, H. Kagan,M. L. Marshak, et al., Phys. Rev. Lett. , 929 (1976).[6] J. Antille, L. Dick, L. Madansky, D. Perret-Gallix,M. Werlen, A. Donidec, K. Kuroda, and P. Kyberd, Phys.Lett. B , 523 (1980).[7] D. L. Adams et al. (FNAL-E581 and E704 Collabora-tions), Phys. Lett. B , 201 (1991).[8] D. L. Adams et al. (FNAL-E704 Collaboration), Phys.Lett. B , 462 (1991).[9] C. E. Allgower et al. (E925 Collaboration), Phys. Rev. D , 092008 (2002).[10] I. Arsene et al. (BRAHMS Collaboration), Phys. Rev.Lett. , 042001 (2008).[11] B. I. Abelev et al. (STAR Collaboration), Phys. Rev.Lett. , 222001 (2008).[12] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. D , 032006 (2012).[13] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. D , 051101 (2012).[14] D. W. Sivers, Phys. Rev. D , 83 (1990).[15] C. Adolph et al., Phys. Lett. B , 383 (2012).[16] A. Airapetian et al. (HERMES Collaboration), Phys.Rev. Lett. , 152002 (2009).[17] S. S. Adler et al. (PHENIX Collaboration), Phys. Rev.Lett. , 202001 (2005).[18] M. Anselmino, U. D’Alesio, S. Melis, and F. Murgia,Phys. Rev. D , 094011 (2006).[19] J. C. Collins, Phys. Lett. B , 43 (2002).[20] Z.-B. Kang, J.-W. Qiu, W. Vogelsang, and F. Yuan,Phys. Rev. D , 094001 (2011).[21] J. C. Collins, Nucl. Phys. B , 161 (1993).[22] K. Abe et al. (Belle Collaboration), Phys. Rev. Lett. ,232002 (2006).[23] R. Seidl et al. (Belle Collaboration), Phys. Rev. D ,032011 (2008).[24] A. Airapetian et al. (HERMES Collaboration), Phys.Lett. B , 11 (2010). [25] C. Adolph et al., Phys. Lett. B , 376 (2012).[26] M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian,F. Murgia, et al., Phys. Rev. D , 054032 (2007).[27] S. Aoki, M. Doui, T. Hatsuda, and Y. Kuramashi, Phys.Rev. D , 433 (1997).[28] M. Wakamatsu, Phys. Rev. D , 014033 (2009).[29] A. V. Efremov and O. V. Teryaev, Phys. Lett. B ,383 (1985).[30] J.-W. Qiu and G. F. Sterman, Phys. Rev. Lett. , 2264(1991).[31] X. Ji, J.-W. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev.Lett. , 082002 (2006).[32] L. Aphecetche et al. (PHENIX Collaboration), Nucl. In-strum. Methods A , 521 (2003).[33] K. Adcox et al. (PHENIX Collaboration), Nucl. Instrum.Methods A , 489 (2003).[34] M. Allen et al. (PHENIX Collaboration), Nucl. Instrum.Methods A , 549 (2003).[35] R. Brun et al., CERN-DD/EE pp. 84–1 (1987).[36] I. Alekseev et al., Nucl. Instrum. Methods A , 392(2003).[37] I. G. Alekseev et al., Phys. Rev. D , 094014 (2009).[38] I. Nakagawa et al., AIP Conf. Proc. , 380 (2008).[39] A. Adare et al. (PHENIX Collaboration), Phys. Rev. D , 112008 (2010).[40] T. Sjostrand, S. Mrenna, and P. Skands, j. High EnergyPhys. (2006) 026.[41] P. Z. Skands, Phys. Rev. D , 074018 (2010).[42] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett , 152302 (2006).[43] I. Arsene et al. (BRAHMS Collaboration), Phys. Rev.Lett. , 252001 (2007).[44] S. S. Adler et al. (PHENIX Collaboration), Phys. Rev.Lett. , 012002 (2007).[45] A. Adare et al. (PHENIX Collaboration), Phys. Rev. D , 051106 (2007).[46] D. L. Adams et al. (FNAL-E704 Collaboration), Phys.Lett. B , 531 (1992).[47] M. Anselmino, M. Boglione, U. D. Alesio, A. Kotzinian,S. Melis, F. Murgia, A. Prokudin, and C. Turk, Eur.Phys. J. A , 89 (2009).[48] L. Gamberg, Z.-B. Kang, and A. Prokudin, Phys. Rev.Lett.110