aa r X i v : . [ nu c l - e x ] M a r Jet quenching in QCD matter: from RHIC to LHC
David d’Enterria
LNS, MIT, Cambridge, MA 02139-4307, USA
Abstract
The current experimental and theoretical status of hadron and jet production at large transverse momentumin high-energy nucleus-nucleus collisions is summarised. The most important RHIC results are compared totheoretical parton energy loss predictions providing direct information on the (thermo)dynamical propertiesof hot and dense QCD matter. Prospects for the LHC are also outlined.
1. Introduction
The physics programme of high-energy nucleus-nucleus ( AA ) collisions is focused on thestudy of the fundamental theory of the strong interaction – Quantum Chromo Dynamics (QCD)– in extreme conditions of temperature, density and small parton momentum fraction (low- x ) –see e.g. [1] for a recent review. By colliding two heavy nuclei at ultrarelativistic energies oneexpects to form a hot and dense deconfined medium whose collective (colour) dynamics canbe studied experimentally. Lattice QCD calculations [2] predict a new form of matter at energydensities (well) above e crit ≈ consisting of an extended volume of deconfined andchirally-symmetric (bare-mass) quarks and gluons: the Quark Gluon Plasma (QGP).One of the first proposed “smoking guns” of QGP formation was jet quenching [3] i.e. theattenuation or disappearance of the spray of hadrons resulting from the fragmentation of a partonhaving suffered energy loss in the dense plasma formed in the reaction (Fig. 1, left). The en-ergy lost by a parton provides “tomographic” information of the matter properties (temperature T , interaction coupling a , thickness L ): D E = f ( E ; T , a , L ) [8]. The “scattering power” of themedium is often encoded in the transport coefficient which describes the average transverse mo-mentum squared transferred to the traversing parton per unit path-length: ˆ q ≡ m D / l = m D r s (here m D is the medium Debye mass, r its density, and s the parton-matter interaction crosssection) . The dominant mechanism of energy loss of a fast parton in a dense QCD plasma is Email address: david.d’[email protected] (David d’Enterria). For an equilibrated gluon plasma at T = . a s ≈ r g = / p z ( ) · T ≈
15 fm − , Debye mass m D = ( pa s ) / T ≈ s gg ≈ q ≃ . c (GeV/ T p - ) c d y ( G e V / T N / dp ] d T p p / [ -9 -8 -7 -6 -5 -4 -3 -2 -1 X @ 200 GeV [0-10%] p fi Au-Au T · X @ 200 GeV p fi p-p ] T -2p T =p i m [CTEQ6, KKP, T · NLO [W.Vogelsang]
Fig. 1. Right: “Jet quenching” in a head-on heavy-ion collision: a fast parton traverses the dense plasma created (withtransport coefficient ˆ q , gluon density dN g / dy and temperature T ), loses energy via “gluonstrahlung” and fragments into a(quenched) jet [4]. Left: Neutral pion spectrum measured by PHENIX at √ s NN = 200 GeV in central AuAu (squares) [5],compared to the ( T AA -scaled) spectrum in pp collisions (circles) [6] and to a NLO pQCD calculation (yellow band) [7]. of radiative nature (“gluonstrahlung”): the parton loses energy mainly by medium-induced mul-tiple gluon emission [10,11,12,13]. Jet quenching in AA reactions is characterised by variousobservable consequences compared to the same “QCD vacuum” measurements in proton-proton( pp ) collisions: (i) suppressed high-p T hadron spectrum ( dN AA / d p T ), (ii) unbalanced back-to-back high-p T dihadron azimuthal correlations ( dN pair / d f ), and (iii) modified energy-particleflow (softer hadron spectra, larger multiplicity, increased angular broadening, ...) within the final jets . A detailed review of these topics can be found in [4], of which a summary is given in thefollowing sections.
2. High- p T single inclusive hadron production If a hard scattered parton suffers energy loss in a heavy-ion collision, the energy available forthe hadrons issuing from its fragmentation will be reduced and their spectrum depleted comparedto pp collisions. The standard method to quantify the medium effects on the yield of a large- p T particle produced at rapidity y in a AA reaction is given by the nuclear modification factor : R AA ( p T , y ; b ) = d N AA / dyd p T h T AA ( b ) i × d s pp / dyd p T , T AA ( b ) being the nuclear overlap function at b , (1)which measures the deviation of AA at impact parameter b from an incoherent superposition ofnucleon-nucleon collisions ( R AA = 1). From the measured suppression factor one can determinevarious medium properties such as its transport parameter ˆ q , via h D E i (cid:181) a s h ˆ q i L [11,13], or itsinitial gluon density dN g / dy , via D E (cid:181) a s C R A ⊥ dN g dy L (for an expanding plasma with original transverse area A ⊥ = p R A ≈
150 fm and thickness L ) [12]. We summarise the main high- p T hadroproduction results in pp and AA collisions, and confront them to jet quenching predictions.2a) Magnitude of the suppression and medium properties.Figure 1 (right) shows the high- p T p spectrum measured at √ s NN = 200 GeV in central AuAu [5] compared to the pp [6] and NLOpQCD [7] spectra scaled by T AA . The AuAu data are suppressed by a factor of 4 – 5 with re-spect to the pp results. The corresponding R AA ( p T ) , Eq. (1), is shown in Fig. 2 (left). Above p T ≈ p [14], h [15], and charged hadrons [16,17] show all a common factor of ∼ R AA = 1 expectation that holds for hard probes, such as direct pho-tons [18,19], which do no interact with the medium. The AuAu high- p T suppression can be well ) c (GeV/ T p0 2 4 6 8 10 12 14 16 18 20 AA R -1 Au+Au - 200 GeV (central collisions):* [PHENIX] g , g Direct [STAR] – Inclusive h [PHENIX] p [PHENIX] h /dy = 1400) g GLV energy loss (dN scaling part
N scaling coll N ) c (GeV/ T p AA R -1 in central AA: p T High p = 17.3 GeV [WA98] NN sPbPb (cid:10) = 200 GeV [PHENIX] NN sAuAu (cid:10) /dy = 400) g GLV energy loss (dN /dy = 1400) g GLV energy loss (dN
SPS RHIC
LHC /dy = 2000 - 4000 g GLV: dN /fm > = 30 - 80 GeVqPQM: < Fig. 2. Left: R AA ( p T ) in central AuAu at 200 GeV for p [5], h [15], charged hadrons [16], and direct g [18,19] comparedto the GLV model ( dN g / dy = R AA ( p T ) for p ’s at SPS [21,22] and RHIC [5] comparedto GLV calculations ( dN g / dy = 400, 1400) and to predictions for central PbPb at √ s NN = 5.5 TeV (yellow bands) [23]:GLV ( dN g / dy = 2000 – 4000) and PQM ( h ˆ q i ≈
30 – 80 GeV /fm ) . reproduced by parton energy loss calculations in a very dense system with initial gluon rapiditydensities dN g / dy ≈ q ≈
13 GeV /fm [5,24], or plasma temperatures T ≈ q , dN g / dy and T values in the various models has been studied e.g. in [4,26]. Whereasthe agreement between the fitted thermodynamical variables dN g / dy and T is good, the valuesof the transport parameter ˆ q favoured by the data are 3 – 4 times larger than perturbative esti-mates [9]. An accord between the obtained ˆ q and dN g / dy can only be achieved assuming parton-medium cross-sections much larger than the s gg ≈ strongly-coupled nature of the QGP produced at RHIC [27].(b) Centre-of-mass energy dependence. As one increases the collision energy in nucleus-nucleus collisions, the produced plasma reaches higher energy and particle densities, the systemstays longer in the QGP phase, and correspondingly the traversing partons are more quenched.Figure 2 (right) compiles the measured R AA ( p T ) for high- p T p in central AA collisions in therange √ s NN ≈
20 – 200 GeV compared to parton energy loss calculations that assume the forma-tion of a QGP with initial gluon densities in the range dN g / dy ≈
400 – 1400 [20,28] or, equiva-lently, averaged transport coefficients h ˆ q i ≈ /fm [24]. The theoretical predictionsreproduce well the magnitude and shape of the experimental data. The SPS R AA ( p T ) [21], thoughconsistent with unity [22], is suppressed compared to the “Cronin enhancement” observed in pe-ripheral PbPb and pPb collisions at the same √ s NN [29].3c) p T -dependence of the suppression.At RHIC top energies, the hadron quenching factorremains basically constant from 5 GeV/c up to the highest transverse momenta measured so far, p T ≈
20 GeV/c (Fig. 2). Full calculations [20,24,30,31] including the combined effect of (i)energy loss kinematics constraints, (ii) steeply falling p T spectrum of the scattered partons, and(iii) O ( p T -dependent (anti)shadowing differences between the proton and nuclear partondistribution functions (PDFs), result in an effectively flat R AA ( p T ) as found in the data. The muchlarger kinematical range opened at LHC energies [23] will allow one to test the p T -dependenceof parton energy loss over a much wider domain than at RHIC (yellow bands in Fig. 2, right).(d) Centrality (system-size) dependence.The volume of the produced plasma in a heavy-ioncollision can be “dialed” by modifying the overlap area between the colliding nuclei either byselecting a given impact-parameter b – i.e. by choosing more central or peripheral reactions – orby colliding larger or smaller nuclei, e.g. Au ( A = 197) versus Cu ( A = 63). The relative energyloss depends on the effective mass number A eff or, equivalently, on the number of participantnucleons in the collision N part , as: D E / E (cid:181) A / (cid:181) N / [24,32]. The measured R AA ( p T ) in central CuCu at 22.4, 62.4, and 200 GeV [33] is a factor of ( A Au / A Cu ) / ≈ AuAu at the same energies. Yet, for a comparable N part value, the suppression in AuAu and
CuCu is very similar. Fitting the N part dependence to R AA = ( − k N a part ) n − yields a = . ± .
10 [5], consistent with parton energy loss calculations.(e) Path-length dependence.Experimentally, one can test the dependence of parton suppressionon the plasma thickness ( L ) by exploiting the spatial asymmetry of the system produced in non-central nuclear collisions. Partons produced “in plane” (“out-of-plane”) i.e. along the short (long)direction of the ellipsoid matter with eccentricity e will comparatively traverse a shorter (longer)thickness. PHENIX has measured the high- p T neutral pion suppression as a function of the anglewith respect to the reaction plane, R AA ( p T , f ) [34]. Each azimuthal angle f can be associated withan average medium path-length L e via a Glauber model. The energy loss is found to satisfy theexpected D E (cid:181) L dependence [12] above a “threshold” length of L ≈ (GeV)s = G e V / c ) T ( p AA R +X 0-7% central [WA98] p fi Pb+Pb +X 0-5% central [CERES] – p fi Pb+Au +X 0-10% central [PHENIX] p fi Au+Au = 9/4 q E D / g E D Energy loss: q E D = g E D Energy loss: NN p T [GeV] R AA ( p T ) + +e - ), QGP dissociation x = 2-3 PHENIX 0.5(e + +e - ), 0-10% Au+Au STAR 0.5(e + +e - ), 0-5% Au+Au STAR 0.5(e + +e - ), 0-12% Au+Au No nuclear effect
Central Au+Au
Fig. 3. Left: R AA ( p T = 4 GeV/c) for p in central AA collisions as function of collision energy compared to non-Abelian(solid) and “non-QCD” (dotted) energy loss curves [35,36]. Right: R AA ( p T ) for decay electrons from D and B mesons incentral AuAu at √ s NN =
200 GeV [37,38,39] compared to a model of D and B meson dissociation in the plasma [40]. C A = C F = 4/3 for quarks.Asymptotically, the probability for a gluon to radiate another gluon is C A / C F = 9/4 times largerthan for a quark and thus g -jets are expected to be more quenched than q -jets in a QGP. Onecan test such a genuine non-Abelian property of QCD energy loss by measuring hadron sup-pression at a fixed p T for increasing √ s [35,36]. At large (small) x , the PDFs are dominated byvalence-quarks (“wee” gluons) and consequently hadroproduction is dominated by quark (gluon)fragmentation. Figure 3 (left) shows the R AA for 4-GeV/c pions measured at SPS and RHIC com-pared to two parton energy loss curves [36]. The lower (upper) curve shows the expected R AA assuming a normal (arbitrary) behaviour with D E g / D E q = 9/4 ( D E g = D E q ). The experimentalhigh- p T p data supports the expected colour-factor dependence of R AA ( √ s NN ) [35].(g) Heavy-quark mass dependence.Due to the “dead cone” effect [42], the radiative energyloss for a charm (bottom) quark is a factor 1- ( m Q / m D ) ≈
25% (75%) smaller than for a light-quark. Yet, RHIC measurements [37,38,39] of high- p T electrons from the semi-leptonic decaysof D - and B -mesons (Fig. 3, right) indicate the same suppression for light and heavy mesons: R AA ( Q ) ∼ R AA ( q , g ) ≈ vacuum hadronisation (after in-medium radiation) implicit inall formalisms may well not hold in the case of heavy quarks. The formation time of D - and B -mesons is of order t form ≈ meson inside the QGP [40]. The expected amount of suppression in that case is larger and consistentwith the data (Fig. 3, right).
3. High- p T di-hadron correlations Jet-like correlations in heavy-ion collisions can be measured on a statistical basis by selectinga high- p T trigger particle and measuring the azimuthal ( Df = f − f trig ) and pseudorapidity ( Dh = h − h trig ) distributions of its associated hadrons ( p assocT < p trigT ): C ( Df , Dh ) = N trig d N pair d Df d Dh . In pp collisions, a dijet signal appears as two distinct back-to-back Gaussian-like peaks at Df ≈ Dh ≈ Df ≈ p (away-side). At variance with such a topology, Fig. 4 showsthe increasingly distorted back-to-back azimuthal correlations in high- p T triggered central AuAu events as one decreases the p T of the associated hadrons (right to left). Whereas, the AuAu and pp near-side peaks are similar for all p T ’s, the away-side peak is only present for the highest partner p T ’s but progressively disappears for less energetic partners [46,45]. Early STAR results [47]showed a monojet-like topology with a complete disappearance of the opposite-side peak for p assocT ≈ Df between a triggerhadron h t and a partner hadron h a in the opposite azimuthal direction can be constructed as afunction of the momentum fraction z T = p assocT / p trigT via a “pseudo-fragmentation function”: The use of high- p T (anti)protons (mostly coming from gluon fragmentation) as an alternative test of the colour chargedependence of the quenching [41] is, unfortunately, distorted by the presence of extra non-perturbative mechanisms ofbaryon production (see discussion in [4]). ig. 4. Comparison of the azimuthal di-hadron correlation dN pair / d Df d h for pp (open symbols) and central AuAu (his-tograms) at √ s NN = 200 GeV for p trigT = p assocT [45]. D awayAA ( z T ) = Z d p trigT Z d p assocT Z Df away > o d Df d s h t h a AA / d p trigT d p assocT d Df d s h t AA / d p trigT . (2)shown in Fig. 5 (top-left) compared to predictions of the HT model for various values of the e parameter quantifying the amount of energy loss [48]. Similarly to R AA , the magnitude ofthe suppression of back-to-back jet-like two-particle correlations can be quantified with the ratio I awayAA = D awayAA / D awaypp . I awayAA is found to decrease with increasing centrality, down to about 0.2 –0.3 for the most central events (Fig. 5, bottom-left) [47,49]. The right plot of Fig. 5 shows the -2 -1 STAR 200GeV d+Au x1.5 AuAu 20-40% AuAu 0-5% I AA ( z T ) z T trigT <15GeV pp x1.5 =1.2M pp x1.5 =0.8 1.8M 20-40% =1.2M =1.68 pQCD NLO 0-5% AuAu h h =1.2M =1.48, 1.68, 2.08 D AA ( z T ) R AA & I AA (GeV/fm) AuAu I AA p trigT =8 .5GeV p assoT =6 .5GeV R AA p T =8 .5GeV Fig. 5. Left: D awayAA ( z T ) distributions for dAu and AuAu and I AA ( z T ) ratio for central AuAu at 200 GeV [49], compared toHT calculations for varying e energy losses [48]. Right: Data vs. theory c values for the fitted e parameter [48]. best e ≈ R AA ( p T ) and I AA ( z T ) factors. Due to theirreducible presence of (unquenched) partons emitted from the surface of the plasma, the single-hadron quenching factor R AA ( p T ) is in general less sensitive to the value of e than the dihadronmodification ratio I AA ( z T ) . 6 . Jet observables The measurements in AA collisions of fully reconstructed (di)jets or of jets tagged by an away-side photon or Z -boson allow one to investigate – in much more detail than with single- or double-hadron observables – the mechanisms of in-medium parton radiation as well as to characterisethe matter properties through modified jet profiles [50,51] and fragmentation functions [52].Experimental reconstruction of jets in nuclear reactions is an involved three-steps exercise [4]:(i) Clustering algorithm : The measured hadrons are clustered together, according to relativedistances in momentum and/or space, following an infrared- and collinear-safe procedurewhich is also fast enough to be run over events with very high multiplicities. The k T andSISCone algorithms implemented in the F AST J ET package [53] fulfill all such conditions.(ii) Background subtraction : Jets are produced on top of a large “underlying event” (UE) ofhadrons coming from other (softer) parton-parton collisions in the same interaction. Incentral
PbPb collisions at the LHC one expects E UET ≈
80 GeV (with large fluctuations) ina cone of radius R = p Dh + Df = .
4. Various UE subtraction techniques are availablein combination with the k T [54], UA1-cone [55] or iterative-cone [56] algorithms.(iii) Jet energy corrections : Data-driven methods are needed to experimentally control the jetenergy-scale which is the single most important source of systematic uncertainties in the jetyield. The non-perturbative effects introduced by the UE and hadronisation can be gaugedby comparing the sensitivity of the jet spectrum obtained with different Monte Carlo’s [4].STAR [57] has a preliminary measurement of jets in
AuAu at 200 GeV (Fig. 6, left) using a conealgorithm with R = 0.4, and estimating the UE background from the average energy in cones without seeds. Control of the jet energy corrections is still work in progress. Jet physics willdefinitely benefit from the highest energies (and therefore statistics) available at the LHC. Theexpected p T reach in PbPb at 5.5 TeV is as large as p T ≈
500 GeV/c (Fig. 6, right). [GeV] T E T d N / d E e v / N -18 -16 -14 -12 -10 -8 -6 -4 -2 |<2 η Calorimeter Jets |0-10% central -1 -2 -3 -4 -5 -6 -7 -8 Fig. 6. Left: Preliminary STAR jet E T spectra in central AuAu (triangles) and pp (squares, scaled by T AA ) at 200 GeV [57].Right: Jet spectra for various PbPb centralities expected at 5.5 TeV in CMS ( R L dt = 0.5 nb − ) [58]. The g -jet (and Z -jet) channel provides a very clean means to determine medium-modifiedparton fragmentation functions (FFs) [59,60]. Since the prompt g is not affected by final-stateinteractions, its transverse energy ( E g T ) can be used as a proxy of the away-side parton energy( E jetT ≈ E g T ) before any jet quenching. The FF, defined as the normalised distribution of hadronmomenta 1 / N jets dN / dz relative to that of the parent parton E jetT , can then be constructed using7 g h = p T / E jetT or, similarly, x = log ( E jetT / p T ) = − log ( z ) , for all particles with momentum p T associated with a jet. In a QCD medium, energy loss shifts parton energy from high- z to low- z hadrons [61], resulting in a higher “hump-back plateau” in the FFs at intermediate x ≈ g -jet channel in central Pb-Pb (Fig. 7, right)indicate that medium modified FFs are measurable with small uncertainties in the ranges z < < x < z = ln(1/ z ) d N / d z in medium, E jet = 17.5 GeVin vacuum, E jet = 17.5 GeVTASSO, (cid:214) s ‘ = 35 GeV ) T /p T =ln(E x x d N / d j e t s / N -3 -2 -1 CMS Preliminary > 100GeV
Clus.T > 1GeV/c, E T Track pUnderlying event subtractedQuenched Fragmentation FunctionMC Truth
Fig. 7. Left: Single inclusive distribution of hadrons vs. x = ln ( E jet / p ) for a 17.5-GeV jet in e + e − collisions (TASSOdata) compared to QCD radiation predictions in the vacuum (solid curve) and in-medium (dashed curve) [61]. Right: FFsas a function of x for quenched partons obtained in CMS g -jet simulations for central Pb-Pb at 5.5 TeV (0.5 nb − ) [62].
5. Summary
The analysis of jet structure modifications in heavy-ion collisions provides quantitative “tomo-graphic” information on the thermodynamical and transport properties of the strongly interactingmedium produced in the reactions. At RHIC energies (up to √ s NN = 200 GeV), strong suppres-sion of the yields of high- p T single hadrons and of dihadron azimuthal correlations, have beenobserved in central AuAu collisions. Most of the properties of the observed suppression are inquantitative agreement with the predictions of parton energy loss models in a very dense QCDplasma. The confrontation of these models to the data permits to derive the initial gluon density dN g / dy ≈ q = O (
10 GeV /fm ) of the produced medium at RHIC.At the upcoming LHC energies, the detailed analysis of jet spectra, jet shapes and the extrac-tion of medium-modified parton-to-hadron fragmentation functions promise to fully unravel themechanisms of parton energy loss in QCD matter. The study of jet quenching phenomena provesan excellent tool to expand our knowledge of the dynamics of the strong interaction at extremeconditions of temperature and density.AcknowledgmentsSpecial thanks to Itzhak Tserruya and the organisers of PANIC’08 for their kind invitation. Sup-port by the 6th EU Framework Programme contract MEIF-CT-2005-025073 is acknowledged.8eferences [1] D. d’Enterria, J. Phys. G , S53 (2007)[2] M. Cheng et al. , Phys. Rev. D , 054507 (2006); Y. Aoki et al. , Phys. Lett. B , 46 (2006)[3] J. D. Bjorken, FERMILAB-PUB-82-059-THY (1982)[4] D. d’Enterria, arXiv:0902.2011 [nucl-ex][5] A. Adare et al. [PHENIX Collaboration], Phys. Rev. Lett. , 232301 (2008)[6] A. Adare et al. [PHENIX Collaboration], Phys. Rev. D , 051106 (2007)[7] F. Aversa, P. Chiappetta, M. Greco and J. P. Guillet, Nucl. Phys. B , 105 (1989); B. Jager, A. Schafer,M. Stratmann and W. Vogelsang, Phys. Rev. D , 054005 (2003); W. Vogelsang (private communication)[8] S. Peign´e and A. V. Smilga, arXiv:0810.5702 [hep-ph][9] R. Baier and D. Schiff, JHEP , 059 (2006)[10] M. Gyulassy, M. Pl¨umer, Phys. Lett. B243 , 432 (1990); X.N. Wang, M. Gyulassy, Phys. Rev. Lett. , 1480 (1992)[11] R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peign´e and D. Schiff, Nucl. Phys. B484 , 265 (1997); R. Baier, D. Schiff,B.G. Zakharov, Ann. Rev. Nucl. Part. Sci. , 37 (2000)[12] M. Gyulassy, P. Levai and I. Vitev, Phys. Rev. Lett. , 5535 (2000); Nucl. Phys. B594 , 371 (2001)[13] U. A. Wiedemann, Nucl. Phys. B , 303 (2000)[14] S.S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. , 072301 (2003)[15] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. , 202301 (2006)[16] J. Adams et al. [STAR Collaboration], Phys. Rev. Lett. , 172302 (2003)[17] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. C69 , 034910 (2004)[18] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. , 232301 (2005)[19] A. Adare et al. [PHENIX Collaboration], arXiv:0804.4168 [nucl-ex][20] I. Vitev and M. Gyulassy, Phys. Rev. Lett. , 252301 (2002); I. Vitev, J. Phys. G , S791 (2004)[21] M. M. Aggarwal et al. [WA98 Collaboration], Eur. Phys. J. C , 225 (2002)[22] D. d’Enterria, Phys. Lett. B , 32 (2004)[23] N. Armesto et al. , J. Phys. G , 054001 (2008)[24] A. Dainese, C. Loizides and G. Paic, Eur. Phys. J. C , 461 (2005)[25] S. Turbide, C. Gale, S. Jeon and G. D. Moore, Phys. Rev. C , 014906 (2005)[26] S. A. Bass et al. , arXiv:0808.0908 [nucl-th][27] M. Gyulassy and L. McLerran, Nucl. Phys. A , 30 (2005)[28] I. Vitev, Phys. Lett. B , 303 (2005)[29] M. M. Aggarwal et al. [WA98 Collaboration], Phys. Rev. Lett. , 242301 (2008)[30] S. Jeon and G. D. Moore, Phys. Rev. C , 034901 (2005)[31] K. Eskola, H. Honkanen, C. Salgado and U. Wiedemann, Nucl. Phys. A , 511 (2005)[32] I. Vitev, Phys. Lett. B , 38 (2006)[33] A. Adare et al. [PHENIX Collaboration], Phys. Rev. Lett. , 162301 (2008)[34] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. C , 034904 (2007)[35] D. d’Enterria, Eur. Phys. J. C43 , 295 (2005)[36] Q. Wang and X.N. Wang, Phys. Rev.
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