10Nuclear Physics Institute AS CR, 250 68Řež/Prague, Czech Republic11Laboratory for High Energy (JINR), Dubna, Russia12Particle Physics Laboratory (JINR), Dubna, Russia
13University of Frankfurt, Frankfurt, Germany14Institute of Physics, Bhubaneswar 751005, India
15Indian Institute of Technology, Mumbai, India16Indiana University, Bloomington, Indiana 47408, USA
17Institut de Recherches Subatomiques, Strasbourg, France18University of Jammu, Jammu 180001, India
19Kent State University, Kent, Ohio 44242, USA20Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
21Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA22Max-Planck-Institut für Physik, Munich, Germany
23Michigan State University, East Lansing, Michigan 48824, USA24Moscow Engineering Physics Institute, Moscow, Russia
25City College of New York, New York City, New York 10031, USA26NIKHEF, Amsterdam, The Netherlands
27Ohio State University, Columbus, Ohio 43210, USA28Panjab University, Chandigarh 160014, India
29Pennsylvania State University, University Park, Pennsylvania 16802, USA30Institute of High Energy Physics, Protvino, Russia
31Purdue University, West Lafayette, Indiana 47907, USA32University of Rajasthan, Jaipur 302004, India33Rice University, Houston, Texas 77251, USA
34Universidade de Sao Paulo, Sao Paulo, Brazil35University of Science & Technology of China, Anhui 230027, China
36Shanghai Institute of Applied Physics, Shanghai 201800, China37SUBATECH, Nantes, France
38Texas A&M University, College Station, Texas 77843, USA39University of Texas, Austin, Texas 78712, USA
40Tsinghua University, Beijing 100084, China41Valparaiso University, Valparaiso, Indiana 46383, USA
42Variable Energy Cyclotron Centre, Kolkata 700064, India43Warsaw University of Technology, Warsaw, Poland
44University of Washington, Seattle, Washington 98195, USA45Wayne State University, Detroit, Michigan 48201, USA
46Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China47Yale University, New Haven, Connecticut 06520, USA
48University of Zagreb, Zagreb, HR-10002, Croatia(Received 15 April 2004; published 6 October 2004)
We present STAR measurements of charged hadron production as a function of centrality in Au+Au colli-sions atÎsNN=130 GeV. The measurements cover a phase space region of 0.2,pT,6.0 GeV/c in transversemomentum and −1,h,1 in pseudorapidity. Inclusive transverse momentum distributions of charged hadronsin the pseudorapidity region 0.5, uhu,1 are reported and compared to our previously published results foruhu,0.5. No significant difference is seen for inclusivepT distributions of charged hadrons in these twopseudorapidity bins. We measureddN/dh distributions and truncated meanpT in a region ofpT.pT
cut, andstudied the results in the framework of participant and binary scaling. No clear evidence is observed forparticipant scaling of charged hadron yield in the measuredpT region. The relative importance of hard scat-tering processes is investigated through binary scaling fraction of particle production.
Quantum chromodynamics(QCD) is considered to be theunderlying theory of the strong interaction which governshadron production in nuclear collisions. The strong interac-tion is usually divided into soft processes, which involvesmall momentum transfer, and hard processes, which can becalculated using perturbative QCD. The Relativistic HeavyIon Collider(RHIC) experiments at the Brookhaven NationalLaboratory investigate the properties and evolution of matterat high temperature and energy density. At RHIC energies,the hard processes become more evident in comparison toprevious heavy ion experiments and can be used to probe theearly state of the collision system. A high energy parton pro-duced via hard scattering may lose energy in the hot/densemedium through gluon bremsstrahlung and multiple scatter-ings before hadronization[1,2], leading to a suppression ofhigh pT hadron production. The magnitude of the energy lossprovides an indirect signature of QGP formation. Since par-ton energy loss is directly proportional to gluon density, theenergy loss would be much larger in a partonic medium thanin hadronic matter[3].
Partonic energy loss can be investigated through compari-son of hadron yield as a function ofpT between nucleus-nucleus collisions andp+p or p̄+p collisions. In order to doso, scaling factors which account for the nuclear geometry,the number of participant nucleons,Npart, and the number ofbinary nucleon-nucleon collisions,Nbin, are calculated fromtheoretical models. Experimental results from the RHIC, in-cluding our earlier analyses in the pseudorapidity regionuhu,0.5, have indicated a suppression of hadron productionfor pT.2 GeV/c in central Au+Au collisions relative top+p and p̄+p collisions [4–6]. This is in contrast to the SPSresult from central Pb+Pb collisions atÎsNN=17 GeV,which shows an excess ofp0 production for2,pT,4 GeV/c [7,8]. The RHIC measurements are strik-ing considering that known nuclear effects, like the Cronineffect [9] and radial flow[10], tend to enhance hadron yieldsat highpT. The RHIC results for highpT hadron suppressionagree qualitatively with calculations based on fragmentationmodels, which attribute the highpT hadron suppression tomedium induced parton energy loss[11].
Another known nuclear effect, nuclear shadowing, alsomodifies particle production at highpT. Calculations of thiseffect [12] based on the EKS98 shadowing parametrization[13] predicted it to be small in thepT and pseudorapidityregion covered in this measurement. However, another study[14] found a much larger shadowing effect for heavy nucleiat the RHIC. Therefore, a measurement of particle produc-tion as a function ofpT and pseudorapidity may provide aconstraint on the shadowing effect.
Partonic energy loss may also be studied by the pseudo-rapidity dependence of hadron production. The change ofpseudorapidity due to change of momentum is
dh =pz
pSdpz
pz−
dpT
pTD . s1d
The pseudorapidity distributions will be modified as a resultof the parton energy loss if the momentum change rate
sdp/pd due to the energy loss is different along the transverseand longitudinal directions. In addition, Polleri and Yuan[15] pointed out that the degree of the energy loss may alsodepend on the pseudorapidity region in which a jet is pro-duced because the energy loss is proportional to the particledensity in pseudorapidity. The pseudorapidity dependence ofhigh pT hadron production provides a means to probe theinitial density of matter along both the transverse and longi-tudinal directions.
In this article, we present measurements of hadron pro-duction in Au+Au collisions atÎsNN=130 GeV as a functionof centrality,pT, andh. In Sec. II we will briefly describe theSTAR experimental setup and then give a description of dataanalysis techniques that were used to obtain the inclusivetransverse momentum distributions for charged hadrons. Wewill also discuss the parametrization of inclusive transversemomentum distributions inp+p collisions atÎs=130 GeVand the calculations ofNpart andNbin. In Sec. III results fromthe data analysis will be reported and compared with modelcalculations. The physics implications of our measurementsare discussed in Sec. IV, and we will then summarize ourmeasurements in Sec. V.
II. ANALYSIS
A. Experimental setup and data
Measurements presented in this article are based on twodata sets of Au+Au collisions atÎsNN=130 GeV, whichwere recorded by the STAR detector at the RHIC. A detaileddescription of the STAR detector can be found elsewhere[16]. The two data sets comprise minimum bias and centralcollision triggered events which correspond to approximatelythe most central 10% of the Au+Au geometric cross section.Charged particle tracks of an event were detected in the timeprojection chamber[17] (TPC) with a pseudorapidity cover-age uhu,1.8 and complete azimuthal symmetry. The trans-verse momentum of a track is determined by fitting a circlethrough the transverse coordinates of the primary event ver-tex and the space points along the track in the TPC. The totalmomentum can be calculated using this radius of curvaturein a 0.25 T magnetic field and the polar angle of the track.The procedure involves a three-dimensional fit using threecoordinates of the primary vertex determined from all of thetracks reconstructed in the TPC. The primary vertex positionalong the beam direction,zvtx, has a wide spread with onestandard deviation about 100 cm. To increase detection effi-ciency of the tracks withinuhu,1, we required the events tohave a primary vertexuzvtxu,75 cm. After the event selectioncuts, the minimum bias data set contained,181 k eventsand the central data set contained,365 k events.
Centrality selection is based on the uncorrected primarycharged particle multiplicity Nch within uhu,0.75 andpT,1.5 GeV/c. The requirement on theh range maximizesthe number of tracks used to define centrality in an eventwhile keeping the tracking acceptance approximately con-stant. The percentage of the geometric cross section is deter-mined in the same way as that published by STAR previ-ously [18], where the negatively charged hadron multiplicityNh− distribution within uhu,0.5 was used. The data set is
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divided into seven centrality bins, and the most central bin is(0–5)% (the top 5% of the multiplicity distribution) while themost peripheral bin is(60–80)%.
The analysis in this article covers a transverse momentumregion of 0.2,pT,6.0 GeV/c. Accepted primary trackshaveuhu,1, at least 25 space points in the TPC used in thetrack fit out of 45 pad rows, a fit probability of being aprimary track greater than 0.05, and a distance of closestapproach to the primary vertex less than 1 cm. These trackquality cuts were varied to estimate the systematic uncer-tainty. Acceptance and efficiency were determined by em-bedding simulated tracks into actual Au+Au collisionevents.
The measured highpT hadron yield is sensitive to smallspatial distortions of the TPC alignments in both azimuthaland longitudinal directions. A measurement of the summedhadron yieldsh++h−d /2 is less sensitive to such distortionsthan the yield of one charge sign alone. We call such distor-tion the charge-sign-dependent distortion. Using 12 sectorsfrom each of the TPC ends as independent detectors for highpT hadrons, we estimated the sectorwise(azimuthal direc-tion) variations of the yields to be less than 5%. The varia-tion of the yield between the hadrons crossing and not cross-ing the central membrane of the TPC was found to beapproximately proportional topT with a value of 11% atpT=5.5 GeV/c. The typical correction factors for the accep-tance and efficiency are given in Table I as “Tracking.” Thesystematic uncertainties incorporate acceptance, efficiency,track quality cuts, and the effects of the spatial nonunifor-mity. The tracking and other correction factors and their sys-tematic uncertainties given in Table I foruhu,0.5 differ fromthose given in our previous paper[4] because different trackquality cuts and other correction procedures were used.
Finite momentum resolution tends to spread particles toneighboring bins in a momentum histogram, especially foran exponentially falling spectrum. This smearing effect can-not be neglected at higherpT where the momentum resolu-tion is limited by the strength of the magnetic field and theTPC spatial resolution. We used the embedding technique todetermine thepT resolution. For pT.0.5 GeV/c withinuhu,0.5 the Gaussian distribution of track curvaturek~1/pT has a relative width of dk/k=0.013+0.015pT/ sGeV/cd for central events anddk/k=0.012+0.012pT/ sGeV/cd for peripheral events. Within0.5, uhu,1,dk/k=0.014+0.010pT/ sGeV/cd for central
events anddk/k=0.014+0.0072pT/ sGeV/cd for peripheralevents.
The fact that thepT resolution for 0.5, uhu,1 is betterthan that foruhu,0.5 is due to the competition between twoopposing effects. For a givenpT track in the TPC, the hadronwith higherh tends to have fewer space points, hence poorerresolution, but shorter drift distance, hence better resolution.
The magnitude of thepT resolution determined from theembedding technique did not include the effect of the pri-mary vertex resolution. The effects of thepT smearing due tothe primary vertex resolution, to the charge-sign-dependentdistortion, and to the weak decay background tracks havebeen empirically derived from the comparison between realand embedded tracks. The combined effect within0.5, uhu,1 was found to be larger than that withinuhu,0.5.This is partially due to the fact that the magnitude of thecharge-sign-dependent distortion in the higherh region islarger.
The two contributions to thepT smearing investigatedabove have been convoluted into a power law function to fitthe data, and then the ratio of the fitted function to its con-voluted one gives thepT smearing correction factor[19].Because the two contributions have oppositeuhu dependence,the overallpT smearing correction factors for the twoh re-gions happen to be comparable. The typicalpT smearing cor-rection factors and their systematic uncertainties are alsogiven in Table I.
B. Background
The most significant backgrounds for the highpT chargedhadron yield as seen in Table I come from particle weakdecays and antinucleon annihilation in detector material. Thecontamination rate for each background source was esti-mated using detector response simulations with events gen-erated by the HIJING model[20]. However, thepT depen-dence of production of weakly decaying particles, primarily
KS0,L ,L̄, and of antinucleonsp̄,n̄ in HIJING is not consis-
tent with experimental measurements. We corrected thosepredicted yields using the measured spectra ofp̄ [21,22], L
and L̄ [23], andKS0 [24], together with those ofh− [18,21],
for pT,2.4 GeV/c in the midrapidity region in the mostcentral bin. The corrections used in calculating the back-ground fractions are shown in the upper panel of Fig. 1. Thecurves are polynomial fits to the data points and are used in
TABLE I. Typical multiplicative correction factors and systematic uncertainties, applied to the yields forperipheral and central collisions withinuhu,0.5 and within 0.5, uhu,1.
the interpolation due to differentpT binning. ForpT.2.4 GeV/c we simply assumed the yield ratios to beconstant[25]. Systematic uncertainties of 50% and 100% ofthe overall background fraction are assigned for the regionsof pT,2.4 GeV/c andpT.2.4 GeV/c, respectively[19].
The contamination rate for all background sources showsalmost no centrality dependence from the Monte CarloHIJING events. Therefore, the centrality dependence of thebackground fraction is mainly determined by the measuredspectra in various centrality bins. In the lower panel of Fig. 1we show the measured transverse masssmT=ÎpT
2+m02d in-
verse slope parameters of exponential fits top̄ [22], L andL̄[23], andKS
0 [24] spectra in the midrapidity region as func-tions of the measured negatively charged hadron multiplicityNh− within uhu,0.5. We use these to correct for differentcentrality binning in our analysis. The polynomial fits areused to interpolate the inverse slope parameters in the cen-trality bins used in this analysis.
Pseudorapidity dependence of the background fraction isstudied using the Monte Carlo HIJING events. ForpT,2 GeV/c theh dependence of backgrounds is negligiblewithin −1,h,1 while for pT.2 GeV/c the backgroundfraction decreases with increasingpT anduhu. For example, atpT=5.5 GeV/c the background fraction predicted within0.5, uhu,1 is only 40% of that withinuhu,0.5. The typicalbackground correction factors and their systematic uncertain-ties are given in Table I. The total systematic uncertainties ofthe measured spectra withinuhu,0.5 s0.5, uhu,1d at thehighest binpT=5.5 GeV/c are <24% s<18%d for centralevents and<17% s<15%d for peripheral events.
C. NN reference
In the absence of anyNN collision data atÎs=130 GeV, aNN reference spectrum is obtained by extrapolation of theUA1 p̄+p data forÎs=200–900 GeV[26]. The UA1 inclu-sive charged particlepT spectra withinuhu,2.5 were fittedby the perturbative QCD(PQCD) inspired power law func-tion
1
2ppT
d2N
dpTdh= CS1 +
pT
p0D−n
. s2d
The fit parameters were used to extrapolate to our energy,giving Csin=267−6
+4 mb/sGeV/cd2 (sin denotes the inelasticcross section ofNN collisions), p0=1.90−0.09
+0.17 GeV/c, andn=12.98−0.47
+0.92 at Îs=130 GeV [4]. The superscripts and sub-scripts are curves that bound the systematic uncertainty.
However, the UA1 acceptance is different from STAR’s.Corrections were made to the UA1 reference for ourhacceptance based on two independent PQCD calculations:those of PYTHIA[27] and Vitev[28]. When theK factor inPYTHIA is set to 1.5, PYTHIA calculations for 200 GeVp̄+p collisions are in reasonable agreement with the UA1measurement of the inclusive charged particlepT spectrum[26] and with the UA5 measurement of the pseudorapiditydensity distribution[29]. Similar PYTHIA calculations are inreasonable agreement with the STAR measurement of theinclusive charged hadronpT spectrum withinuhu,0.5 for p+p collisions at Îs=200 GeV [5]. Figure 2 shows thepT-dependent correction functions for twoh regions atÎs=130 GeV, obtained by averaging over the two PQCD cal-culations. The solid curve is the ratio ofd2N/dpTdh withinuhu,0.5 to that withinuhu,2.5, and the shaded area showsits systematic uncertainty. The dot-dashed curve shows thesame ratio for 0.5, uhu,1, and the similar magnitude of theuncertainty on the ratio of 0.5, uhu,1 to uhu,2.5 is notshown. Multiplicative corrections of 1.35±0.09 and1.33±0.09 at pT=5.5 GeV/c have been obtained foruhu,0.5 and for 0.5, uhu,1, respectively. The differencebetweenuhu,0.5 and 0.5, uhu,1 is quite small, indicatinga relatively flath distribution within −1,h,1 for a broad
FIG. 1. Measurements used in background studies. Upper panel:ratios of the measuredpT yield ratios to those of HIJING in themost central bin. Lower panel: measuredmT inverse slope param-eters as functions of centrality represented by measured negativelycharged hadron multiplicityNh− within uhu,0.5. Curves are poly-nomial fits to data points.
FIG. 2. h acceptance correction function from model calcula-tions: ratios ofpT spectra in two differenth regions to that withinuhu,2.5, in which the UA1 Collaboration published its inclusivecharged particlepT spectra.
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pT region. The STAR measurement[5] is consistent with theUA1 p̄+p data for 200 GeV after applying a similarh ac-ceptance correction.
We derivedsin in the NN reference atÎs=130 GeV of40±3 mb by requiringdN/dh suhu,0.5d, which was ob-tained by integrating the extrapolated spectrum after apply-ing the h acceptance correction, to be 2.25, which was de-termined from the energy dependence ofdN/dh sh=0d [30].
D. Participant and binary collision determination
The number of participant nucleons,Npart, and the numberof binary nucleon-nucleon collisions,Nbin, in a nucleus-nucleus collision are used to compare experimental resultswith model predictions. Unfortunately, at RHICNpart andNbin cannot be measured directly and have to be obtained ina model-dependent way. Considerable discrepancy existsamong various model calculations, especially for peripheralcollisions [31].
We first investigateNpart andNbin obtained from a MonteCarlo (MC) Glauber model calculation[4,32]. In the MonteCarlo Glauber model, each of the nucleons in a nucleusA israndomly distributed using a Woods-Saxon nuclear densitydistribution
rsrd =r0
1 + expfsr − r0d/Dg, s3d
with normalization toersrddr=A and parameters nuclear ra-dius r0 and surface diffusenessD. All nucleons in eithernucleus for a nucleus-nucleus collision are required to beseparated by a minimum distance. The calculatedds /dNpartor ds /dNbin distribution was divided into bins correspondingto common fractions of the total geometric cross section toextract the averageNpart or Nbin for each centrality bin. Thesystematic uncertainties onNpart andNbin were estimated byvarying the Woods-Saxon parameters, by varying thesinvalue, and by including a 5% uncertainty in the determina-tion of the total geometric cross section.
We also investigate calculations ofNpart and Nbin usingtwo dynamic models, HIJING[20] and VENUS [33]. We
compare these calculations with results from the MonteCarlo Glauber model calculation to shed light on the model-dependent uncertainties ofNpart andNbin.
The VENUS model is based on the Gribov-Regge theoryand string fragmentation. The HIJING generator is an ex-ample of a two-component model: the momentum transfer ofthe soft process is treated phenomenologically and the hardprocesses are calculated by PQCD. The excited nucleons af-ter collisions are stretched out as quark-diquark strings andfragments based on the Lund fragmentation scheme[34].The parton energy loss in a dense medium(quenching) andnuclear modification of parton structure functions(shadow-ing) are also modeled in HIJING.
Both dynamic models describe nuclear collision geometryusing the Woods-Saxon nuclear density distribution and theeikonal formalism to determine the probability for each bi-nary nucleon-nucleon collision, and to computeNpart andNbin. Table II shows the comparisons of the nuclear geom-etries implemented in HIJING, VENUS, and the MonteCarlo Glauber model for Au+Au collisions atÎsNN=130 GeV. The overlap function, which defines the prob-ability for a nucleon-nucleon collision at a given impact pa-rameterb, has the form of 1−expf−2Vsbdg in HIJING withVsbd defined in Table II[m0=3.9 andpb0
2ssd=ssoftssd /2]while it is a step functionusR−bd in VENUS and MCGlauber.
The correspondence between the centrality classes definedby measured charged particle multiplicity and those definedby modeled impact parameter was used to extract the aver-age Npart and Nbin from these dynamic models for a givencentrality bin. Variations of averageNpart andNbin for differ-ent centrality selections were estimated using the MonteCarlo events from the HIJING model. The event classes cor-responding to the same fractional cross section were selectedby cuts onb,Nch,Npart, andNbin. The averageNpart andNbinby different cuts in HIJING are consistent within 2% foreach centrality bin except the(60–80)% most peripheral bin,where the discrepancy is at a level of 6%.
The results ofNpart andNbin from the models are shown inFig. 3 as their ratios toNpart or Nbin from the Monte CarloGlauber calculation. The participant scaling exponentsa,
TABLE II. Comparisons of nuclear geometries implemented in various models for 130 GeV Au+Aucollisions.
Model HIJING 1.35 VENUS 4.12 MC Glauber
Woods-Saxonparameters
r0=6.38 fmD=0.535 fm
r0=6.64 fmD=0.540 fm
r0=6.5±0.1 fmD=0.535±0.027 fm
Minimum distanceof two nucleons
0.4 fm 0.8 fm 0.4 fm
Nucleon-nucleonoverlap function
Vsbd=s1+sjet/ssoftdx0sjdj=b/b0ssd x0sjd=m0
2sm0jd3K3sm0jd /96usR−bd usR−bd
Maximum impactparameter
25.6 fm 24.1 fm No restriction
Nucleon-nucleoncross sectionsin
38.7 mb 37.4 mb 41±1 mb
Total geometriccross section
7.27 b 7.34 b 6.9±0.4 b
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which are defined in the expression ofNbin=B·Nparta , were
obtained by fit to be 1.41±0.08,1.34±0.08, and 1.38±0.08for HIJING, VENUS, and MC Glauber. The scaling expo-nentsa for these models are approximately 4/3 due to thefact thatNpart~A1 andNbin~A4/3.
It is worthwhile to note here that distribution differencesamong HIJING and VENUS are mainly due to differentoverlap functions. TheNpart andNbin distributions from themare nearly identical if the same overlap functions are used inthese two model calculations. Figure 3 shows that over abroad range of centrality the model-dependent uncertaintiesof Npart andNbin are within 10% and 20%, respectively.
III. RESULTS
Inclusive pT distributions of sh++h−d /2 within uhu,0.5have been published previously[4]. The independent analy-sis reported in this article shows that the differences from thepublished results for all measuredpT points are within 10%,which is comparable to the systematic uncertainties forpT,2 GeV/c and is less than the systematic uncertaintiesfor the highpT region. Figure 4 shows inclusivepT distribu-tions of sh++h−d /2 within 0.5, uhu,1 for various centralitybins. The error bars are the quadrature sum of statistical errorand systematic uncertainty, and are dominated by the latterexcept for the highestpT point in the peripheral bins. Thecurves in Fig. 4 are power law function[Eq. (2)] fits to thespectra.
Figure 5 shows ratios ofpT distributions within0.5, uhu,1 to those withinuhu,0.5 in various centralitybins. Note that Fig. 5 and the succeeding figures utilize thepT distributions withinuhu,0.5 obtained here. Using identi-
cal cuts and correction procedures across the full pseudora-pidity region minimizes the systematic uncertainties in therelative comparisons. The error bars in Fig. 5 show statisticalerrors only while the caps are the quadrature sum of statisti-cal errors and systematic uncertainties which cannot be can-celed out. Remaining systematic uncertainty includes thevariation due to track quality cuts, the uncertainties of thepTsmearing corrections for the twoh regions, and the partialuncertainty of background subtraction related to theh-dependent part discussed in Sec. II.
FIG. 3. Ratio of the number of participants,Npart (upper panel),or the number of binary collisions,Nbin (lower panel), determinedfrom different models to that from a Monte Carlo Glauber calcula-tion. Shaded areas show the uncertainties ofNpart or Nbin from theMonte Carlo Glauber calculation. Curves are to guide the eye.
FIG. 4. Inclusive pT distributions of sh++h−d /2 within0.5, uhu,1. Noncentral bins are scaled down by the indicated fac-tors. The combined statistical and systematic errors are shown.Curves are fits to the power law function. Tick marks at the topindicate bin boundaries forpT.1.5 GeV/c.
FIG. 5. Ratios ofpT distributions within 0.5, uhu,1 to thosewithin uhu,0.5 in various centrality bins. Error bars show statisticalerrors while caps are the quadrature sum of statistical errors andremaining systematic uncertainties.
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Figure 6 shows the same ratio of 0.5, uhu,1 to uhu,0.5in the (0–5)% most central bin. The points are our measure-ments and the error bars include statistical and remainingsystematic uncertainties. The solid curve is the same ratiofrom PYTHIA calculations[27] for 130 GeVp+p collisions.Other curves are ratios from HIJING predictions of 130 GeVAu+Au collisions without shadowing and without quenching(dotted curve), with shadowing and without quenching(dashed curve), and with shadowing and with partonic en-ergy loss being 2.0 GeV/fm(dot-dashed curve). The resultsshow that the effects on the pseudorapidity dependence ofboth nuclear shadowing and partonic energy loss as imple-mented in HIJING are too small to be tested in the measuredkinematic region under current experimental uncertainties.
No significant differences are observed in the compari-sons of the inclusive charged hadron yields between the twoh regions in Fig. 5 and Fig. 6 over a broad range of centralityfor all measuredpT points. It suggests that an approximateboost invariant condition might be established in the earlystage of collisions. The suppression pattern of the particleyield has littleh dependence in the measured region thoughthe particle yield itself is sensitive to partonic energy loss. Ameasurement of this ratio betweenh=2.2 andh=0 from theBRAHMS Collaboration shows that the ratio is below unityat pT,4 GeV/c [35].
Figure 7 showsdN/dh distributions for pT.2 GeV/cand −1,h,1 in various centrality bins. The error barsshow statistical uncertainties while the caps are the quadra-ture sum of statistical and systematic uncertainties. The sys-tematic uncertainties are dominant and highly correlated. ThedN/dh distributions are scaled byNbin and divided by theNN reference. Due to nearly completeh independence of theNN reference data forpT.0.2 GeV/c within −1,h,1 asshown in Fig. 2 and Fig. 6, constantdN/dh values of theNNreference are used in Fig. 7. Therefore, the shapes of the
dN/dh distributions for the Au+Au collisions are preserved.The uncertainties on bothNbin and theNN reference data areshown in the shaded regions around the lines at unity whichrepresent the binary collision scaling. Ratios below unity inthe figure show that the highpT hadrons over 2 GeV/c aresuppressed with respect to those inp+p collisions. Theshape ofdN/dh for the high pT hadrons is nearly flat. Nosignificant centrality dependence of thedN/dh shapes within−1,h,1 is observed. Similar behaviors are observed forpT.4 GeV/c except larger suppressions in the central bins.For example, in the(0–5)% most central bin, the averageratio is 0.41±0.10 forpT.4 GeV/c while it is 0.64±0.10for pT.2 GeV/c.
IV. DISCUSSION
The charged hadron yield per participant pair atÎsNN=130 GeV shows a slow increase as a function ofNpart[4,36,37]. Such a slow increase of hadron multiplicity as afunction of centrality at the RHIC has been considered byKharzeevet al. [38] in the framework of parton saturation.They argued that the hadron multiplicity as a function ofcentrality would increase faster if the produced jets lose en-ergy, radiating soft gluons that in turn fragment into hadronsat midrapidity. As a result of the parton saturation, it is pre-dicted that hadron multiplicity should scale withNpart at amoderately highpT (up to 6–8 GeV/c at RHIC energies).An explanation of the slower than expected increase in frag-mentation models is that the effective energy loss is signifi-cantly reduced in a thermal environment due to detailed bal-ance[8]. Recent experimental results ind+Au collisions atÎsNN=200 GeV support the idea that the suppression of highpT hadron production in Au+Au collisions at midrapidity isdue to final state interactions rather than parton saturation inthe initial state[35,39].
FIG. 6. Ratio of pT distribution within 0.5, uhu,1 to thatwithin uhu,0.5 in the 0–5% most central bin. Points are measure-ments and error bars include statistical and remaining systematicuncertainties. Curves are described in the text.
FIG. 7. dN/dh distributions forpT.2 GeV/c and −1,h,1scaled byNbin and divided by theNN reference.
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In the upper panel of Fig. 8, we plot charged hadron yieldper participant pair withinuhu,1 normalized to that ofnucleon-nucleon collisions as a function ofNpart for pT=2.05 GeV/c. The error bars are the uncertainties of datawhile the caps are the quadrature sum of the uncertainties ofboth data andNpart. The shaded regions around unity showsystematic uncertainties of theNN reference data. The resultshows that the ratio is above unity and increases withNpart.
Dependence of the charged hadron yield onNpart can bestudied by fitting the yield by the following function:
d2N
dpTdh= B ·Npart
n s4d
in different pT bins. Such an example is shown as a curve inthe upper panel of Fig. 8 forpT=2.05 GeV/c. The fit param-eternspTd is given in the lower panel of Fig. 8 as a functionof pT. The error bars are the uncertainties of the fit param-eters associated with the uncertainties of data. The lines andshaded regions are binary collisionsNbind and participantsNpartd scaling exponents and uncertainties toNpart. No clearevidence of participant scaling over the whole measuredpTregion is observed. The approximate participant scaling ofthe hadron yield at highpT observed by PHOBOS[40] ap-pears to be accidental.
In a scenario with continuous energy loss of particlesthrough a medium, the energy loss would lead to a shift inthe meanpT of these particles. If the energy loss contributesto additional particle production in the lowpT region, themeanpT of low pT particles will also be modified. The trun-cated meanpT, defined as
kpTtrunclspT
cutd =epT
cut` pT ·dN/dpT ·dpT
epTcut
` dN/dpT ·dpT
− pTcut, s5d
is used to study the variation of meanpT as a function ofpTscale with respect toNN reference data. Figure 9 shows thetruncated meanpT ratios between Au+Au andp+p colli-sions as a function ofpT
cut for central[(0–5)%] and peripheral[(60–80)%] collisions. The errors are combined statisticaland systematic uncertainties while the caps are the quadra-ture sum of the uncertainties of both the Au+Au data and theNN reference data.
In peripheral collisions at highpT spTcut*3 GeV/cd the
truncated meanpT of particles is approximately the same asfor p+p collisions above the samepT
cut (Fig. 9). The ratio inthe low pT region is above unity indicating the effects of theCronin effect and/or radial flow in peripheral collisions. Forcentral collisions, the truncated meanpT for pT
cut*3 GeV/cis approximately 15% lower than the truncated meanpT fromp+p collisions at the samepT
cut, consistent with the scenariofor partonic energy loss in thispT region. The significantlylarger ratio in the lowpT region probably reflects the com-bined effects of larger radial flow, the Cronin effect, andpTshift of particles due to energy loss, which cannot be decou-pled with the present data.
Figure 8 (bottom panel) indicates that over a broadpTregion particle production falls between participant and bi-nary scalings. In two-component particle production models,the binary scaling has been associated with hard parton scat-terings and the participant scaling with the soft processes. Inour study we empirically decompose the particle yield intoNpart andNbin scaling components, i.e.,
dN/dhspTcutd = f1 − xspT
cutdgnppspTcutd ·
Npart
2
+ xspTcutdnppspT
cutd ·Nbin, s6d
where nppspTcutd and xspT
cutd are the hadron multiplicity andthe fraction of particle yield attributable to hard processes inp+p collisions, respectively. Figure 10 shows the binary
FIG. 8. Upper panel: ratio of charged hadron yields withinuhu,1 for Au+Au relative to theNN reference, scaled byNpart/2 asa function of centrality for apT bin atpT=2.05 GeV/c. The curve isfitted to B·Npart
n . Lower panel: participant scaling exponentn ofcharged hadron yields as a function ofpT within uhu,1.
FIG. 9. Ratio of truncated meanpT in pT.pTcut within uhu,1 as
a function ofpTcut for central and peripheral collisions.
CENTRALITY AND PSEUDORAPIDITY DEPENDENCE OF… PHYSICAL REVIEW C 70, 044901(2004)
044901-9
scaling fraction in Au+Au collisions, defined as
FspTcutd =
xspTcutdnppspT
cutd ·Nbin
dN/dhspTcutd
. s7d
Note thatFspTcutd does not depend onnppspT
cutd since bothnumerator and denominator of Eq.(7) contain nppspT
cutd.There is a distinguishable trend as a function ofNpart frompT
cut=3.8 GeV/c to lower pTcut. This trend is consistent with
the nspTd dependence in Fig. 8. It is worth noting thatF
<70% in central Au+Au collisions atpTcut=3.8 GeV/c.
However, one should exercise caution when relating thisfraction to hard parton scattering processes, particularly atlower pT where highpT particles may suffer large energylosses in the medium and become soft.
V. CONCLUSION
We have presented inclusive distributions ofsh++h−d /2from STAR at the RHIC in the region 0.5, uhu,1 and com-pared them to distributions foruhu,0.5, finding no signifi-cant differences in the region of 0.2,pT,6.0 GeV/c. Wefind that thedN/dh distributions for −1,h,1 are nearlyflat for all centralities. The charged hadron yield as a func-tion of pT shows no clear participant scaling in the measuredpT region. The binary scaling fraction in the two-componentmodel shows a decrease with centrality forpT
cut.2 GeV/cand is about 70% atpT
cut=3.8 GeV/c for central collisions.
ACKNOWLEDGMENTS
We thank the RHIC Operations Group and RCF at BNL,and the NERSC Center at LBNL for their support. This workwas supported in part by the HENP Divisions of the Office ofScience of the U.S. DOE; the U.S. NSF; the BMBF of Ger-many; IN2P3, RA, RPL, and EMN of France; EPSRC of theUnited Kingdom; FAPESP of Brazil; the Russian Ministry ofScience and Technology; the Ministry of Education and theNNSFC of China; SFOM of the Czech Republic; FOM andUU of the Netherlands; DAE, DST, and CSIR of the Gov-ernment of India; and the Swiss NSF.
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