Physics and Astronomy Publications Physics and Astronomy

5-22-2003

Centrality dependence of the high (PT) chargedhadron suppression in Au+Au collisions at roots(NN)=130 GeVK. AdcoxVanderbilt University

Sergey BelikovIowa State University

John C. HillIowa State University, jhill@iastate.edu

John G. LajoieIowa State University, lajoie@iastate.edu

Alexandre LebedevIowa State University, lebedev@iastate.edu

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Centrality dependence of the high (PT) charged hadron suppression inAu+Au collisions at root s(NN)=130 GeV

AbstractPHENIX has measured the centrality dependence of charged hadron p(T) spectra from Au + Au collisions atroot(s)NN = 130 GeV The truncated mean p(T) decreases with centrality for p(T) > 2 GeV/c, indicating anapparent reduction of the contribution from hard scattering to high p(T) hadron production. For centralcollisions the yield at high p(T) is shown to be suppressed compared to binary nucleon-nucleon collisionscaling of p + p, data. This suppression is monotonically increasing with centrality, but most of the changeoccurs below 30% centrality, i.e., for collisions with less than similar to 140 participating nucleons. Theobserved p(T) and centrality dependence is consistent with the particle production predicted by modelsincluding hard scattering and subsequent energy loss of the scattered partons in the dense matter created inthe collisions.

DisciplinesElementary Particles and Fields and String Theory | Physics

CommentsThis is a manuscript of an article published as Adcox, K., S. S. Adler, N. N. Ajitanand, Y. Akiba, J. Alexander, L.Aphecetche, Y. Arai et al. "Centrality dependence of the high p T charged hadron suppression in Au+ Aucollisions at sNN= 130 GeV." Physics Letters B 561, no. 1 (2003): 82-92. DOI:10.1016/S0370-2693(03)00423-4. Posted with permission.

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This work is licensed under a Creative Commons Attribution 4.0 License.

AuthorsK. Adcox, Sergey Belikov, John C. Hill, John G. Lajoie, Alexandre Lebedev, Craig Ogilvie, Athanasios Petridis,Marzia Rosati, F. K. Wohn, et al., and PHENIX Collaboration

This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/physastro_pubs/359

Physics Letters B 561 (2003) 82–92

www.elsevier.com/locate/npe

Centrality dependence of the highpT charged hadron suppressionin Au + Au collisions at

√sNN = 130 GeV

PHENIX Collaboration

K. Adcoxan, S.S. Adlerc, N.N. Ajitanandaa, Y. Akiban, J. Alexanderaa,L. Aphecetcheah, Y. Arai n, S.H. Aronsonc, R. Averbeckab, T.C. Awesac, K.N. Barishe,P.D. Barness, J. Barretteu, B. Bassallecky, S. Bathev, V. Baublisad, A. Bazilevskyl,af,

S. Belikovl,m, F.G. Bellaicheac, S.T. Belyaevp, M.J. Bennetts, Y. Berdnikovai,S. Botelhoag, M.L. Brookss, D.S. Brownz, N. Brunery, D. Bucherv, H. Bueschingv,

V. Bumazhnovl, G. Buncec,af, J. Burward-Hoyab, S. Butsykab,ad, T.A. Careys,P. Chandb, J. Change, W.C. Changa, L.L. Chavezy, S. Chernichenkol, C.Y. Chih,J. Chiban, M. Chiuh, R.K. Choudhuryb, T. Christab, T. Chujoc,am, M.S. Chungo,s,

P. Chungaa, V. Ciancioloac, B.A. Coleh, D.G. D’Enterriaah, G. Davidc,H. Delagrangeah, A. Denisovl, A. Deshpandeaf, E.J. Desmondc, O. Dietzschag,B.V. Dineshb, A. Dreesab, A. Duruml, D. Duttab, K. Ebisux, Y.V. Efremenkoac,

K. El Chenawian, H. En’yoq,ae, S. Esumiam, L. Ewell c, T. Ferdousie, D.E. Fieldsy,S.L. Fokinp, Z. Fraenkelap, A. Franzc, A.D. Frawleyi, S.-Y. Funge, S. Garpmant,

T.K. Ghoshan, A. Glennaj, A.L. Godoiag, Y. Gotoaf, S.V. Greenean,M. Grosse Perdekampaf, S.K. Guptab, W. Gurync, H.-Å. Gustafssont, J.S. Haggertyc,H. Hamagakig, A.G. Hansens, H. Karax, E.P. Hartounir, R. Hayanoal, N. Hayashiae,

X. Hej, T.K. Hemmickab, J.M. Heuserab, M. Hibinoao, J.C. Hillm, D.S. Hoaq,K. Hommak, B. Hongo, A. Hooverz, T. Ichiharaae,af, K. Imaiq,ae, M.S. Ippolitovp,

M. Ishiharaae,af, B.V. Jacakab,af, W.Y. Jango, J. Jiaab, B.M. Johnsonc,∗, S.C. Johnsonr,ab,K.S. Joow, S. Kametaniao, J.H. Kangaq, M. Kannad, S.S. Kapoorb, S. Kellyh,

B. Khachaturovap, A. Khanzadeevad, J. Kikuchiao, D.J. Kimaq, H.J. Kimaq, S.Y. Kimaq,Y.G. Kim aq, W.W. Kinnisons, E. Kistenevc, A. Kiyomichi am, C. Klein-Boesingv,

S. Klinksieky, L. Kochendaad, V. Kochetkovl, D. Koehlery, T. Kohamak,D. Kotchetkove, A. Kozlov ap, P.J. Kroonc, K. Kuritaae,af, M.J. Kweono, Y. Kwonaq,

G.S. Kylez, R. Laceyaa, J.G. Lajoiem, J. Lauretaa, A. Lebedevm,p, D.M. Lees,M.J. Leitchs, X.H. Li e, Z. Li f,ae, D.J. Limaq, M.X. Liu s, X. Liu f, Z. Liu f,

C.F. Maguirean, J. Mahonc, Y.I. Makdisic, V.I. Mankop, Y. Maof,ae, S.K. Marku,S. Markacsh, G. Martinezah, M.D. Marxab, A. Masaikeq, F. Matathiasab,

0370-2693 2003 Published by Elsevier Science B.V.doi:10.1016/S0370-2693(03)00423-4

Open access under CC BY license.

PHENIX Collaboration / Physics Letters B 561 (2003) 82–92 83

T. Matsumotog,ao, P.L. McGaugheys, E. Melnikovl, M. Merschmeyerv, F. Messerab,M. Messerc, Y. Miakeam, T.E. Miller an, A. Milov ap, S. Mioduszewskic,aj,

R.E. Mischkes, G.C. Mishraj, J.T. Mitchellc, A.K. Mohantyb, D.P. Morrisonc,J.M. Mosss, F. Mühlbacherab, M. Muniruzzamane, J. Murataae, S. Nagamiyan,

Y. Nagasakax, J.L. Nagleh, Y. Nakadaq, B.K. Nandie, J. Newbyaj, L. Nikkinenu,P. Nilssont, S. Nishimurag, A.S. Nyaninp, J. Nystrandt, E. O’Brienc, C.A. Ogilviem,H. Ohnishic,k, I.D. Ojhad,an, M. Onoam, V. Onuchinl, A. Oskarssont, L. Östermant,

I. Otterlundt, K. Oyamag,al, L. Paffrathc,1, A.P.T. Palouneks, V.S. Pantuevab,V. Papavassiliouz, S.F. Patez, T. Peitzmannv, A.N. Petridism, C. Pinkenburgc,aa,R.P. Pisanic, P. Pitukhinl, F. Plasilac, M. Pollackab,aj, K. Popeaj, M.L. Purschkec,

I. Ravinovichap, K.F. Readac,aj, K. Reygersv, V. Riabovad,ai, Y. Riabovad, M. Rosatim,A.A. Rosean, S.S. Ryuaq, N. Saitoae,af, A. Sakaguchik, T. Sakaguchig,ao, H. Sakoam,T. Sakumaae,ak, V. Samsonovad, T.C. Sangsterr, R. Santov, H.D. Satoq,ae, S. Satoam,

S. Sawadan, B.R. Schleis, Y. Schutzah, V. Semenovl, R. Setoe, T.K. Sheac, I. Sheinl,T.-A. Shibataae,ak, K. Shigakin, T. Shiinas, Y.H. Shinaq, I.G. Sibiriakp, D. Silvermyrt,

K.S. Simo, J. Simon-Gillos, C.P. Singhd, V. Singhd, M. Sivertzc, A. Soldatovl,R.A. Soltzr, S. Sorensenac,aj, P.W. Stankusac, N. Starinskyu, P. Steinbergh, E. Stenlundt,A. Sterar, S.P. Stollc, M. Sugiokaae,ak, T. Sugitatek, J.P. Sullivans, Y. Sumik, Z. Sunf,M. Suzukiam, E.M. Takaguiag, A. Taketaniae, M. Tamaiao, K.H. Tanakan, Y. Tanakax,

E. Taniguchiae,ak, M.J. Tannenbaumc, J. Thomasab, J.H. Thomasr, T.L. Thomasy,W. Tianf,aj, J. Tojoq,ae, H. Torii q,ae, R.S. Towells, I. Tserruyaap, H. Tsuruokaam,

A.A. Tsvetkovp, S.K. Tulid, H. Tydesjöt, N. Tyurinl, T. Ushirodax, H.W. van Heckes,C. Velissarisz, J. Velkovskaab, M. Velkovskyab, A.A. Vinogradovp, A.M. Volkov p,

A. Vorobyovad, E. Vznuzdaevad, H. Wange, Y. Watanabeae,af, S.N. Whitec, C. Witzigc,F.K. Wohnm, C.L. Woodyc, W. Xiee,ap, K. Yagiam, S. Yokkaichiae, G.R. Youngac,

I.E. Yushmanovp, W.A. Zajch, Z. Zhangab, S. Zhouf

a Institute of Physics, Academia Sinica, Taipei 11529, Taiwanb Bhabha Atomic Research Centre, Bombay 400 085, India

c Brookhaven National Laboratory, Upton, NY 11973-5000, USAd Department of Physics, Banaras Hindu University, Varanasi 221005, India

e University of California, Riverside, CA 92521, USAf China Institute of Atomic Energy (CIAE), Beijing, People’s Republic of China

g Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japanh Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, USA

i Florida State University, Tallahassee, FL 32306, USAj Georgia State University, Atlanta, GA 30303, USA

k Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japanl Institute for High Energy Physics (IHEP), Protvino, Russia

m Iowa State University, Ames, IA 50011, USAn KEK, High Energy Accelerator Research Organization, Tsukuba-shi, Ibaraki-ken 305-0801, Japan

o Korea University, Seoul, 136-701, South Koreap Russian Research Center “Kurchatov Institute”, Moscow, Russia

q Kyoto University, Kyoto 606, Japan

84 PHENIX Collaboration / Physics Letters B 561 (2003) 82–92

r Lawrence Livermore National Laboratory, Livermore, CA 94550, USAs Los Alamos National Laboratory, Los Alamos, NM 87545, USA

t Department of Physics, Lund University, Box 118, SE-221 00 Lund, Swedenu McGill University, Montreal, PQ H3A 2T8, Canada

v Institut fur Kernphysik, University of Münster, D-48149 Münster, Germanyw Myongji University, Yongin, Kyonggido 449-728, South Korea

x Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japany University of New Mexico, Albuquerque, NM 87131, USA

z New Mexico State University, Las Cruces, NM 88003, USAaa Chemistry Department, State University of New York, Stony Brook, NY 11794, USA

ab Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794, USAac Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

ad PNPI, Petersburg Nuclear Physics Institute, Gatchina, Russiaae RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan

af RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USAag Universidade de São Paulo, Institute de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil

ah SUBATECH (Ecole des Mines de Nantes, 1N2P3/CNRS, Universite de Nantes) BP 20722 - 44307, Nantes cedex 3, Franceai St. Petersburg State Technical University, St. Petersburg, Russia

aj University of Tennessee, Knoxville, TN 37996, USAak Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

al University of Tokyo, Tokyo, Japanam Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan

an Vanderbilt University, Nashville, TN 37235, USAao Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan

ap Weizmann Institute, Rehovot 76100, Israelaq Yonsei University, IPAP, Seoul 120-749, South Korea

ar KFKl Research Institute for Particle and Nuclear Physics (RMKI), Budapest, Hungary 2

Received 17 July 2002; received in revised form 21 March 2003; accepted 21 March 2003

Editor: J.P. Schiffer

Abstract

PHENIX has measured the centrality dependence of charged hadronpT spectra from Au+Au collisions at√

sNN = 130 GeV.The truncated meanpT decreases with centrality forpT > 2 GeV/c, indicating an apparent reduction of the contribution fromhard scattering to highpT hadron production. For central collisions the yield at highpT is shown to be suppressed compared tobinary nucleon–nucleon collision scaling of p+ p data. This suppression is monotonically increasing with centrality, but mostof the change occurs below 30% centrality, i.e., for collisions with less than∼ 140 participating nucleons. The observedpT andcentrality dependence is consistent with the particle production predicted by models including hard scattering and subsequentenergy loss of the scattered partons in the dense matter created in the collisions. 2003 Published by Elsevier Science B.V.

1. Introduction

Particle production at large transverse momentum(pT ) provides a new tool to study hot and dense

* Corresponding author.E-mail address: brant@bnl.gov (B.M. Johnson).

1 Deceased.2 Not a participating institution.

nuclear matter created in high energy nuclear col-lisions. In nucleon–nucleon collisions, hadrons withpT � 2 GeV/c are believed to originate mostly fromthe jet fragmentation of constituent partons, quarksand gluons, that were scattered with large momentumtransferQ2 [1]. In nuclear collision these hard scatter-ing processes between constituent partons occur earlycompared to the lifetime of the strongly interactingmatter. Thus the hard scattered partons may traverse

Open access under CC BY license.

PHENIX Collaboration / Physics Letters B 561 (2003) 82–92 85

the highest energy density matter produced. Theoreti-cal studies of the propagation of partons in high den-sity matter suggest that they lose a significant fractionof their energy through gluon bremsstrahlung [2] andthat the energy lost reflects the density of color chargesin the matter through which they pass [3]. The energyloss reduces the momenta of the partons, which resultsin a corresponding reduction of the momenta of thefragmentation products [4], observable as a reducedyield of highpT hadrons.

The first measurements of hadron spectra at theBrookhaven National Laboratory Relativistic HeavyIon Collider (RHIC) facility indicate a suppressionof high-pT hadron production in central Au+ Aucollisions relative to a binary collision scaling ofp + p andp̄ + p data [5,6]. No suppression is foundfor peripheral Au+ Au collisions. So far no uniqueexplanation of this apparent absence of the expectedjet contribution to thepT spectrum above 2 GeV/chas been identified.

Models of parton energy loss can reproduce theobserved suppression in central Au+ Au collisions[7–9]. Other final state effects such as rescattering ofhadrons originally produced via the jet fragmentationhave been proposed to explain the suppression [10]. Itshould be noted that models invoking thermal hadronproduction combined with collective transverse ex-pansion of the reaction volume successfully describethe transverse momentum distributions of identifiedhadrons up to 3 GeV/c [11,12]. However, the mecha-nism of equilibration, which requires a reduction of thehighpT particle yield, is not specified in these models.

Alternatively, the initial state may be modified suchthat the number of hard scatterings is reduced. It iswell known that nuclear modifications of the partondistributions exist [13]. These modifications cannotexplain the suppression, since in the kinematic rangeof the measurements anti-shadowing enhances the par-ton distributions in nuclei [14–16]. However, modelsusing a classical QCD picture of a highly relativis-tic nucleus [17,18] suggest that gluon distributions aresaturated for momenta below a scaleQs and thus re-duced compared to expectations based on perturbativeQCD [19]. As a consequence, a considerable suppres-sion of hadron production might be expected even wellaboveQs [20].

In this Letter we present the centrality dependenceof the suppression of the high-pT hadron yield to

provide new experimental constraints on theoreticaldescriptions. These data are complementary to theprevious study of the absolute yields [5] and havedifferent systematic errors.

2. Experimental setup and data analysis

The results are obtained from 1.4 × 106 minimumbias Au+ Au collisions at

√sNN = 130 GeV recorded

by the PHENIX experiment during the Run-1 opera-tion of RHIC (August–September 2000). Details onthe PHENIX detector and its configuration in Run-1operation can be found in [5,21].

In PHENIX semi-inclusive charged hadron spectraare measured over the range 0.5 < pT < 5.0 GeV/c

in the east central arm spectrometer using data froma drift chamber (DC) and two segmented cathode padchambers (PC1 and PC3), located outside of an axialmagnetic field at a radial distance of 2.2, 2.5 and 5 mfrom the beam axis. The detectors cover an azimuthalacceptance of 90◦ and a pseudo-rapidity range of|η| < 0.35. In this analysis an additional fiducialcut |η| < 0.18 is applied to guarantee homogeneoustrack acceptance for collisions within|zvtx| < 30 cmof the nominal interaction point. About∼ 25% ofthe azimuthal acceptance is covered by a time-of-flight system which allows proton identification outto 3.5 GeV/c, where the measurement is limited bystatistics [22].

A pair of beam–beam counters provides the vertexposition along the beam direction(z). Each chargedtrack is reconstructed from the DC measurements ofits projection into the bend plane of the magnetic fieldand two space points provided by PC1 and PC3. Theunphysical background, resulting from false associa-tions of drift chamber projections with pad chamberpoints, is estimated and subtracted by forming artifi-cial events with the locations of pad chamber pointsinverted around the symmetry axis of the spectrometer.Physical background from decays in flight and photonconversions close to the DC, which only partially tra-verse the field and thus mimic high momentum tracks,are removed by requiring the track to point back tothe event vertex within|zvtx| < 2.5 cm. The remainingbackground level is negligible below 4 GeV/c and lessthan 40% at 5 GeV/c; this upper estimate is includedin the systematic errors.

86 PHENIX Collaboration / Physics Letters B 561 (2003) 82–92

Fig. 1. Functions used to correct the charged particlepT spectra. Upper left panel shows the centrality dependent correctionc(Npart) and theright panel shows thepT dependent correctionc(pT ). The systematic uncertainties are indicated by the dashed lines. The two correctionsfactorize, so that for any centrality the full correction function is given byc(pT ) × c(Npart). The accuracy of this factorization is demonstratedin the lower panel. The ratio of the full correction for central collisions (top 5%) to the correction for single particle events varies by less than2% above 1 GeV/c.

Corrections of the data are determined by tracingindividual particles through a full GEANT simulation,simulating the detector response, then merging this re-sponse with that of all particles from a real event andpassing the composite event through the PHENIX re-construction software. The average track reconstruc-tion efficiency in the active detector area is larger than98% in peripheral collisions and decreases to 68± 6%for central collisions. The corresponding correction isshown on the upper left-hand side of Fig. 1. The fullcorrection also depends onpT . It is plotted for periph-eral collision on the upper right-hand side of the fig-ure. Between 0.8 and 2.5 GeV/c the correction factorvaries slowly withpT . Its value of∼ 25 corrects forgeometrical acceptance (�φ = π/4;�η = 0.36), deadareas of the detectors (45% DC, 5% PCs), and lossesdue to 2σ track matching cuts. At lowerpT the cor-rection increases reflecting the gradual loss of accep-tance. At higherpT the observed particle yield is artifi-cially increased because of the finite momentum reso-lution (δp/p � 0.6%⊕3.6%p (GeV/c)) and thereforethe correction function decreases. Since this correctiondepends on the spectral shape of the truepT distribu-tion it was determined iteratively. At 5 GeV/c the cor-

rection is reduced by a factor of∼ 2. The systematicuncertainties are indicate by the dashed lines; they arealso tabulated in Table 1. As shown in the lower part ofFig. 1 correction factorizes into functions of centrality(i.e., detector occupancy) andpT within 2% system-atic uncertainty in the range from 2 to 5 GeV/c.

Events are selected according to centrality follow-ing the procedure described in [5]. Six exclusive cen-trality bins are established using the energy mea-sured in two zero-degree calorimeters and the num-ber of charged-particles detected in the two beam–beam counters. A Monte Carlo simulation using mea-sured nucleon density distributions calculated in theGlauber eikonal approximation was used to estimatethe average number of binary nucleon–nucleon colli-sions(Ncoll) and the corresponding average number ofparticipating nucleons(Npart) for each bin. The resultsare quoted in Table 2.

3. Results

Fig. 2 presents charged hadronpT spectra for thesix centrality bins. For peripheral collisions the spectra

PHENIX Collaboration / Physics Letters B 561 (2003) 82–92 87

Table 1Upper bounds of the systematic error on thepT dependent single particle correction function

pT (GeV/c) δtrack (%) δdecay(%) δreso(%) δbgr (%) Total

1 ±13.5 +10 ±0 0 −13.5+16.42 ±13.5 +5 ±1 0 −13.7+14.43 ±13.5 +2.5 ±4 −1.6 −14.2+14.24 ±13.5 +1.25 ±9 −11.5 −20+ 165 ±13.5 +0.6 ±15 −40 −45+ 16

Here δtrack includes the uncertainties of the acceptance, dead areas, track matching cuts and the track reconstruction efficiency. Theδdecayterm accounts for the uncertainty of the decay correction. The effect of the momentum resolution contributes withδresoto the systematic error.Uncertainties due to potentially unsubtracted background are quantified byδbgr. The total systematic error given in the last column is calculatedas quadrature sum of the individual contributions. It is calculated separately for positive and negative errors.

Table 2Number of participants and binary collisions and their systematic errors for the individual centrality selections used in this analysis

Bin Relative fraction (%) Npart Ncoll Ncentralcoll /Ncoll 2Ncoll/Npart

1 80–92 5.5±2.6 4.1±1.7 246± 98 1.5± 0.52 60–80 19.5±3.5 20± 6 50.4± 13 2.1± 0.53 30–60 79± 4.6 131± 23 7.68± 1.1 3.4± 0.64 15–30 180± 6.6 406± 46 2.49±0.13 4.5± 0.55 5–15 271± 9 712± 72 1.41±0.03 5.2± 0.66 0–5 348± 10 1009± 101 1 5.8± 0.6

Also given is the ratio of the number of binary collisions for the most central sample relative to the one for each sample. The last columnquantifies the ratio of binary collisions to participant pairs.

Fig. 2. The left panel showspT spectra of charged hadrons from six Au+Au centrality selections. Error bars indicate statistical errors only. ThepT dependent systematic errors are independent of centrality and not shown, they are given in Table 1. The centrality dependent errors are lessthan 10% and small compared to the symbol size. The right panel shows the ratio of each of the centrality selectedpT spectra to the minimumbias spectrum. Ratios for peripheral selections are scaled for clarity. Dotted lines indicate the average ratios for each centrality selection.

88 PHENIX Collaboration / Physics Letters B 561 (2003) 82–92

Fig. 3. The ratio p/h represents the proton plus anti-proton yieldrelative to the total charged hadron multiplicity. The top panelshows thepT dependence of p/h for minimum bias events. Inthe bottom panel we show the centrality dependence of p/h forpT > 1.8 GeV/c. Only statistical errors are shown.

are more concave than those for central collisions.This shape difference is seen more clearly by takingthe ratio of the spectrum for each centrality bin tothe minimum-bias spectrum, as shown on the right-hand side of Fig. 2. In these ratios most systematicerrors cancel or affect the overall scale only. Theratios for the central bins are almost independent ofpT since central collisions dominate the minimumbias yields. The peripheral bins show a decreasingratio between 0.5 and 1.5 GeV/c thus in peripheralcollisions the yield in this region decreases morerapidly with increasingpT than in central collisions.ForpT above 1.5 GeV/c this trend is inverted.

Before analyzing the centrality dependence in moredetail we demonstrate that the observed suppressionof the yield at highpT does not result from a reducedyield of protons and anti-protons [22]. To evaluate theeffect of the (anti-)protons, we plot in the top panel ofFig. 3 thepT dependence of p/h, the ratio of protonplus anti-proton yields to the total charged hadron

Fig. 4. Centrality dependence of〈ptruncT

〉, the averagepT of charged

particles withpT above a thresholdpminT minus the thresholdpmin

T .

Shown are values for twopminT

cuts, one atpT > 0.5 GeV/c

representing all data presented in Fig. 2 and the other one atpT > 2 GeV/c. Only statistical errors are shown; see the textfollowing Eq. (1) for a discussion of the systematic errors.

yield for minimum bias collisions, which increasessteadily. Above 1.5 GeV/c the ratio seem to saturatereaching a value of∼ 0.5 around 3 GeV/c. In thebottom panel of Fig. 3 we show p/h for pT above1.8 GeV/c as a function of centrality. Since thereis clearly no significant decrease of the p/h ratiowith either centrality orpT , the observed hadronsuppression is not due to a larger suppression ofthe (anti-)proton component than that of the mesons.On the contrary, within the range of the presentedmeasurement the apparent slight increase in p/h withNpart could indicate a larger suppression of the mesoncomponent relative to all charged hadrons.

To evaluate the change of the hadron spectra morequantitatively we calculate the truncated averagepT :

(1)⟨ptrunc

T

⟩ ≡∫ ∞pmin

TpT dN/dpT∫ ∞

pminT

dN/dpT

− pminT

for pminT = 0.5 GeV/c and forpmin

T = 2.0 GeV/c foreach centrality selection.3 In Fig. 4 〈ptrunc

T 〉 is plot-ted as a function ofNpart. The value of〈ptrunc

T 〉 is

3 The value of〈ptruncT 〉 is closely related to the local inverse slope

which is slightly smaller. The conversion to local slope depends onthe spectral shape and also onpmin

T. For an exponential spectrum

PHENIX Collaboration / Physics Letters B 561 (2003) 82–92 89

Fig. 5. Nuclear modification factor(RAA) for the 60–80%, 30–60%, 15–30%, and 5–15% centrality selections compared to the one for themost central sample (0–5%). Due to insufficient statisticsRAA is not shown for the 80–92% sample. The solid error bars on each data point arestatistical. The systematic error between the more peripheral and the central sample are given as brackets for the more peripheral data points.The error bar on the left-hand side of each panel indicates the overall systematic error on theRAA scale.

insensitive to the normalization of the spectra. Sys-tematic uncertainties of∼ 20(50) MeV/c for pmin

T =0.5(2.0) GeV/c result from an 1–2% uncertainty onthe momentum scale and thepT dependent uncertain-ties on the correction function. Since the centrality andpT dependence of the correction factorize the erroron 〈ptrunc

T 〉 is independent of centrality to better than2 MeV/c.

The 〈ptruncT 〉 for pmin

T = 0.5 GeV/c increases withNpart similar to the averagepT of identified chargedhadrons [22]. For higherpmin

T = 2.0 GeV/c the〈ptrunc

T 〉 drops by∼ 60 MeV/c with Npart, distinctlydifferent from the expected increased role of hardparticle production in the more central collisions.Absent any collective effects, the hard scatteringcontribution should increase relative to soft productionby the factorNcoll/Npart which grows from 1.5 to∼ 6from peripheral to central collisions. Since the relativecontribution of the hard component to the spectrumincreases withpT , this should lead to a rise of〈ptrunc

T 〉

with an inverse slope of 350 MeV/c the conversion is approximately−80(−60) MeV/c for pmin

T= 0.5(2.0) GeV/c.

for sufficiently largepminT . The drop of〈pT 〉 therefore

indicates the suppression of the highpT relative to thelow pT hadron yield independent of systematic errorsassociated with the absolute normalization of thespectra or any nucleon–nucleon reference distribution.

Changes of the hadron spectra at highpT are of-ten presented in terms of the nuclear modification fac-tor RAA. This measure relies on the absolute normal-ization and a reference and therefore has intrinsicallylarger systematic uncertainties, but it allows to quan-tify the suppression. We have calculatedRAA for eachcentrality bin as:

RAA(pT ,η) =(

1

Nevt

d2NA+A

dpT dη

)

(2)×( 〈Ncoll〉

σN+Ninel

d2σN+N

dpT dη

)−1

.

For the N+ N charged hadron cross section weuse a power-law parameterization 1/π d2σ/dp2

T =A/(1 + pT /p0)

n, with A = 330 mb/(GeV/c)2, p0 =1.72 GeV/c, andn = 12.4. The parameters were ob-tained by interpolating p+ p andp̄+ p data to

√s =

130 GeV as described in [5]. In Fig. 5 theRAA(pT )

90 PHENIX Collaboration / Physics Letters B 561 (2003) 82–92

values for all centrality bins excluding the most pe-ripheral one are compared to the central (0–5%) bin.The systematic uncertainties in the normalization ofthe data, inNcoll, and in the N+ N reference (20%)result in overall systematic errors of about 41%, 34%,31%, 31% and 30% for centrality bins 2–6, respec-tively. The errors are quoted for the range from 1 to3.5 GeV/c; they increase somewhat towards higherpT . ComparingRAA for a given centrality bin to themost central bin, the systematic errors reduce to∼ 6%for bin 5 (5–15%) and nearly 27% for bin 2(60–80%).They are dominated the uncertainty inNcoll listed inTable 2.

For the 60–80% centrality bin,RAA increases withpT and reaches unity at highpT . In comparison tothe 60–80% bin, theRAA values for the most centralbin remain significantly below unity at a value of0.55 for pT > 2 GeV/c. At high pT approximatelyconstantRAA values are detected in all centralitybins. The highpT values decrease monotonically withcentrality, clearly indicating that the magnitude ofthe suppression of highpT hadrons increases withcentrality. This is shown clearly in the upper part ofFig. 6, which presentsRAA obtained for the threepT bins 1.6 to 2.6 GeV/c, 2.6 to 3.6 GeV/c, andabove 3.6 GeV/c as a function of centrality. Forcentral collisions we observe a suppression of about afactor of 2± 0.6 compared to binary collision scaling.Relative to peripheral collisions the suppression factorin central collisions increases withpT from 1.25±0.2 to 1.5 ± 0.2 to 1.8 ± 0.3 for the threepT bins,respectively.

We note that for peripheral collisions the data donot indicate a significant increase ofRAA above unity,unlike data at lower energies [23]. However, suchan increase, attributed to initial state scattering, theCronin effect [24], may well be consistent with the pe-ripheral data due to the large systematic uncertaintyof the RAA scale. While the relative difference be-tween the peripheral and central spectra increases withpT , the roughly constant nuclear modification factor atlargepT suggests an approximatelypT independentsuppression of hard scattering contributions over therange 2< pT < 4.5 GeV/c.

The physics that controls the production of high-pT particles or the suppression of the hard scatteringyields in the measuredpT range may not dependdirectly onNcoll. Thus, we have calculated a different

Fig. 6. The top panel gives the nuclear modification factorRAA

for three exclusivepT regions as a function of the centrality ofthe collision. The lower panel shows essentially the same quantitybut normalized to the number of participant pairs rather than tothe number of binary collisions. The dotted line indicates theexpectation for scaling with the number of binary collisions (top)or with the number of participants (bottom). Only statistical errorsare shown. The systematic error on the scale and the centralitydependence are identical to the errors shown in Fig. 5. Theseerrors are correlated, i.e., take their maximum or minimum valuesimultaneously for all centrality andpT selections. In addition,there are alsopT dependent systematic errors, which are given inTable 1. The systematic errors do not alter the trends in the data.

ratio, RpartAA , defined similarly toRAA but with Ncoll

replaced by the number of participant pairs,Npart/2.If particle production increases proportional to thenumber of participants,Rpart

AA = 1.The obtainedR

partAA values are shown in Fig. 6

(bottom) for the threepT bins used above. The valuesof R

partAA are larger thanRAA by a factor equal to

2Ncoll/Npart the average number of nucleon–nucleoncollisions suffered by each participant. For allpT

bins the yield per participant is consistent with unityfor peripheral collisions as expected since peripheralcollisions should closely resemble N+ N collisions.For central collisionsRpart

AA increases to approximatelythree. Most of this change occurs in the range ofNpartfrom 40 to 140. For largerNpart the yield in the highestpT bin is approximately constant while in both lowerpT bins it increases by 20 to 30%.

PHENIX Collaboration / Physics Letters B 561 (2003) 82–92 91

4. Concluding discussion

In this Letter we have presented the centrality de-pendence of charged hadronpT spectra focusing onthe behavior of the spectra at highpT . A strikingchange of the spectral shape is observed when compar-ing spectra from different centrality selections. For pe-ripheral collisions the spectrum exhibits a pronouncedconcave shape which is modified towards a more ex-ponential spectrum as the centrality increases. The ob-served lack of variation with centrality in the protonto charged ratio at large transverse momenta indicatesthat the modification is not due to a change in the rel-ative yields of protons.

We observe a decrease of〈ptruncT 〉 for pT >

2 GeV/c with increasing centrality, which is distinctlydifferent from the increase of〈pT 〉 and demonstratesthe suppression of the highpT hadron yield indepen-dent of systematic errors associated with the absolutenormalization of the spectra. The data are not con-sistent with binary collision scaling of hard scatter-ing processes, which would results in an increase of〈ptrunc

T 〉. If the pT spectra above 2 GeV/c are stronglyaffected by collective motion of matter before freeze-out, we would also expect an increase〈ptrunc

T 〉 sincethe corresponding flow velocities should increase inmore central collisions [25]. Similarly, if gluon satu-ration is important for particle production in thepT

range above 2 GeV/c, 〈ptruncT 〉 should increase with

increasingNpart due to the predicted logarithmic in-crease ofQs [26]. In contrast, the data are consistentwith models assuming energy loss of hard scatteredpartons, which results in an increasing reduction ofthe hard scattering contribution to the hadron spectrumwith increasing centrality of the collisions [7–9]. It re-mains to be seen whether this explanation is unique.

Comparing the measured differential yields in fivecentrality bins to anNcoll scaling of the N+ Nreference yields we see a suppression of the yieldsin central collisions at highpT , consistent with theresults in [5,6]. In the 0–30% centrality range (bins1–3) the suppression is approximately independentof pT for 2 < pT < 5 GeV/c at a value ofRAA ∼0.6 and simultaneously nearly independent within20% of centrality. The suppression sets in graduallywith the largest change occurring over the 30–60%centrality range. This centrality bin covers a broadrange of collision geometries. Whether the change

is continuous or exhibits a threshold behavior, aspredicted in [27], cannot be judged from the presentdata. The observed suppression is consistent withparton energy loss scenarios. In these models, thevalue ofRAA and itspT dependence are very sensitiveto the actual energy loss prescription. Due to the largesystematic errors on theRAA scale, the contributionfrom the protons and the limitedpT reach of thedata presented here, we cannot distinguish between thedifferent energy loss prescriptions on the basis ofRAA.

In summary, a detailed analysis of the centrality de-pendence of charged particle data from Au–Au col-lisions at

√sNN = 130 GeV measured by PHENIX

reveals interesting features of the observed highpT

hadron suppression. The decrease of the averagepT

with increasing centrality seems to favor models ofparticle production that consider energy loss effects,rather than saturation- or hydrodynamics-based ap-proaches for thispT range. The suppression sets ingradually with the largest changes occurring for pe-ripheral collisions with less than about 140 participat-ing nucleons. From there on it does not change sub-stantially towards more central collisions.

Note added in proof

After submission of our manuscript, data fromAu–Au collisions at

√sNN = 200 GeV were presented

by the PHOBOS Collaboration [28,29], with an em-phasis on the lack of variation in the scaled yields withNpart for Npart> 65. Keeping in mind that results fromdifferent energies are not directly comparable, we notethat the broader range inNpart presented here showsthat this effect does not apply over the entire range ofcentralities, and that when normalized with the appro-priate p–p yields, is simply an aspect of the smoothvariation ofRpart

AA visible in Fig. 6.

Acknowledgements

We thank the staff of the Collider-Accelerator andPhysics Departments at BNL for their vital contribu-tions. We acknowledge support from the Departmentof Energy and NSF (USA), MEXT and JSPS (Japan),RAS, RMAE, and RMS (Russia), BMBF, DAAD,and AvH (Germany), VR and KAW (Sweden), MIST

92 PHENIX Collaboration / Physics Letters B 561 (2003) 82–92

and NSERC (Canada), CNPq and FAPESP (Brazil),IN2P3/CNRS (France), DAE and DST (India), KRFand CHEP (Korea), the US CRDF for the FSU, andthe US-Israel BSF.

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