Comparison of transverse single-spin asymmetries for forward π0 production inpolarized pp, pAl and pAu collisions at nucleon pair c.m. energy

√sNN = 200 GeV

J. Adam6, L. Adamczyk2, J. R. Adams39, J. K. Adkins30, G. Agakishiev28, M. M. Aggarwal41, Z. Ahammed61,

I. Alekseev3,35, D. M. Anderson55, A. Aparin28, E. C. Aschenauer6, M. U. Ashraf11, F. G. Atetalla29, A. Attri41,

G. S. Averichev28, V. Bairathi53, K. Barish10, A. Behera52, R. Bellwied20, A. Bhasin27, J. Bielcik14, J. Bielcikova38,

L. C. Bland6, I. G. Bordyuzhin3, J. D. Brandenburg6, A. V. Brandin35, J. Butterworth45, H. Caines64,

M. Calderon de la Barca Sanchez8, D. Cebra8, I. Chakaberia29,6, P. Chaloupka14, B. K. Chan9, F-H. Chang37,

Z. Chang6, N. Chankova-Bunzarova28, A. Chatterjee11, D. Chen10, J. Chen49, J. H. Chen18, X. Chen48,

Z. Chen49, J. Cheng57, M. Cherney13, M. Chevalier10, S. Choudhury18, W. Christie6, X. Chu6, H. J. Crawford7,

M. Csanad16, M. Daugherity1, T. G. Dedovich28, I. M. Deppner19, A. A. Derevschikov43, L. Didenko6, C. Dilks42,

X. Dong31, J. L. Drachenberg1, J. C. Dunlop6, T. Edmonds44, N. Elsey63, J. Engelage7, G. Eppley45, S. Esumi58,

O. Evdokimov12, A. Ewigleben32, O. Eyser6, R. Fatemi30, S. Fazio6, P. Federic38, J. Fedorisin28, C. J. Feng37,

Y. Feng44, P. Filip28, E. Finch51, Y. Fisyak6, A. Francisco64, L. Fulek2, C. A. Gagliardi55, T. Galatyuk15,

F. Geurts45, A. Gibson60, K. Gopal23, X. Gou49, D. Grosnick60, W. Guryn6, A. I. Hamad29, A. Hamed5,

S. Harabasz15, J. W. Harris64, S. He11, W. He18, X. H. He26, Y. He49, S. Heppelmann8, S. Heppelmann42,

N. Herrmann19, E. Hoffman20, L. Holub14, Y. Hong31, S. Horvat64, Y. Hu18, H. Z. Huang9, S. L. Huang52,

T. Huang37, X. Huang57, T. J. Humanic39, P. Huo52, G. Igo9, D. Isenhower1, W. W. Jacobs25, C. Jena23,

A. Jentsch6, Y. Ji48, J. Jia6,52, K. Jiang48, S. Jowzaee63, X. Ju48, E. G. Judd7, S. Kabana53, M. L. Kabir10,

S. Kagamaster32, D. Kalinkin25, K. Kang57, D. Kapukchyan10, K. Kauder6, H. W. Ke6, D. Keane29,

A. Kechechyan28, M. Kelsey31, Y. V. Khyzhniak35, D. P. Kiko la 62, C. Kim10, B. Kimelman8, D. Kincses16,

T. A. Kinghorn8, I. Kisel17, A. Kiselev6, M. Kocan14, L. Kochenda35, D. D. Koetke60, L. K. Kosarzewski14,

L. Kramarik14, P. Kravtsov35, K. Krueger4, N. Kulathunga Mudiyanselage20, L. Kumar41, S. Kumar26,

R. Kunnawalkam Elayavalli63, J. H. Kwasizur25, R. Lacey52, S. Lan11, J. M. Landgraf6, J. Lauret6, A. Lebedev6,

R. Lednicky28, J. H. Lee6, Y. H. Leung31, C. Li49, C. Li48, W. Li45, W. Li50, X. Li48, Y. Li57, Y. Liang29,

R. Licenik38, T. Lin55, Y. Lin11, M. A. Lisa39, F. Liu11, H. Liu25, P. Liu52, P. Liu50, T. Liu64, X. Liu39, Y. Liu55,

Z. Liu48, T. Ljubicic6, W. J. Llope63, R. S. Longacre6, N. S. Lukow54, S. Luo12, X. Luo11, G. L. Ma50, L. Ma18,

R. Ma6, Y. G. Ma50, N. Magdy12, R. Majka64, D. Mallick36, S. Margetis29, C. Markert56, H. S. Matis31,

J. A. Mazer46, N. G. Minaev43, S. Mioduszewski55, B. Mohanty36, M. M. Mondal65, I. Mooney63,

Z. Moravcova14, D. A. Morozov43, M. Nagy16, J. D. Nam54, Md. Nasim22, K. Nayak11, D. Neff9, J. M. Nelson7,

D. B. Nemes64, M. Nie49, G. Nigmatkulov35, T. Niida58, L. V. Nogach43, T. Nonaka58, A. S. Nunes6,

G. Odyniec31, A. Ogawa6, S. Oh31, V. A. Okorokov35, B. S. Page6, R. Pak6, A. Pandav36, Y. Panebratsev28,

B. Pawlik40, D. Pawlowska62, H. Pei11, C. Perkins7, L. Pinsky20, R. L. Pinter16, J. Pluta62, J. Porter31,

M. Posik54, N. K. Pruthi41, M. Przybycien2, J. Putschke63, H. Qiu26, A. Quintero54, S. K. Radhakrishnan29,

S. Ramachandran30, R. L. Ray56, R. Reed32, H. G. Ritter31, O. V. Rogachevskiy28, J. L. Romero8, L. Ruan6,

J. Rusnak38, N. R. Sahoo49, H. Sako58, S. Salur46, J. Sandweiss64, S. Sato58, W. B. Schmidke6, N. Schmitz33,

B. R. Schweid52, F. Seck15, J. Seger13, M. Sergeeva9, R. Seto10, P. Seyboth33, N. Shah24, E. Shahaliev28,

P. V. Shanmuganathan6, M. Shao48, A. I. Sheikh29, W. Q. Shen50, S. S. Shi11, Y. Shi49, Q. Y. Shou50,

E. P. Sichtermann31, R. Sikora2, M. Simko38, J. Singh41, S. Singha26, N. Smirnov64, W. Solyst25, P. Sorensen6,

H. M. Spinka4, B. Srivastava44, T. D. S. Stanislaus60, M. Stefaniak62, D. J. Stewart64, M. Strikhanov35,

B. Stringfellow44, A. A. P. Suaide47, M. Sumbera38, B. Summa42, X. M. Sun11, X. Sun12, Y. Sun48, Y. Sun21,

B. Surrow54, D. N. Svirida3, P. Szymanski62, A. H. Tang6, Z. Tang48, A. Taranenko35, T. Tarnowsky34,

J. H. Thomas31, A. R. Timmins20, D. Tlusty13, M. Tokarev28, C. A. Tomkiel32, S. Trentalange9, R. E. Tribble55,

P. Tribedy6, S. K. Tripathy16, O. D. Tsai9, Z. Tu6, T. Ullrich6, D. G. Underwood4, I. Upsal49,6, G. Van Buren6,

J. Vanek38, A. N. Vasiliev43, I. Vassiliev17, F. Videbæk6, S. Vokal28, S. A. Voloshin63, F. Wang44,

G. Wang9, J. S. Wang21, P. Wang48, Y. Wang11, Y. Wang57, Z. Wang49, J. C. Webb6, P. C. Weidenkaff19,

L. Wen9, G. D. Westfall34, H. Wieman31, S. W. Wissink25, R. Witt59, Y. Wu10, Z. G. Xiao57, G. Xie31,

W. Xie44, H. Xu21, N. Xu31, Q. H. Xu49, Y. F. Xu50, Y. Xu49, Z. Xu6, Z. Xu9, C. Yang49, Q. Yang49,

S. Yang6, Y. Yang37, Z. Yang11, Z. Ye45, Z. Ye12, L. Yi49, K. Yip6, Y. Yu49, H. Zbroszczyk62, W. Zha48,

C. Zhang52, D. Zhang11, S. Zhang48, S. Zhang50, X. P. Zhang57, Y. Zhang48, Y. Zhang11, Z. J. Zhang37,

Z. Zhang6, Z. Zhang12, J. Zhao44, C. Zhong50, C. Zhou50, X. Zhu57, Z. Zhu49, M. Zurek31, M. Zyzak17

1Abilene Christian University, Abilene, Texas 796992AGH University of Science and Technology, FPACS, Cracow 30-059, Poland

3Alikhanov Institute for Theoretical and Experimental Physics NRC ”Kurchatov Institute”, Moscow 117218, Russia

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4Argonne National Laboratory, Argonne, Illinois 604395American University of Cairo, New Cairo 11835, New Cairo, Egypt

6Brookhaven National Laboratory, Upton, New York 119737University of California, Berkeley, California 947208University of California, Davis, California 95616

9University of California, Los Angeles, California 9009510University of California, Riverside, California 92521

11Central China Normal University, Wuhan, Hubei 43007912University of Illinois at Chicago, Chicago, Illinois 60607

13Creighton University, Omaha, Nebraska 6817814Czech Technical University in Prague, FNSPE, Prague 115 19, Czech Republic

15Technische Universitat Darmstadt, Darmstadt 64289, Germany16ELTE Eotvos Lorand University, Budapest, Hungary H-1117

17Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany18Fudan University, Shanghai, 200433

19University of Heidelberg, Heidelberg 69120, Germany20University of Houston, Houston, Texas 7720421Huzhou University, Huzhou, Zhejiang 313000

22Indian Institute of Science Education and Research (IISER), Berhampur 760010 , India23Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India

24Indian Institute Technology, Patna, Bihar 801106, India25Indiana University, Bloomington, Indiana 47408

26Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 73000027University of Jammu, Jammu 180001, India

28Joint Institute for Nuclear Research, Dubna 141 980, Russia29Kent State University, Kent, Ohio 44242

30University of Kentucky, Lexington, Kentucky 40506-005531Lawrence Berkeley National Laboratory, Berkeley, California 94720

32Lehigh University, Bethlehem, Pennsylvania 1801533Max-Planck-Institut fur Physik, Munich 80805, Germany34Michigan State University, East Lansing, Michigan 48824

35National Research Nuclear University MEPhI, Moscow 115409, Russia36National Institute of Science Education and Research, HBNI, Jatni 752050, India

37National Cheng Kung University, Tainan 7010138Nuclear Physics Institute of the CAS, Rez 250 68, Czech Republic

39Ohio State University, Columbus, Ohio 4321040Institute of Nuclear Physics PAN, Cracow 31-342, Poland

41Panjab University, Chandigarh 160014, India42Pennsylvania State University, University Park, Pennsylvania 16802

43NRC ”Kurchatov Institute”, Institute of High Energy Physics, Protvino 142281, Russia44Purdue University, West Lafayette, Indiana 47907

45Rice University, Houston, Texas 7725146Rutgers University, Piscataway, New Jersey 08854

47Universidade de Sao Paulo, Sao Paulo, Brazil 05314-97048University of Science and Technology of China, Hefei, Anhui 230026

49Shandong University, Qingdao, Shandong 26623750Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800

51Southern Connecticut State University, New Haven, Connecticut 0651552State University of New York, Stony Brook, New York 11794

53Instituto de Alta Investigacion, Universidad de Tarapaca, Arica 1000000, Chile54Temple University, Philadelphia, Pennsylvania 1912255Texas A&M University, College Station, Texas 77843

56University of Texas, Austin, Texas 7871257Tsinghua University, Beijing 100084

58University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan59United States Naval Academy, Annapolis, Maryland 21402

60Valparaiso University, Valparaiso, Indiana 4638361Variable Energy Cyclotron Centre, Kolkata 700064, India62Warsaw University of Technology, Warsaw 00-661, Poland

63Wayne State University, Detroit, Michigan 4820164Yale University, New Haven, Connecticut 06520 and

65Institute of Physics, Bhubaneswar 751005, India

(STAR Collaboration)

3

The STAR Collaboration reports a measurement of the transverse single-spin asymmetries, AN ,for neutral pions produced in polarized proton collisions with protons (pp), with aluminum nuclei(pAl) and with gold nuclei (pAu) at a nucleon-nucleon center-of-mass energy of 200 GeV. Neutralpions are observed in the forward direction relative to the transversely polarized proton beam, inthe pseudo-rapidity region 2.7 < η < 3.8. Results are presented for π0s observed in the STARFMS electromagnetic calorimeter in narrow Feynman x (xF ) and transverse momentum (pT ) bins,spanning the range 0.17 < xF < 0.81 and 1.7 < pT < 6.0 GeV/c. For fixed xF < 0.47, theasymmetries are found to rise with increasing transverse momentum. For larger xF , the asymmetryflattens or falls as pT increases. Parametrizing the ratio r(A) ≡ AN (pA)/AN (pp) = AP over thekinematic range, the ratio r(A) is found to depend only weakly on A, with 〈P 〉 = −0.027 ± 0.005.No significant difference in P is observed between the low-pT region, pT < 2.5 GeV/c, where gluonsaturation effects may play a role, and the high-pT region, pT > 2.5 GeV/c. It is further observedthat the value of AN is significantly larger for events with a large-pT isolated π0 than for eventswith a non-isolated π0 accompanied by additional jet-like fragments. The nuclear dependence r(A)is similar for isolated and non-isolated π0 events.

I. INTRODUCTION

The measurements and the evolving interpretationsof transverse single-spin asymmetries for forward pionproduction in high energy pp collisions have a rich his-tory [1–7]. These measurements guided the develop-ment of Quantum Chromo-Dynamics (QCD) based mod-els that incorporated quark helicity conservation, QCDfactorization, the nature of initial state parton motionor angular momentum, and the dynamics of fragmenta-tion within the scattering processes for polarized protons.The new transverse asymmetry measurements, presentedhere, again challenge aspects of current models for theapplication of QCD to the spin dependence of cross sec-tions. The π0 single-spin asymmetry, AN , is measured asa function of pion kinematics for collisions between po-larized protons and protons (pp), aluminum nuclei (pAl)and gold nuclei (pAu). Because AN for this process isexpected to be very sensitive to the QCD fields in thevicinity of a struck quark, the nuclear dependence of ANshould be sensitive to phenomena that modify the localfields, for example, gluon saturation effects.

This analysis presents the dependence of AN in the for-ward π0 production process, p↑+ p(or A)→ π0 + X. It isuseful to first define a simple azimuthal angle-dependentasymmetry, aN (xF , pT , φ), as the ratio of the differencein cross section for the two proton transverse spin states,σ↑ and σ↓, to the sum of those cross sections for a pionproduced at xF (Feynman X) and pT (transverse mo-mentum),

aN (xF , pT , φ) =σ↑(xF , pT , φ)− σ↓(xF , pT , φ)

σ↑(xF , pT , φ) + σ↓(xF , pT , φ)(1)

= AN (xF , pT ) cosφ. (2)

The three components of pion momentum are specifiedwith coordinates xF , pT and φ. The dependence ofthe pion differential cross section on transverse spin, ex-pressed as the pion momentum dependent asymmetryaN (xF , pT , φ) and the transverse single-spin asymmetry,AN (xF , pT ), are defined in terms of the simple asym-metry accordingly, (Eq. 2). Referring to a right-handedcoordinate system, an initial state polarized proton is re-

ferred to as spin “up” if it has a positive spin projectionalong the y axis while proton momentum is along the zaxis. This polarized proton collides with an unpolarizedproton or nucleus traveling along the −z axis. A forwardpion has a positive longitudinal component of momen-

tum pπL, given by a positive fraction xF = 2pπL√s

of the

polarized proton momentum. The angle φ is the pionazimuthal angle about the z axis measured from the xaxis positive direction. Equation 2 defines AN (xF , pT )in terms of cross sections, which are differential in xF ,pT and φ, with superscript arrows indicating the spindirections up or down, respectively. Symmetry requiresthat the φ dependence be proportional to cosφ.

II. THE RELATION BETWEEN SCATTERINGWITH LONGITUDINAL AND TRANSVERSE

POLARIZATION

The unique features of the spin dependence of scatter-ing from quarks or gluons in transversely polarized pro-tons are best understood when contrasted with scatteringof partons in longitudinally (helicity) polarized protons.For a longitudinally polarized Dirac fermion, the depen-dence of cross section on the initial state spin is connectedto helicity conservation. For a relativistic electron orquark, the absorption or emission of a virtual photon (orsimilarly a gluon) cannot flip the helicity of a relativisticfermion. However, in a one dimensional scattering ex-ample, where a virtual photon is in a particular helicitystate, and is absorbed by a free quark at rest, the longitu-dinal spin component of the quark must flip as one unitof photon spin is absorbed by the quark, changing thestruck quark spin by one unit. Such a photon can be ab-sorbed by only one of the two possible initial quark spinstates, so cross sections thus can depend on initial statequark spin component along the final state direction or onthe final state helicity. But with absorption from a trans-versely polarized quark, where transverse spin states arecomposed of equal magnitude combinations of the twohelicity states, the cross section is the same for eithertransverse spin state. For scattering between small masselectrons and quarks, this generalizes to a cross section,

4

that depends on Dirac fermion helicities but not on theirtransverse spins. Any cross section dependence on trans-verse spin is associated with the negligibly small helicityflip amplitudes.

In the original quark model, where the spin of a polar-ized proton was attributed to the polarized quarks, it wasclear that the longitudinal polarization of these quarkscould be observed by the double helicity measurements inscattering between protons and electrons. Because deepinelastic scattering cross sections were most sensitive tothe up quarks, due to their larger electric charge, it wasa very early prediction of the quark model that the lon-gitudinal polarization of up quarks within the polarizedproton could be observed by measuring the dependenceof the lepton-proton cross section on the proton and lep-ton longitudinal spins [8].

The longitudinal double spin lepton-proton scatteringmeasurements provided the mechanism for the first mea-surements of quark momentum dependent longitudinallypolarized quark distributions in a longitudinally polar-ized proton [9, 10]. Similar longitudinal double spinproton-proton cross sections depended upon the longitu-dinal polarization of partons, including gluons. Measure-ments and analysis of longitudinally polarized protonsremain an important topic for the STAR experiment, toconstrain longitudinal polarization densities of partons inthe proton. Global analyses of many experiments [11–13]have integrated the experimental results.

In a frame where the proton was highly relativistic,where each quark momentum was nearly parallel to theproton momentum, the cross section did depend directlyon the helicity of the struck quark. The cross sectionassociated with a longitudinally polarized, nearly free,quark was calculable from hard scattering in helicity con-serving perturbative processes. The longitudinal doublespin asymmetry was then sensitive to the longitudinallypolarized struck quark in the longitudinally polarizedproton. However, the scattering cross section for sucha quark did not depend on the components of its spinmeasured along a transverse axis. Such a dependencewould have been associated with the parton flipping he-licity as it interacted, by absorbing or emitting a photonor gluon. Because the quark helicity-flip amplitude wasvanishingly small at high energies, early predictions, thatthe transverse spin dependence of the quark scatteringprocess should vanish at high energy, implied that ANshould be small for high energy collisions [14]. Trans-verse spin dependence of cross sections are known to befurther suppressed because such dependencies requiredan interference between helicity amplitudes with differ-ent phases. Such a phase-shifted amplitude is not presentin the hard scattering part of leading twist perturbativeQCD (pQCD) processes.

From the above discussion, it is clear that the helicityconserving hard parton amplitudes, which are apparentlydominant in the unpolarized cross sections, imply calcu-lable sensitivity of the parton cross sections to partonhelicity. This leads to longitudinal asymmetries, reflect-

ing the polarization of partons in the proton. In contrast,the corresponding hard isolated amplitudes are insensi-tive to the transverse spin of the partons. The largetransverse spin asymmetries, AN , in pp collisions revealphysics beyond that of hard isolated parton scattering.

III. MECHANISMS FOR NON-ZEROTRANSVERSE ASYMMETRY

The measurement of transverse spin asymmetries issensitive to effects that are very different than the physicsresponsible for longitudinal asymmetries. The traditionalpQCD calculations for hard scattering from protons re-lied on collinear factorization [15], where all parton mo-menta were characterized as propagating parallel to theparent proton momentum. Within this framework, thetransverse spin dependence was limited by the suppres-sion of hard scattering helicity-flip amplitudes. But morenuanced pictures of scattering of quarks in a transverselypolarized proton have emerged, utilizing parton densitydistributions that characterize both transverse and lon-gitudinal components of parton momentum. With sucha parton density distribution, the initial state partonmotion need not be parallel to the proton momentum,meaning that a helicity frame for the proton may notcompletely align with the helicity frame of the quark.

A transverse momentum offset of ~kT , representing theaverage transverse momentum of the initial/final statequark relative to the initial/final state parent hadron,

respectively, is added to the transverse momentum ~PTfrom the hard scattering process to form the observed

pion transverse momentum, pπT = |~PT + ~kT |. So whilethe quark scattering cross section has little direct depen-dence on the transverse spin of the quark, the pion pro-duction cross section can depend on the transverse spinof the proton through initial and final state interactions

leading to non-zero ~kT . If this bias of ~kT is correlatedwith the transverse spin of the proton, then non-zero ANwill result. This kind of proton spin dependence of theobserved pion cross section is amplified by the extremepT dependence of the hard pion cross section.

The general expectation that the pion AN should fallwith increasing pT for pT above a nominal QCD momen-tum scale can be demonstrated in a simple model. If oneassumes that the forward hard scattering cross section ofa quark, with momentum fraction x, falls with increas-ing transverse momentum, pT , by a power law form withpower N , then

dσ

dpT∝ p−NT , (3)

where pT = |~PT |. If the scattered quark acquires trans-

verse momentum ~kT = ±kT x from initial or final stateinteractions that is correlated with the polarized protonspin in the ±y directions, then we see that AN will alsofall with increasing pT . Assuming the hard scattering

5

transverse momentum is much greater than the initialstate or final state transverse momentum (pT � kT ),then the difference in cross section when pπT is measuredalong the ±x direction leads to AN as in Eq. 4. If we as-sume a cross section form for pT , as in Eq. 3, expressingAN as a left-right asymmetry, we have

AN (xF , pT ) =σ↑(xF , pT , 0)− σ↑(xF , pT , π)

σ↑(xF , pT , 0) + σ↑(xF , pT , π)

' (pπT − kT )−N − (pπT + kT )−N

(pπT − kT )−N + (pπT + kT )−N

' N kTpπT

(4)

for small kT /pπT . This demonstrates that if the kT shift is

independent of the hard scattering pT , it is very naturalto expect the magnitude of the asymmetry to fall withincreasing observed transverse momentum pT at large pT .In previous measurements [5] of the pT dependence forAN with charged pions, the asymmetry has been seen toincrease with pT up to about pT < 1 GeV/c. In an earlierSTAR measurement [7], it was observed that there waslittle evidence for AN falling with pT up to at least 3GeV/c. In this paper, the data are analyzed to separatethe independent effects of pT and xF .

Two classes of models have been introduced for for-ward AN , both involved the hard scattering of a leadingmomentum quark in the polarized proton and both de-pended upon secondary interactions to generate a spin

dependent contribution ~kT to the pion final state trans-verse momentum. The Sivers effect [16] involved aninitial state interaction before the hard scattering of aquark in a polarized proton, leading to initial state par-ton transverse momentum that depended on the protontransverse polarization. The Collins effect [17] generateda transverse spin dependent component to the final statepion transverse momentum from the fragmentation pro-cess of the scattered quark, which retained its initial statetransverse polarization through the hard scattering pro-cess. Closely related to Collins and Sivers models was anapproach involving higher twist calculation, where thescattered quark was correlated with a soft gluon, whichalso lead to a significant transverse asymmetry [18].

Many model calculations attempt to describe forwardpion transverse spin asymmetries using one of these ap-proaches. While for both types of models the basicmechanism involves the production of a final state pionfrom fragmentation of a hard scattered parton, only theCollins approach explains large AN arising from the frag-mentation process. In contrast to pion production, jetproduction does not involve fragmentation. The Collinseffect therefore does not contribute to that asymmetry.Jet AN measurements in this kinematic region have beenpublished and the values of AN were observed to besmaller than measured pion asymmetries [19].

Both the Sivers and the Collins approaches introduceda parton transverse momentum relative to the initial orfinal state hadron momentum to generate a transverse

asymmetry without violating helicity conservation. Inthe Sivers picture, transverse momentum of initial statequarks can be connected to the initial state orbital an-gular momentum of a struck quark along the polariza-tion axis. While an orbiting quark does not, on average,have transverse momentum, Sivers argued that absorp-tive effects could break the left-right symmetric partonkT distribution to generate the required non-vanishing

average kT =⟨~kT · x

⟩. Even though absorption does in-

troduce phase changes, the calculation of this phase inthe conventional perturbative calculation was not fullyappreciated until it was noted in [20] that the Wilsonline contribution, formally required in the pQCD calcu-lation, did provide exactly the needed phase change fora non-zero AN [21].

The emerging physical picture is that unlike the casefor longitudinal spin dependence, the observed large val-ues of AN derive not from the spin dependence of thehard scattering process between the pair of partons, butfrom the interaction between the scattered quark and theother constituents or fragments of the polarized proton.While from symmetry, AN must vanish at pT = 0, theexample of Eq. 4 demonstrates that the asymmetry isexpected to fall with transverse momentum above some

nominal scale, ~kT . In recent years, there have been manycalculations based on Collins, Sivers or twist-3 collinearmethods, with a goal to reproduce the basic nature of ANdependence on kinematics [22–26]. Within the Collins orSivers methods it was necessary to account for the longi-tudinal and transverse momentum distributions of par-ton momentum within hadrons while traditional collinearparton densities or fragmentation functions involved onlylongitudinal distributions. In the twist-3 approach, onestarted with those traditional collinear parton densitiesor fragmentation functions and dynamically generatedthe transverse motion from interactions with other fieldsin the nucleon. A twist-3 calculation [24], involving fitsto many parameters, resulted in calculations that were inagreement with single inclusive deep inelastic scatteringasymmetries and with the xF dependence of π0 AN inpp collisions. This calculation also resulted in a nearlyflat, or very slowly falling, pT dependence above about3 GeV/c for the π0 AN in pp scattering. While not ris-ing with pT , as do the new AN pp data presented in thispaper, the nearly flat pT dependence from the twist-3 cal-culation is interesting. It shows that the intuitive pictureof AN falling with PT , based on the simple arguments ofEq. 4, can involve a surprisingly large kT scale, well abovethe nominal QCD scale.

IV. MEASUREMENTS OF AN INPROTON-NUCLEUS COLLISIONS

If the observed transverse single-spin dependent ampli-tude for forward pion production arises completely fromthe localized quark-gluon hard scattering process, then

6

the environment that provides the soft gluon in the sec-ond proton or nucleus would not likely impact AN . Butwe know that the important source of AN is not thehard quark-gluon scattering process itself but primarilyinvolves the additional interactions with other fields inthe nucleon or nucleus, perhaps manifested by the gen-eration of parton transverse momentum relative to theparent hadron momentum. Because the mechanism re-sponsible for transverse spin asymmetries is not a simplelocal leading twist interaction but depends on the envi-ronment in which a parton interaction occurs, it is clearthat AN could be different for pp, pAl and pAu collisions.Even the simple model of Eq. 4 reminds us that a changein the shape of the pT dependence for pion productiondue to either nuclear absorption, rescattering, or modifi-cation of the gluon distribution, could lead to dependenceof AN on nuclear size.

The measurement of how AN changes when the beamremnant partons of the proton are replaced with specta-tor partons of a nucleus is a subject of this paper. It isclear that the phase from the Wilson line integral, a lineintegral of the gauge vector potential color field alongthe struck quark trajectory, can give rise to color forcesbetween the struck quark and the rest of the polarizedproton. If there are also important color forces betweenthe hard scattering constituents and the residual specta-tor nucleus, then nuclear dependence of AN in pA scat-tering could result. Studies of the spin dependence ofthe interaction between the interacting quark and theresidual spectator nucleus have predicted large nuclearA-dependent transverse spin effects but at a lower trans-verse momentum scale than that of this analysis [27].A more recent calculation was based on lensing forces,with specific reference to the kinematics of this experi-ment [28]. The model addressed the dependence of ANon nuclear saturation as well as the pT dependence ofAN .

One mechanism that could provide nuclear A depen-dence of AN relates to the increase in gluon density inthe soft gluon distribution probed in forward scatter-ing. It is predicted that at low gluon x, when the gluondensity becomes large, saturation effects begin to playan important role. For interactions between soft gluonsand hard partons producing scattered pions in the range1.5 < pT < 2.5 GeV/c, saturation effects might modifythe interaction, creating significant differences betweenthe corresponding scattering process in pp and pA col-lisions. Specific saturation models, such as the ColorGlass Condensate [29], predict interactions of the scat-tered quark with a condensate of gluons rather than ahard scatter from a single gluon. Such saturation cal-culations predict a change in the pT distribution of thecross section in regions of pT near the saturation scale,with a suppression of the cross section that increases withnuclear size. In the pT ≈ 2 GeV/c range and at moreforward pseudo-rapidity than this measurement (η ≈ 4),STAR has reported that the nuclear modification ratioRdAu in dAu scattering to produce π0 mesons [30] is sig-

nificantly less than unity, suggesting a difference in thescattering process as the size of the nucleus is varied.In the same pT and rapidity range presented here, mea-surements of the nuclear modification factors for chargedhadrons (mostly charged pions) [31] showed suppressionin RdAu. This paper addresses the nuclear dependence ofAN , noting, in particular, the lower end of the pT rangewhere evidence for saturation effects has already beenseen in the corresponding dA cross sections [30].

V. PHOTON AND π0 DETECTION IN THE FMS

These data from the Solenoidal Tracker At RHIC(STAR) experiment at the Relativistic Heavy Ion Col-lider (RHIC) were collected during the 2015 RHIC run,involving collisions between nucleons at center-of-massenergy

√sNN = 200 GeV per nucleon pair. The pho-

ton pair from the decay of the π0 was detected with theSTAR forward electromagnetic calorimeter, referred to asthe Forward Meson Spectrometer (FMS) [32]. To mea-sure AN for forward π0 production, the STAR detectorsused in this analysis were the FMS and the Beam-BeamCounters (BBC).

The two RHIC beams (yellow and blue beams) arebunched with up to 120 bunches in each ring. The smallangle scattering from the blue beam is associated withpositive rapidity. Only 111 bunches in each beam arefilled and a contiguous set of 9 bunches (the abort gap)are unfilled. Bunch spacing is 106 ns and the transversepolarization pattern is chosen for each fill according to apredefined pattern (either alternating the polarization di-rection from bunch to bunch or for pairs of bunches). Theblue beam polarization ranged between 50% and 60%.

The BBCs are located at a distance of ±3.75 meterseast and west of the nominal STAR interaction point,concentric with the beam line, and covering pseudo-rapidity range 3.3 < η < 5.2 [33, 34]. On both the eastand west sides of STAR, each BBC detector consists ofan inner and outer hexagonal plane of scintillators. Forheavy-ion collisions, the summed energy deposited in theBBC detectors is related to charged particle multiplicityin nucleus-nucleus collisions and is sensitive to the eventcollision centrality. As discussed below, for pA collisionswe remove events with small signals in the east BBC,on the opposite side to the FMS, to reduce single beambackground.

The FMS is a Pb-glass electromagnetic calorimeterconsisting of 1264 rectangular lead glass blocks or cells,stacked in a wall with front surface transverse to theSTAR beam line as shown in Fig. 1. The FMS cov-ers the range of forward pseudo-rapidity, 2.7 < η < 3.8.The blocks are of two types, small and large cells. Detailsabout the detection of π0s in the STAR FMS have beendiscussed elsewhere [32].

The small and large FMS cells have Pb-glass with dif-ferent compositions. For small and large cells the ratioof cell sizes is chosen to be proportional to the ratio of

7

FIG. 1. The layout for the FMS calorimeter around theRHIC beam-line located about seven meters west of the nom-inal STAR interaction point. The FMS consists of lead glassblocks with lengths corresponding to 18 radiation lengths.There are 788 outer blocks with front face dimensions of 5.8× 5.8 cm. and 476 inner blocks with front face dimensions of3.8 × 3.8 cm.

Moliere radii (transverse electro-magnetic shower dimen-sion); therefore a photon in the large cells will deposit itsenergy into a similar number of cells as a photon of thesame energy in the small cells. For a 10 GeV photon, theshower distributes measurable energy into about 10 cells.For higher energy photons, the number of involved cellsincreases. For a 30 GeV photon from the nominal inter-action point, incident at the center of a cell, about 80%of the photon energy is deposited in that cell. Fitting thedistribution of energy in cells to an expected distributionfrom a known shower shape, the transverse coordinatesof the incident photon (at shower maximum depth) canbe obtained with a resolution of about 20% of the celldimension.

In the kinematic range discussed in this paper, ob-served photons from π0 decays have a separation rangingfrom a few cells to less than one cell. For the highest en-ergy π0s, above 60 GeV, the shower shape from the twophotons starts to overlap into a small cell single cluster.Therefore, to reconstruct the highest energy π0s, the dis-tribution of deposited energies in cells is fitted to a twophoton hypothesis, with parameters that represent thetwo photon energies and transverse position coordinates.The quality of these fits begins to degrade when the pho-ton separation is on the order of a single cell width.

In addition to photons from π0 decays, the FMS mea-sures electrons and positrons. It also has some sensi-

tivity to charged hadrons, such as π±. On average, acharged pion deposits about 1/3 of its energy in theFMS. If the π0 is from the fragmentation of a high pTjet, the FMS sees many of the associated hadronic frag-ments with degraded energy sensitivity. These chargedhadron showers are fit to the photon shower shape and ifthe deposited energy is greater than 1 GeV, they are in-cluded in the list of low energy photon candidates. TheFMS is triggered by high transverse momentum local-ized FMS signals. Because these cross sections have asevere transverse momentum dependence, the partiallymeasured charged hadronic background contributes lit-tle to the trigger rate but does contribute background toπ0 photon pair signals at high pT .

The events from the FMS where obtained from twotrigger methods. The first method is called the boardsum trigger, which demands transverse energy to be de-posited in localized overlapping rectangles of the 32 FMScells. The second method is called the jet trigger, which issatisfied by deposition of transverse energy, with a higherthreshold than that of the board sum triggers, measuredwithin overlapping azimuthal regions of angle ∆φ = π/2.Three parallel implementations of the board sum trig-gers are used to select events, each with π0 pT aboveone of three adjustable thresholds, typically 1.6, 1.9 and2.2 GeV/c. Triggers were prescaled to conserve detectorreadout bandwidth while sampling the different pT re-gions with similar statistical uncertainties. The pp datasample presented in this paper corresponds to an inte-grated luminosity of 34 pb−1 using the highest thresh-old triggers, which are not prescaled. The correspondinganalyzed luminosity for proton-nucleus collisions is 905

nb−1 = 24.5 pb−1

27 and 206 nb−1 = 40.6pb−1

197 for pAl andpAu, respectively, where the numerators are provided fordirect comparison of proton-nucleon luminosities.

For each event, photon candidates are sorted into “coneclusters.” Each cone cluster includes a subset of the pho-ton candidates for which the momentum direction iswithin an angular cone of 0.08 radians about the conemomentum direction of included photons. For each pho-ton in the pT sorted photon event list, the photon istested for inclusion in the cone cluster list, testing thelargest pT clusters first. If not included in an existingcluster, this becomes the seed of a new cluster. Usu-ally, only one of these cone clusters will be associatedwith the large pT trigger. For this analysis of triggeredevents, only the leading pT cone cluster is searched forπ0 candidates. This 0.08 radian cone radius, with nomi-nal kinematic pair cuts and for the pion energies around40 GeV, restricts the selected diphoton mass of photonpairs within a cone cluster to typically less than about 1GeV/c2. Searching for π0 candidates within a cone clus-ter greatly reduces the combinatorial photon pair possi-bilities and reduces diphoton background.

At higher energy, the separation between π0 photonsbecomes small, on the scale of the cell size. In this case,fits to a two photon hypothesis tend to overestimate theseparation between these photons. For large energy pi-

8

ons, or equivalently large xF , as seen in Fig. 2, cal-culated masses are preferentially smeared to larger val-ues. The π0 mass resolution is broadened significantlyto higher mass for π0 energies Eπ0 > 35 GeV in thelarge cells (lower pseudo-rapidity region) and for ener-gies above Eπ0 > 50 GeV in the small cells and higherpseudo-rapidity region of the FMS.

The leading energy pair of photons in the highest pTcluster was analyzed, with selection based on the de-cay distribution of that two-photon pair. The conditionZ < 0.7 is utilized, where Z = |E1−E2

E1+E2| and E1 and E2

are the energies of the two photons. This selection waspreferred over a less restrictive one because it decreasesbackground under the π0 mass peak. It is the accountingfor background under the π0 peak that represents the ma-jority of the systematic uncertainty for the measurementof AN .

While it is the intention to measure AN for inclusiveπ0 production, the selection of the highest-energy twophotons for the π0 candidates does sacrifice 10-15% ofthe pions, depending on kinematics. In proton-nucleuscollisions (pAl and pAu), we apply an additional selec-tion criterion in order to remove a specific RHIC back-ground which is seen in the “abort-gap” events, betweenbuckets where the nuclear beam is not present. Theseevents are referred to as single-beam events. For pA col-lisions, we require that the east BBC have a minimumsignal (caused by the breakup of the nuclei). This re-moves about 5% of the lowest activity including mostperipheral collisions from this analysis, but also removesnearly all of the single-beam background. The residualsingle-beam background contributes significantly to thesystematic error only for a few of the high-xF bins.

The residual single-beam background fraction in eachkinematic bin is estimated from events seen in the abort-gap bunches. The ratio of asymmetry for the single-beambackground to the π0 asymmetry is to be defined as RNB ,soANB = RNBAN , whereAN is the π0 asymmetry in theparticular kinematic bin. Consistent with asymmetriesobserved in the small number of events in the abort gap,we conservatively assume that RNB = 0.5± 0.5.

VI. THE INCLUSIVE AN MEASUREMENTS

In this paper AN for forward π0 production is mea-sured for pp, pAl, and pAu collisions. The high trans-verse momentum forward π0 is detected with the FMScalorimenter, detecting pions with pion pseudo-rapidity2.7 < η < 3.8. Candidate photon pairs passing the selec-tion are independently analyzed within kinematic regionsof pT and xF . In Fig. 2, the diphoton mass, Mγγ , dis-tributions are shown for two example kinematic regions,for pp, pAl and pAu collisions. The two-photon mass dis-tributions are initially fitted to a quadratic backgroundshape plus a Gaussian pion shape in the mass region be-low the η peak. The Gaussian only approximately repre-sents the shape of the pion peak and that Gaussian shape

is only used to determine a mass range above the pionpeak. To finally determine the background fraction, thequadratic background shape is constrained to be zero ata mass of zero and is fit to the mass distribution in thelimited mass region above the pion peak. Examples ofthese background fits are shown in Fig. 2. The pion sig-nal is obtained by counting the events in the pion peak,0.015 < Mγγ < 0.255 GeV/c2, and subtracting the fit-ted background contribution in that region. The typicalfraction fB of background under the pion peak rangesfrom about 20% at very low xF to a few percent whenthe pion energy is larger. We define AB = RBAN is theasymmetry of the background under the π0 peak whereRB is the fraction of non-pion background and AN is theπ0 asymmetry.

The value RB = 0.33 ± 0.33 was conservatively de-termined based on the asymmetry in the mass region(0.3 < Mγγ < 0.4 GeV/c2) above the pion peak andbelow the η meson peak . This background asymmetrycannot be well measured with significance within a singlekinematic bin, but is estimated based on an average overmany kinematic bins. Uncertainty in this backgroundcorrection is the most important contribution to the sys-tematic uncertainty in the π0 measurement of AN . ANfor a given bin in xF and pT is extracted from the fits tothe uncorrected asymmetries, a0(φ), which is determinedin each φ bin from the number of pions (N↑ and N↓) de-tected when the proton polarization is up↑/down↓ (seeFig. 3). The uncorrected asymmetry is

a0(φ) =N↑(φ)−N↓(φ)

N↑(φ) +N↓(φ). (5)

The azimuthal dependence of a0(φ) is fit to the form

a0(φ) = p0 + p1 cosφ. (6)

The parameter p1 is proportional to AN but must becorrected for the polarization of the proton beam PB anda factor K to account for background effects,

AN = p1K

PB. (7)

The beam polarization varied for different RHIC fills.The polarization and beam luminosity were largest atthe start of a fill and decayed during the fill. To max-imize the use of available data acquisition bandwidth,STAR adjusts the FMS trigger prescale factors duringthe fill, collecting a larger fraction of available low pTcross section when the luminosity is lower. The analysisof RHIC polarization has been described by the RHICPolarimetry group [35]. In this analysis, the average po-larization for each kinematic data point is calculated byfolding the run by run polarization with the trigger ratecontributing to each kinematic point. For a given beamfill, there is variation in the average polarization of 1-2%for different kinematic regions. The variation of AN fromthese different polarizations is small with respect to theoverall uncertainties. The uncertainty on polarization is

9

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

050

100150200250300350

310×

c<2.2 GeV/T

p<0.27 2.0<F

x: 0.21<pp

2c<0.255 GeV/γγM0.015<=0.18

Bf

(0.0005)±0.0026±=0.009NA

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

0

20

40

60

80

1003

10×c<3.5 GeV/

Tp<0.47 3.0<

Fx: 0.37<pp

2c<0.255 GeV/γγM0.015<=0.09

Bf

(0.0014)±0.0042±=0.044NA

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

020406080

100120140

310×

c<2.2 GeV/T

p<0.27 2.0<F

xAl: 0.21<p

2c<0.255 GeV/γγM0.015<=0.30

Bf

(0.0008)±0.0042±=0.008NA

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

0

20

40

60

80

1003

10×c<3.5 GeV/

Tp<0.47 3.0<

FxAl: 0.37<p

2c<0.255 GeV/γγM0.015<=0.12

Bf

(0.0014)±0.0048±=0.035NA

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

0100200300400500600700800

310×

c<2.2 GeV/T

p<0.27 2.0<F

xAu: 0.21<p

2c<0.255 GeV/γγM0.015<=0.23

Bf

(0.0011)±0.0017±=0.014NA

)2c (GeV/γγM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eve

nts

0

20

40

60

80

100

310×

c<3.5 GeV/T

p<0.47 3.0<F

xAu: 0.37<p

2c<0.255 GeV/γγM0.015<=0.11

Bf

(0.0016)±0.0038±=0.042NA

FIG. 2. Example invariant mass spectra for diphoton pairs selected within two kinematic regions (two columns) and threecollision types (rows: pp, pAl, pAu). The asymmetries AN for pion peaks are obtained within the mass region 0.015 < Mγγ <0.255 Gev/c2. For the indicated fitted backgrounds under the peaks, the fraction of background events is fB . The measuredAN for the π0, with all corrections applied, is included within each panel with statistical uncertainty followed by systematicuncertainty in parentheses.

divided between scale uncertainties common throughoutthe running period and non-scale uncertainties that varyfill by fill. The scale uncertainties, ∆P/P , are 3%, 3.1%,and 3.2% for pp, pAu, and pAl, respectively, and are notincluded in the point-by-point polarization measurement.When ratios of asymmetries are taken, the dominant po-larization uncertainty, like many of the other systematicuncertainties, tends to cancel in the ratio.

In Eq. 7, K represents a correction factor to the asym-metry based on the estimates of backgrounds in the massregion 0.015 < Mγγ < 0.255 GeV/c2. The largest partof the correction K of Eq. 7 was obtained from thebackground fraction fB under the peak with asymme-try AB = RBAN . The fraction fNB represents a smalladditional background fraction (typically 1 to 3%) frominteractions that cannot be associated with polarized ppor pA collisions with asymmetry ANB = RNBAN . Thenthe factor K is

K =

[1

1 + fB(RB − 1)

] [1

1 + fNB(RNB − 1)

]. (8)

The systematic uncertainties on AN come from threesources: polarization error (typically < 0.5%, exclud-ing the overall polarization scale uncertainty); the beambackground (typically 1 − 30%); and the single-beambackground (typically 1 − 3%). The uncertainty in themultiplicative factor K is the largest source of systematicerror in our measurement of AN . These uncertainties arecalculated individually for each given kinematic bin.

The various systematic contributions to our pT uncer-tainty have been discussed in detail in a previous anal-ysis [32]. The transverse momentum error analysis us-ing that data, collected in 2012 and 2013, is applicablefor these 2015 data. That analysis determined the finalσpT /pT to be approximately 5-6%, an estimate we willadopt here. In both analyses, the dominant contributionlies in the uncertainty on the energy calibration of thedetector (σC ≈ 5%). The energy calibration of the FMSis based on an analysis of the π0 mass for 20-30 GeV π0

photon pairs in the large cells and 40-50 GeV pairs in thesmall cells. We have conservatively set our final error intransverse momentum, σpT /pT = 7%, allowing for minor

10

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.02

0.04

0.06

0.08 c<2.2 GeV/T

p<0.27 2.0<F

xpp: 0.21<

0.0013±=0.0038 1

p 0.0009 ±0.0026 =0

p

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.02

0.04

0.06

0.08 c<3.5 GeV/T

p<0.47 3.0<F

xpp: 0.37<

0.0022±=0.0230 1

p 0.0015 ±0.0046 =0

p

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.02

0.040.06

0.08 c<2.2 GeV/T

p<0.27 2.0<F

xAl: 0.21<p

0.0019±=0.0036 1

p 0.0012 ±-0.0006 =0

p

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.02

0.040.06

0.08 c<3.5 GeV/T

p<0.47 3.0<F

xAl: 0.37<p

0.0024±=0.0181 1

p 0.0016 ±0.0001 =0

p

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.020.04

0.06

0.08 c<2.2 GeV/T

p<0.27 2.0<F

xAu: 0.21<p

0.0009±=0.0074 1

p 0.0006 ±-0.0001 =0

p

0πφ

3− 2− 1− 0 1 2 3

)φ( 0a

0.04−0.02−

0

0.020.04

0.06

0.08 c<3.5 GeV/T

p<0.47 3.0<F

xAu: 0.37<p

0.0021±=0.0231 1

p 0.0014 ±-0.0014 =0

p

FIG. 3. Uncorrected transverse spin asymmetries for the same 6 kinematic regions as in Fig. 2. The azimuthal φπ0

distributions of the uncorrected asymmetries, a0(φ), are shown for events in the mass range 0.015 < Mγγ < 0.255 GeV/c2.Fits to the functional form from Eq. 6 are shown with fitted parameter values p0 and p1.

differences with this analysis and the previous analysis.

The value of the parameter p0 from Eq. 6 indicates theasymmetry of relative integrated luminosity, as measuredin the given kinematic region. RHIC spin patterns arechanged for each fill so the integrated luminosities forspin up and spin down bunches are nearly equal. Thedistributions of parameters p0 for the three collision sys-tem data sets (pp, pAl and pAu) have weighted means of(0.0032± 0.0002, −0.0009± 0.0002 and 0.0001± 0.0002),respectively. The fits over all kinematic regions to a sin-gle constant value, p0, have corresponding χ2 values of32, 57 and 45 for 40 kinematic regions (39 degrees of free-dom). While the extracted values for AN depend only onthe p1 parameter, it is seen from the above that the val-ues of p0 parameters are small and for each beam dataset, the measurements of p0 in different kinematic regionsare internally consistent within each set.

An AN point is extracted from each of 110 kinematicand “collisions beam type” bins based on the value ofparameter p1 from the fit to Eq. 6. As shown for a fewexample kinematic regions and beam types in Fig. 3,each two-parameter fit to the 20 azimuthal points results

in a χ2 value. Over this large ensemble of such fits, thedistribution of measured χ2 values is in good agreementwith the theoretical χ2 distribution. For the pp, pAl andpAu data sets, the average χ2s for the fits to Eq. 6 are18.5, 18.1 and 18.4 for 18 degrees of freedom, respectively.

The examples shown in Figs. 2 and 3 represent only sixkinematic regions of 110 kinematic points at which ANhas been calculated. The transverse single-spin asymme-try for the full data set is shown in Fig. 4.

Even though AN is observed to differ among differ-ent nuclear collisions systems by 10% to 20%, it is aninstructive exercise to combine the data sets from differ-ent collision systems. In Fig. 5, the data points fromall beams and all transverse momenta are combined ineach of the six xF bins shown in other figures, with cen-ters located at xF = {0.19, 0.24, 0.32, 0.42, 0.54, 0.71}.All data from pp, pAl and pAu collisions are combinedand show the xF dependence for several pT regions. ForxF < 0.47, AN seems to depend only weakly on trans-verse momentum, with a gentle increase in asymmetry atlarger pT , but at larger xF > 0.47, it appears that AN

11

)c (GeV/T

p1.4 1.6 1.8 2 2.2 2.4 2.6

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 STAR 200 GeV0π pp

Al pAu p

<0.21Fx0.17<

)c (GeV/T

p2 2.5 3 3.5 4 4.5 5 5.5

NA

0

0.02

0.04

0.06

0.08

0.1

0.12<0.47Fx0.37<

)c (GeV/T

p1.5 2 2.5 3 3.5

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07<0.27Fx0.21<

)c (GeV/T

p2 3 4 5 6

NA

0

0.02

0.04

0.06

0.08

0.1

0.12<0.61Fx0.47<

)c (GeV/T

p1.5 2 2.5 3 3.5 4 4.5

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07<0.37Fx0.27<

)c (GeV/T

p2.5 3 3.5 4 4.5 5 5.5 6

NA

0

0.02

0.04

0.06

0.08

0.1

0.12<0.81F0.61<x

FIG. 4. The transverse momentum pT dependence of AN for 6 bins in Feynman xF . The events contributing are inclusiveπ0s with selection in the invariant mass window 0.015 < Mγγ < 0.255 GeV/c2. Results for the three collision systems areshown, black squares for pp, blue circles for pAl and red triangles for pAu collisions. The event selection criteria are given in thetext. The statistical uncertainties are shown with vertical error bars and the filled boxes indicate the horizontal and verticalsystematic uncertainties.

12

Fx

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12Au+pAlpp+pSTAR

c<2.0GeV/TP<c1.5 GeV/

c<3.0GeV/TP<c2.0 GeV/c<4.0GeV/TP<c3.0 GeV/

c<5.0GeV/TP<c4.0 GeV/

c<7.0GeV/TP<c5.0 GeV/

FIG. 5. The xF dependence of the π0 AN is shown with data from the combined pp, pAl, and pAu data points, collectingpoints within xF intervals for frames from Fig.4 and the indicated pT range. Data points are shown separately for five intervalsof transverse momentum indicated by different symbols and plotted horizontally at the average xF for each combined point.Vertical error bars represent statistical uncertainties and the systematic horizontal and vertical uncertainties are shown withfilled boxes.

13

may flatten or perhaps falls with pT .For each xF region, the ratios of AN for pAu(pAl) to

AN for pp scattering are shown as a function of pT in Fig.6(7). The pT dependences of these ratios are consistentwith a constant ratio. Nevertheless, the AN ratios shownin Fig. 6 and Fig. 7 were separately averaged for low pT(1.5 GeV/c < pT < 2.5 GeV/c) and high pT (pT > 2.5GeV/c). The fitted average values of AN ratios for eachplot in Figs. 6 and 7, averaging over the full pT rangefor each xF , are plotted in Fig. 8 as a function of logA.The systematic uncertainties in Fig. 6 and Fig. 7 arereduced to account for the correlated background correc-tions between pp and pA distributions. The non-beambackgrounds thus contribute the most to these system-atic errors with statistical uncertainty dominating.

We parameterize the dependence of AN on nuclear sizeA with a power law form

AN (pA) = AN (pp)AP . (9)

To determine the exponent P for each of the six xFbins, the weighted means shown in Fig. 8 are fitted tothe power law form,

r(pA) =

⟨AN (pA)

AN (pp)

⟩all pT

= AP . (10)

The ratios, r(pA), as defined in Eq. 10, represent the ra-tio of nuclear suppression of AN in pA to AN observedpp scattering, averaged over the full observed pT range.For each region of xF , we fit to a power law in nuclearsize A with a fitted exponent, P . Recognizing that theuncertainties in the ratio of pA to pp are correlated, thesimple χ2 fit in the figure can be biased in the determi-nation of the exponent, P . We refer to this simple fit,with correlated uncertainties in the ratios, as a “Type 1”determination of P .

A second method for determining the exponent, P ,without correlated uncertainties is to fit each point in pTand xF to the two-parameter form of Eq. 9, with param-eters AN (pp) and P . These fits are two-parameter fits tothree measurements within each kinematic region. Thenwith a weighted mean over pT of the exponents from fits,an average P is obtained for each xF region. This isreferred to as the “Type 2” method, and the bands cor-responding to the one sigma uncertainties in this “Type2” fit are shown in Fig. 8 as the shaded regions.

Fitting the exponent of the A dependence of the ratiosseparately for the low and high pT regions, the exponentsPL and PH are obtained,

rL(pA) =

⟨AN (pA)

AN (pp)

⟩pT<2.5 Gev/c

= APL (11)

rH(pA) =

⟨AN (pA)

AN (pp)

⟩pT>2.5 GeV/c

= APH . (12)

Calculations of AN ratios by Hatta et al. [36] iden-tify an amplitude that is thought to be dominant in

the saturation region and would scale as AN ∝ A−13 in

p↑ + A → π0X. These calculations could apply to ourpresent measurements of AN for pp, pAl and pAu in thetransverse momentum range 1.5 < pT < 2.5 GeV/c.

Comparing gold with A=197 and proton collisions withA=1, this implies a reduction of AN for pAu by morethan a factor of 5. Above the saturation region, theypredict the AN will scale as A0, indicating that the trans-verse single-spin asymmetry at larger pT could be similarfor pp and pAu collisions. The fitted values of the expo-nents PL and PH as functions of xF are shown in Fig. 9.The exponents are generally within about 5% of zero inboth the low and high pT regions and significantly dif-ferent from the value of − 1

3 that has been predicted toapply in the region below the saturation scale.

Another approach [37], based on a geometrical scalingof gluon distributions and with Collins-type fragmenta-tion, has also been used to calculate the transverse single-spin asymmetry. They predicted that for pion transversemomentum below the saturation scale, p2T << Q2

s, the

AN ratio is AN (pA)/AN (pp) ' Q2sp

Q2sA

, where Q2sA is the

square of the saturation scale for a nucleus with A nucle-ons. For pT well above the saturation scale, the ratio wasexpected to be 1. Models, which suggest that at large pTthe ratio should approach a form with exponent zero, arein good agreement with these data.

VII. ISOLATED AN MEASUREMENTS

It is observed here that the presence of soft photons orhadronic fragments in the vicinity of the highest pT pioncan decrease the asymmetry significantly, cutting AN inhalf in most kinematic regions. For a subset of the eventsshown in Fig. 4, there are exactly two photons with en-ergy greater than 1 GeV in the 0.08 radian cone aroundthe π0 event. We refer to “isolated” events as those witha highest pT cone cluster with only a single pair of pho-ton candidates. “Non-isolated” events are more jet-like,having at least three photon candidates within the cone.For a large fraction of the covered kinematics, about 1/3of the inclusively selected π0 events contributing to Fig.4 have an isolated π0. These more exclusive events havegenerally larger values of AN .

It is seen from the comparison of Fig. 4 with Figs.10, 11, and 12 that AN for isolated π0s is significantlygreater than for the complementary part of the inclusiveevent set with additional fragments observed.

The electromagnetic calorimeter has limited sensitiv-ity to charged pions, so isolation does not guarantee theabsence of hadrons other than π0s. However, this ob-servation hints at the possibility that the asymmetry forjets with a leading energy π0 is much less than the sin-gle π0 asymmetry in this forward kinematic region. Theenhanced AN for events with no observed jet fragmentmay indicate that these events are not related to jet pro-duction with fragmentation.

14

)c (GeV/T

p1.6 1.8 2 2.2 2.4 2.6 2.8

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.139± 0.686 T

pAll

0.139± 0.686 T

pLow

<0.21F

x0.17<

)c (GeV/T

p2 2.5 3 3.5

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.046± 0.740 T

pAll 0.303± 1.123

TpLow

0.047± 0.731 T

pHigh

<0.27F

x0.21<

)c (GeV/T

p2 2.5 3 3.5 4 4.5

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.034± 0.855 T

pAll 0.112± 0.874

TpLow

0.036± 0.853 T

pHigh

<0.37F

x0.27<

)c (GeV/T

p2 3 4 5

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.046± 0.879 T

pAll 0.085± 0.807

TpLow

0.055± 0.910 T

pHigh

<0.47F

x0.37<

)c (GeV/T

p2 3 4 5 6

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.073± 0.964 T

pAll 0.246± 1.247

TpLow

0.076± 0.937 T

pHigh

<0.61F

x0.47<

)c (GeV/T

p2 3 4 5 6

(pp)

N)/

AA

u(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.234± 0.924 T

pAll

0.234± 0.924 T

pHigh

<0.81F

x0.61<

FIG. 6. The transverse momentum pT dependence of the ratio of AN for pAu scattering to that for pp for six Feynman xFranges. This figure refers to the same data as is plotted in Fig. 4. The event selection criteria are given in the text. Thestatistical uncertainties are shown with vertical error bars, and the filled boxes indicate systematic uncertainties appropriatefor the ratio. Horizontal lines indicate the fit to the average ratio over the region 1.5 < pT < 2.5 GeV/c, 2.5 < pT < 7.5 GeV/cand for the combined pT range.

The observation that isolated π0 events have largerAN does not appear to depend upon the nuclear size Ain pA collisions. In Fig. 13 the determination of theexponent P in the A dependence, defined in Eq. 9, hasbeen analyzed separately for isolated and non-isolatedevents. The average exponents are similar for these twosubsets of the data.

This dependence of the measured AN on event topol-ogy is further described in a jet analysis [39], with someof these same data. Although technical aspects of thatanalyses differ from this one, the results are consistent inthose cases where the same quantity is measured.

VIII. CONCLUSIONS

This new measurement of AN for forward π0 produc-tion, in pp, pAl and pAu collisions, determines the depen-dence on xF and pT . It is observed that AN generallyincreases with increeasing pT at fixed xF (0.17 < xF <

0.47), for pT up to 5 GeV/c. In many calculations, ex-emplified by the simple model of Eq. 4, AN is expectedto fall with pT when pT is significantly larger than somenominal QCD scale kT , representing the spin dependentpart of the transverse momentum shift due to initial orfinal interactions. The persistent rise in AN for pT wellbeyond the 1 GeV/c scale, is unexpected.

Furthermore, the asymmetry AN , for forward π0 pro-duction is significantly larger for events with an observedisolated π0 than for events that show evidence of addi-tional fragmentation products. It is interesting to com-pare this result to the published AN for jets, from [19],where the asymmetry was observed to be small comparedto this π0 measurement. The Sivers picture, where aproton spin dependent transverse momentum kT is ac-quired from initial state interactions, is not the naturalchoice for explaining the difference in AN for isolatedand non-isolated π0s in the final state. But neither isthe enhancement of AN for isolated pions expected inthe Collins picture, where jet fragmentation into multi-

15

)c (GeV/T

p1.6 1.8 2 2.2 2.4 2.6 2.8

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.214± 0.734 T

pAll

0.214± 0.734 T

pLow

<0.21F

x0.17<

)c (GeV/T

p2 2.5 3 3.5

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.057± 0.819 T

pAll 0.548± 0.899

TpLow

0.057± 0.818 T

pHigh

<0.27F

x0.21<

)c (GeV/T

p2 2.5 3 3.5 4 4.5

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.041± 0.821 T

pAll 0.147± 0.568

TpLow

0.042± 0.841 T

pHigh

<0.37F

x0.27<

)c (GeV/T

p2 3 4 5

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.057± 0.822 T

pAll 0.141± 0.691

TpLow

0.062± 0.848 T

pHigh

<0.47F

x0.37<

)c (GeV/T

p2 3 4 5 6

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.081± 0.824 T

pAll 0.371± 1.196

TpLow

0.083± 0.805 T

pHigh

<0.61F

x0.47<

)c (GeV/T

p2 3 4 5 6

(pp)

N)/

AA

l(p

NA

0

0.5

1

1.5

2

2.5

3 STAR

0.239± 0.422 T

pAll

0.239± 0.422 T

pHigh

<0.81F

x0.61<

FIG. 7. Similar to Fig. 6 but the ratio of AN in pAl to that in pp.

ple hadrons imparts a spin dependent momentum kT tothe observed pion, to generate pion asymmetry.

The kinematic dependence of AN on xF and pT issimilar for the three collision systems. The suppressionof AN in collisions with nuclear beams is modest, withthe typical AN ratios between pAu and pp greater than80%. When the suppression of AN is fit to a power lawnuclear A dependence, AN (A) ∝ AP , the measured ex-ponents from Type 2 fits are in the range of −0.075 <P < 0.00. The weighted average exponent in Fig. 9 is〈P 〉 = −0.027 ± 0.005. This corresponds to a reductionof r(Au) = 0.87± 0.02. For the Type 1 fits in the low pTregion, the weighted average is 〈PL〉 = −0.037 ± 0.013,implying rL(Au) ' 0.82 ± 0.06. In the high pT region,the weighted average is 〈PH〉 = −0.039±0.0048, implyingrH(Au) ' 0.81 ± 0.02. There is no significant differencebetween the exponent PH in the higher pT region andPL in the low pT region, where gluon saturation effectscould be most relevant. The general agreement betweenType 1 and Type 2 fits helps to give confidence in thefitting methods.

This nuclear suppression of π0 AN is much lessthan that reported by the PHENIX collaboration, forpositively charged hadrons at somewhat lower pseudo-

rapidity or lower xF . The fits from the PHENIX mea-surement favored an exponent P = −0.37 [38]. Un-like the result of this paper, the PHENIX results arenominally consistent with the prediction of Hatta et al.,(P = −1/3).

It is noted that the range of xF coverage by thePHENIX measurement, 0.1 < xF < 0.2, is below therange presented here, shown in Fig. 9. The range ofgluon momentum fractions, x, probed within the unpo-larized beams in this measurement is x < 0.005, be-low the x range probed in the PHENIX measurement.The distribution of exponents shown in Fig. 9 indi-cates that the P exponents slowly increase with increas-ing xF . The Type 2 data points can be fit to the lin-ear form P (xF ) = P0 + P ′0xF , yielding fitted parametersP0 = −0.08±0.02 and P ′0 = 0.14±0.05. Linear extrapo-lation of these data into the center of the PHENIX accep-tance gives an exponent P (xF = 0.15) = −0.06 ± 0.02.The PHENIX measurement reported a χ2 = ±1 con-fidence range, expressed here as a P range, of approx-imately −0.6 < P < −0.25. Comparing this to theSTAR extrapolated value, the difference appears signifi-cant. From the χ2 plot in the PHENIX paper, the value,P = −0.06, corresponds to χ2 ' 13. Of course, the linear

16

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2PSTAR Fit to Ratio = A

0.036 (Type1) ±P= -0.075

0.042 (Type2)±P= -0.049

<0.21F

x0.17<

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2PSTAR Fit to Ratio = A

0.010 (Type1) ±P= -0.058

0.012 (Type2)±P= -0.054

<0.27F

x0.21<

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2PSTAR Fit to Ratio = A

0.007 (Type1) ±P= -0.037

0.008 (Type2)±P= -0.026

<0.37F

x0.27<

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2PSTAR Fit to Ratio = A

0.009 (Type1) ±P= -0.032

0.010 (Type2)±P= -0.020

<0.47F

x0.37<

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2PSTAR Fit to Ratio = A

0.013 (Type1) ±P= -0.019

0.014 (Type2)±P= -0.001

<0.61F

x0.47<

Log A0 1 2 3 4 5

(pp)

N(p

A)/

AN

A

00.20.40.60.8

11.21.4

1.61.8

2<0.81Fx0.61<

PSTAR Fit to Ratio = A

0.056 (Type1) ±P= -0.075

0.047 (Type2)±P= 0.000

<0.81Fx0.61<

FIG. 8. The ratio of AN for pA scattering to that for pp scattering is shown for six xF regions, averaging over the full range ofpT dependence. The fitted form for these ratios as a function of A is obtained using Type 1 and Type 2 analyses as described inthe text. The dependence of AN as a function of logA is displayed with a filled error band, obtained from the Type 2 analysis,shown as the dashed line.

extrapolation is just an assumption.Combining all beam types to maximize statistics for

AN measurements, for Feynman xF < 0.47 the asymme-try AN increases with xF and with pT . For xF > 0.47the trend moderates, as the dependence of AN on pTflattens or may begin to fall with pT over the measuredpT range.

These measurements of the dependence of AN , for for-ward π0 production, on kinematics and event topology,should provide new input for ongoing theoretical studiesof the underlying dynamics for these processes. In pAcollisions, the dependence of AN on nuclear size A hasbeen measured and is small.

ACKNOWLEDGMENTS

We thank the RHIC Operations Group and RCF atBNL, the NERSC Center at LBNL, and the Open Sci-ence Grid consortium for providing resources and sup-port. This work was supported in part by the Office

of Nuclear Physics within the U.S. DOE Office of Sci-ence, the U.S. National Science Foundation, the Min-istry of Education and Science of the Russian Federa-tion, National Natural Science Foundation of China, Chi-nese Academy of Science, the Ministry of Science andTechnology of China and the Chinese Ministry of Educa-tion, the Higher Education Sprout Project by Ministryof Education at NCKU, the National Research Founda-tion of Korea, Czech Science Foundation and Ministryof Education, Youth and Sports of the Czech Republic,Hungarian National Research, Development and Innova-tion Office, New National Excellency Programme of theHungarian Ministry of Human Capacities, Departmentof Atomic Energy and Department of Science and Tech-nology of the Government of India, the National ScienceCentre of Poland, the Ministry of Science, Education andSports of the Republic of Croatia, RosAtom of Russia andGerman Bundesministerium fur Bildung, Wissenschaft,Forschung and Technologie (BMBF), Helmholtz Associ-ation, Ministry of Education, Culture, Sports, Science,and Technology (MEXT) and Japan Society for the Pro-

17

Fx0.2 0.3 0.4 0.5 0.6 0.7

P

0.4−

0.3−

0.2−

0.1−

0

0.1

STAR

TP from Type 2 Fit, Averaged over All p

T from Type 1 Fit, Averaged over Low pLP

T from Type 1 Fit, Averaged over High pHP

STAR

TP from Type 2 Fit, Averaged over All p

T from Type 1 Fit, Averaged over Low pLP

T from Type 1 Fit, Averaged over High pHP

P(pp)=AN

(pA)/ANA Dependence: AFit to Power Law

FIG. 9. Analyzing separately the low pT (1.5 < pT < 2.5 GeV/c) data and the higher pT data, the exponent, P , for nuclear A

dependence of the asymmetry ratio AN (pA)AN (pp)

= AP is shown as a function of xF . Points are included, averaging over the low pT

region and high pT regions (pT > 2.5 GeV/c) separately. Examples of one parameter power law fits for P are shown in Fig. 8,where power dependence exponent P is plotted as a function of Feynman xF . The uncertainties shown are from fits describedin the text and are dominated by statistical uncertainties. The systematic uncertainties are small, mostly cancelling, in ratiosbetween different nuclear A data sets and are not separately shown.

motion of Science (JSPS).

18

)c (GeV/T

p

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 STAR 200 GeV0π not isolated pp

isolatedpp

<0.21Fx0.17<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.47Fx0.37<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.27Fx0.21<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.61Fx0.47<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4 4.5 5

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.37Fx0.27<

)c (GeV/T

p

2.5 3 3.5 4 4.5 5 5.5 6

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.81F0.61<x

FIG. 10. The transverse momentum pT dependence of AN for pion production in six (xF ) regions for pp collisions. The datafrom Fig. 4 have been divided into two parts based on whether the π0 is produced with additional jet-like fragments of energymore than 1 GeV, shown with filled markers, or in isolation shown with open markers. The event selection criteria for isolatedand non-isolated events are given in the text. The statistical uncertainties are shown with vertical error bars. The filled boxesindicate horizontal and vertical systematic uncertainties.

19

)c (GeV/T

p

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 STAR 200 GeV0π

Al not isolatedp

Al isolatedp

<0.21Fx0.17<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16<0.47Fx0.37<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.27Fx0.21<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16<0.61Fx0.47<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4 4.5 5

NA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.37Fx0.27<

)c (GeV/T

p

2.5 3 3.5 4 4.5 5 5.5 6

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16<0.81F0.61<x

FIG. 11. This plot is similar to Fig. 10 but for pAl collisions.

20

)c (GeV/T

p

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 STAR 200 GeV0π

Au not isloatedp

Au isolatedp

<0.21Fx0.17<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.47Fx0.37<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.27Fx0.21<

)c (GeV/T

p

2 3 4 5 6 7

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.61Fx0.47<

)c (GeV/T

p

1.5 2 2.5 3 3.5 4 4.5 5

NA

0.01−

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08<0.37Fx0.27<

)c (GeV/T

p

2.5 3 3.5 4 4.5 5 5.5 6

NA

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<0.81F0.61<x

FIG. 12. This plot is similar to Fig. 10 but for pAu collisions.

21

Fx0.2 0.3 0.4 0.5 0.6 0.7

P

0.4−

0.3−

0.2−

0.1−

0

0.1P(pp)=A

N(pA)/ANA Dependence: AFit to Power Law

STAR

Isolated Type 2 Fit

Non-Isolated Type 2 Fit

FIG. 13. Comparison of the nuclear A dependence of AN for events with isolated π0s and events with non-isolated π0s. Theexponent P of the nuclear A dependence is shown as a function of xF . The exponent is defined in Eq. 9. The points shown areaveraged over the full pT range with a Type 2 fit at each pT and xF similar to the points of Fig. 9.

22

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