Hunting the Quark Gluon Plasma

ASSESSMENTS BY THE EXPERIMENTAL COLLABORATIONS

Relativistic Heavy Ion Collider (RHIC) Brookhaven National Laboratory, Upton, NY 11974-5000

RESULTS FROM THE FIRST 3 YEARS AT RHIC

managed for the U.S. Department of Energy by Brookhaven Science Associates, a company founded by Stony Brook University and Battelle

April 18, 2005

BNL -73847-2005Formal Report

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third partys use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

CONTENTS

Forward i Quark Gluon Plasma and Color Glass Condensate at RHIC? The Perspective from the BRAHMS Experiment 1 Formation of Dense Partonic Matter in Relativistic Nucleus-Nucleus Collisions at RHIC: Experimental Evaluation by the PHENIX Collaboration .. 33 The PHOBOS Perspective on Discoveries at RHIC .... 159 Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaborations Critical Assessment of the Evidence from RHIC Collisions . 253

Forward The U.S. Department of Energys Relativistic Heavy Ion Collider (RHIC) construction project was completed at BNL in 1999, with the first data-taking runs in the summer of 2000. Since then the early measurements at RHIC have yielded a wealth of data, from four independent detectors, each with its international collaboration of scientists: BRAHMS, PHENIX, PHOBOS, and STAR [1]. For the first time, collisions of heavy nuclei have been carried out at colliding-beam energies that have previously been accessible only for high-energy physics experiments with collisions of elementary particles such as protons and electrons. It is at these high energies that the predictions of quantum chromodynamics (QCD), the fundamental theory that describes the role of quarks and gluons in nuclear matter, come into play, and new phenomena are sought that may illuminate our view of the basic structure of matter on the sub-atomic scale, with important implications for the origins of matter on the cosmic scale. The RHIC experiments have recorded data from collisions of gold nuclei at the highest energies ever achieved in man-made particle accelerators. These collisions, of which hundreds of millions have now been examined, result in final states of unprecedented complexity, with thousands of produced particles radiating from the nuclear collision. All four of the RHIC experiments have moved quickly to analyze these data, and have begun to understand the phenomena that unfold from the moment of collision as these particles are produced. In order to provide benchmarks of simpler interactions against which to compare the gold-gold collisions, the experiments have gathered comparable samples of data from collisions of a very light nucleus (deuterium) with gold nuclei, as well as proton-proton collisions, all with identical beam energies and experimental apparatus. The early measurements have revealed compelling evidence for the existence of a new form of nuclear matter at extremely high density and temperature a medium in which the predictions of QCD can be tested, and new phenomena explored, under conditions where the relevant degrees of freedom, over nuclear volumes, are expected to be those of quarks and gluons, rather than of hadrons. This is the realm of the quark gluon plasma, the predicted state of matter whose existence and properties are now being explored by the RHIC experiments. Many theorists have concluded that the results to date provide sufficient evidence that the quark gluon plasma has indeed been observed. [2] They state that the analyses of all four experiments point to the existence, in the evolution of the system immediately following a gold-gold collision, of a near-thermal, strongly interacting medium whose energy-density and temperature clearly exceed the critical values predicted by QCD calculations for a transition from ordinary hadronic states to a quark gluon plasma. However, detailed analyses of the data also make it clear that this hot, dense medium has properties that are surprising, and not yet fully understood in terms of the early expectations for the quark gluon plasma. For example, it was often stated, prior to the RHIC data, that the quark gluon plasma should behave like an ideal gas of quarks and gluons (i.e., like a weakly-coupled plasma state). The data now indicate that the observed medium behaves more like an ideal fluid, in analogy to a strongly coupled plasma state. Some theorists have referred to this state as the strongly coupled quark gluon plasma, or sQGP.

i

ii

The white papers collected here represent the independent assessments from each of

the experimental collaborations of what has been learned so far from their respective experiments regarding the existence and properties of the quark gluon plasma. The four collaborations state that the new phenomena they observe are signals of the creation of a new form of nuclear matter. However, they argue that the surprising properties of this collective medium seen in the present data need to be augmented with additional key measurements and also need to be better understood in terms of theoretical models for the formation, evolution, and freeze-out of a quark gluon plasma. These white papers are very much in the nature of status reports, providing a snapshot of rapidly evolving programs of data analysis. Much more will be learned over the next year from the analysis of Run IV data, obtained in the early months of 2004, which exceed the previous full-energy gold-gold data samples by a factor of ten. A key result of the early measurements at RHIC is the demonstration that detailed exploration of the properties of new matter produced in the collisions can be carried out using experimental probes that are sensitive to the properties of the initial collective medium. What is more, it has been demonstrated that certain experimental probes are accessible that carry information directly from the thermal volume of hot matter during its lifetime. Such probes include the spectra of heavy quarks (charm and bottom) that are formed in the earliest stages of the collision, and are so massive that their dynamical properties would not be lost to thermalization at the temperatures and densities that prevail in the plasma of light quarks and gluons. Another class of such probes is the measurement and classification of high-momentum jets of particles and high-momentum photons corresponding to energetically scattered quarks and gluons. Accurate measurements of large samples allow experiments to perform tomography on the initial dense matter with beams of quarks and gluons.

These measurements, and others like them, along with continued progress in theory as the data become more precise, will provide the key to identifying and understanding the new form of matter produced at RHIC, and what it can reveal about the fundamental properties of the strong interaction.

S. Aronson and T. Ludlam Brookhaven National Laboratory April 2005 References:

1. The Relativistic Heavy Ion Collider Project: RHIC and its Detectors, M. Harrison et al., ed., Nuclear Instruments and Methods in Physics Research A 499 (2003)

2. See, for example, New Discoveries at RHIC A Case for the Strongly Interactive Quark-Gluon Plasma, a collection of presentations at the RIKEN BNL Research Center, May 14-15, 2004, D. Rischke and G. Levin, ed., Nuclear Physics A750, issue 1 (2005)

Quark Gluon Plasma

and Color Glass Condensate at RHIC?

The perspective from the BRAHMS

experiment.

I. Arsene j, I. G. Bearden g, D. Beavis a, C. Besliu j, B. Budick f ,H. Bggild g, C. Chasman a, C. H. Christensen g,

P. Christiansen g, J. Cibor c, R. Debbe a, E. Enger `,J. J. Gaardhje g, M. Germinario g, O. Hansen g, A. Holm g,A. K. Holme `, K. Hagel h, H. Ito a, E. Jakobsen g, A. Jipa j,F. Jundt b, J. I. Jrdre i, C. E. Jrgensen g, R. Karabowicz e,

E. J. Kim a,k, T. Kozik e, T. M. Larsen g,`, J. H. Lee a,Y. K. Lee d, S. Lindahl ` G. Lvhiden `, Z. Majka e,

A. Makeev h, M. Mikelsen `, M. J. Murray h,k, J. Natowitz h,B. Neumann k, B. S. Nielsen g, D. Ouerdane g, R. Planeta e,

F. Rami b, C. Ristea g,j, O. Ristea j, D. Rohrich i,B. H. Samset `, D. Sandberg g, S. J. Sanders k, R. A. Scheetz a,P. Staszel g, T. S. Tveter `, F. Videbk a, R. Wada h, Z. Yin i,

I. S. Zgura j,

aBrookhaven National Laboratory, Upton, New York 11973, USAbInstitut de Recherches Subatomiques et Universite Louis Pasteur, Strasbourg,

FrancecInstitute of Nuclear Physics, Krakow, Poland

dJohns Hopkins University, Baltimore 21218, USAeM. Smoluchkowski Inst. of Physics, Jagiellonian University, Krakow, Poland

fNew York University, New York 10003, USAgNiels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark

hTexas A&M University, College Station, Texas, 17843, USAiUniversity of Bergen, Department of Physics, Bergen, Norway

jUniversity of Bucharest, RomaniakUniversity of Kansas, Lawrence, Kansas 66045, USA

`University of Oslo, Department of Physics, Oslo, Norway

Preprint submitted to Elsevier Science 25 January 2005

Abstract

We review the main results obtained by the BRAHMS collaboration on the prop-erties of hot and dense hadronic and partonic matter produced in ultrarelativisticheavy ion collisions at RHIC. A particular focus of this paper is to discuss to whatextent the results collected so far by BRAHMS, and by the other three experimentsat RHIC, can be taken as evidence for the formation of a state of deconfined par-tonic matter, the so called quark-gluon-plasma (QGP). We also discuss evidence fora possible precursor state to the QGP, i.e. the proposed Color Glass Condensate.

Key words:PACS: 25.75.q, 25.40.-h, 13.75.-n

1 Introduction

From the onset of the formulation of the quark model and the first under-standing of the nature of the binding and confining potential between quarksabout 30 years ago it has been conjectured that a state of matter character-ized by a large density of quarks and gluons (together called partons) mightbe created for a fleeting moment in violent nuclear collisions [1]. This highenergy density state would be characterized by a strongly reduced interactionbetween its constituents, the partons, such that these would exist in a nearlyfree state. Aptly, this proposed state of matter has been designated the quarkgluon plasma (QGP)[2]. It is now generally thought that the early universewas initially in a QGP state until its energy density had decreased sufficiently,as a result of the expansion of the universe, that it could make the transitionto ordinary (confined) matter.

Experimental attempts to create the QGP in the laboratory and measure itsproperties have been carried out for more than 20 years, by studying collisionsof heavy nuclei and analyzing the fragments and produced particles emanatingfrom such collisions. During that period, center of mass energies per pair ofcolliding nucleons have risen steadily from the

sNN 1GeV domain of the

Bevalac at LBNL, to energies ofsNN = 5 GeV at the AGS at BNL, and to

sNN = 17 GeV at the SPS accelerator at CERN. No decisive proof of QGPformation was found in the experiments at those energies, although a numberof signals suggesting the formation of a very dense state of matter, possiblypartonic, were found at the SPS [3,4].

With the Relativistic Heavy Ion Collider, RHIC, at Brookhaven National Lab-oratory, the center of mass energy in central collisions between gold nucleiat 100AGeV + 100AGeV is almost 40TeV, the largest so far achieved innucleus-nucleus collisions under laboratory conditions. This energy is so large

2

that conversion of a sizeable fraction of the initial kinetic energy into matterproduction creates many thousands of particles in a limited volume leadingto unprecedented large energy densities and thus presumably ideal conditionsfor the formation of the quark gluon plasma.

RHIC started regular beam operations in the summer of year 2000 with ashort commissioning run colliding Au nuclei at

sNN = 130GeV. The first

full run at the top energy (sNN = 200GeV) took place in the fall/winter of

2001/2002. The third RHIC run during the winter/spring of 2003 focussed ond+Au and p+p reactions. Recently, in 2004, a long high luminosity Au+Aurun at

sNN = 200GeV and a short run at

sNN = 62.4GeV have been

completed. The collected data from the most recent runs are currently beinganalyzed and only a few early results are thus available at the time of writingof this document.

The aim here is to review the available information obtained from the firstRHIC experiments with the purpose of determining what the experimentalresults, accumulated so far, allow us to say about the high energy densitymatter that is created at RHIC in collisions between heavy atomic nuclei.

We concentrate primarily on results from the BRAHMS detector, one of thefour detectors at RHIC, but naturally also refer to results obtained by theother three experiments (STAR, PHENIX and PHOBOS) insofar as they com-plement or supplement information obtained from BRAHMS. The BRAHMSexperiment is a two arm magnetic spectrometer with excellent momentum res-olution and hadron identification capabilities. The two spectrometers subtendonly a small solid angle (a few msr) each, but they can rotate in the hori-zontal plane about the collision point to collect data on hadron productionover a wide rapidity range (0-4), a unique capability among the RHIC experi-ments. For details about the BRAHMS detector system we refer the reader to[5,6]. The large number of articles already produced by the four experimentsat RHIC may be found on their respective homepages [7]. Recent extensivetheoretical reviews and commentaries may be found in refs. [810].

2 What is the QGP and what does it take to see it?

The predicted transition from ordinary nuclear matter, which consists of hadronsinside which quarks and gluons are confined, to the QGP, a state of matterin which quarks and gluons are no longer confined to volumes of hadronic di-mensions, can in the simplest approach, be likened to the transition betweentwo thermodynamic states in a closed volume.

As energy is transferred to the lower energy state a phase transition to the

3

higher energy state occurs, akin to a melting or an evaporation process. Fora first order phase transition (PT), the transformation of one state into theother occurs at a specific temperature, termed the critical temperature, andthe process is characterized by absorption of latent heat during the phaseconversion, leading to a constancy or discontinuity of certain thermodynamicvariables as the energy density or temperature is increased. In this picture, itis tacitly assumed that the phase transition occurs between states in thermo-dynamic equilibrium. From such thermodynamical considerations, and frommore elaborate models based on the fundamental theory for the strong inter-action, Quantum Chromo Dynamics (e.g. lattice QCD calculations), estimatesfor the critical temperature and the order of the transition can be made. Cal-culations indicate that the critical temperature should be Tc 175MeV inthe case of a vanishing baryon chemical potential [11]. The order of the tran-sition at various values of the chemical potential is not known. In general, adecreasing critical temperature with increasing chemical potential is expected.Likewise, at non-zero chemical potential a mixed phase of coexisting hadrongas, HG, and QGP is predicted to exist in a certain temperature intervalaround the critical temperature. Recently calculational techniques have pro-gressed to the point of allowing an extension of the lattice methods also tofinite chemical potential. Such calculations also suggest the existence of a crit-ical point at larger chemical potential above which, the transition may be offirst order.

The transition from ordinary matter to the QGP is thus primarily a deconfine-ment transition. However, it is also expected, due to the vanishing interactionbetween partons in the QGP phase, that hadron masses will be lowered. Inthe limit of chiral symmetry the expectation value of the quark condensate,< qq >, vanishes and opposite parity states (chiral partners) are degenerate.As a consequence of the QGP to HG transition, the chiral symmetry is brokenand the hadrons acquire definite and nondegenerate masses. According to lat-tice QCD calculations chiral symmetry should be restored at sufficiently hightemperature (T >> Tc).

It is, however, at the onset not at all clear that the transition to the QGP, asit is expected to be recreated in nucleus-nucleus collisions, proceeds betweenstates of thermodynamic equilibrium as sketched above. The reaction, fromfirst contact of the colliding nuclei to freeze-out of the created fireball, occurson a typical timescale of about 10 fm/c and is governed by complex reactiondynamics so that non-equilibrium features may be important. Likewise therecan be significant rescattering of the strongly interacting components of thesystem, after its formation, that tends to obscure specific features associatedwith a phase transition.

Many potential experimental signatures for the existence of the QGP havebeen proposed. These can be roughly grouped into two classes: 1) evidence

4

for bulk properties consistent with QGP formation, e.g. large energy density,entropy growth, plateau behavior of the thermodynamic variables, unusualexpansion and lifetime properties of the system, presence of thermodynamicequilibration, fluctuations of particle number or charge balance etc, and 2)evidence for modifications of specific properties of particles thought to arisefrom their interactions with a QGP, e.g. the modification of widths and massesof resonances, modification of particle production probabilities due to colorscreening (e.g. J/ suppression) and modification of parton properties due tointeraction with other partons in a dense medium (e.g. jet quenching), etc.

We may ask the following questions: 1) What is the requirement for calling astate of matter a QGP, and 2) What would constitute proof of QGP formationaccording to that definition?

As far as the first question is concerned it would seem obvious that the deter-mining factor is whether the high density state that is created in the nuclearcollisions clearly has properties that are determined by its partonic composi-tion, beyond what is known at the nucleon level in elementary nucleon-nucleoncollisions (e.g. p+p collisions). It has often been presupposed that the plasmashould be in thermodynamical equilibrium. However, this may not be realizedwithin the short time scales available for the evolution of the reaction fromfirst contact to freeze-out, and is perhaps not necessary in the definition of theversion of the QGP that may be observable in relativistic heavy ion collisions.Finally, it may be asked whether chiral symmetry restoration is essential. Itwould seem that even in a situation in which the partons of the system are still(strongly) interacting one may speak of a QGP as long as the constituents arenot restricted to individual hadrons. Thus it would appear that deconfinementis the foremost property needed to define the QGP state, and the one thatneeds to be demonstrated by experiment.

Clearly, the observation of all, or at least of a number of the effects listed above,in a mutually consistent fashion, would serve to constitute a strong case for theformation of a QGP. Ideally, the observed effects must not be simultaneouslydescribable within other frameworks, e.g. those based on purely hadronic in-teractions and not explicitly involving the partonic degrees of freedom. Thissuggests the requirement that a proof, in addition to having consistency withQGP formation, also must contain elements that are only describable in termsof QGP formation, phase transition etc.

Finally, if a sufficiently good case exists, we may also ask if there are anyspecific features that may falsify the conclusion. To our knowledge no testshave been proposed that may allow falsification of either a partonic scenarioor a hadronic scenario, but it would be important if any such exclusive testswere to be formulated.

5

In this report we address some of the signatures discussed above, notably theenergy density, which can be deduced from the measured particle multiplici-ties, the thermal and dynamical properties of the matter at freeze-out whichmay be inferred from the abundances and spectral properties of identified par-ticles, and the modifications of spectral properties arising from the interactionof particles with the high energy-density medium.

3 Reactions at RHIC: how much energy is released?

The kinetic energy that is removed from the beam and which is available forthe production of a state such as the QGP depends on the amount of stoppingbetween the colliding ions.

The stopping can be estimated from the rapidity loss experienced by thebaryons in the colliding nuclei. If incoming beam baryons have rapidity, ybrelative to the CM (which has y = 0) and average rapidity

< y >= yb0

ydN

dydy/

yb0

dN

dydy (1)

after the collision, the average rapidity loss is y = yb < y > [12,13]. HeredN/dy denotes the number of net-baryons (number of baryons minus numberof antibaryons) per unit of rapidity. Thus, for the case of full stopping: y = yb.

At AGS energies the number of produced antiprotons is quite small and thenet-baryon distribution is similar to the proton distribution [1517]. The net-proton rapidity distribution is centered around y = 0 and is rather narrow.The rapidity loss for central collisions is about 1 for a beam rapidity of approx.1.6. At CERN-SPS energies (

sNN = 17GeV, 158AGeV Pb+ Pb central re-

actions) the rapidity loss is slightly less than 2 for a beam rapidity of 2.9 [18],about the same relative rapidity loss as at the AGS. The fact that the ra-pidity loss is large on an absolute scale means, however, that there is still asizeable energy loss of the colliding nuclei. This energy is available for parti-cle production and other excitations, transverse and longitudinal expansion.Indeed, in collisions at the SPS, multiplicities of negatively charged hadronsare about dN/dy = 180 around y = 0. At SPS another feature is visible (seefig. 1): the net proton rapidity distribution shows a double hump with a diparound y = 0. This shape results from the finite rapidity loss of the collidingnuclei and the finite width of each of the humps, which reflect the rapiditydistributions of the protons after the collisions. This picture suggests that thereaction at the SPS is beginning to be transparent in the sense that fewer ofthe original baryons are found at midrapidity after the collisions, in contrastto the situation at lower energies.

6

CMy-4 -2 0 2 4

dN/d

y ne

t-pro

tons

0

20

40

60

80 pAGS y

pSPS y

pRHIC y

AGS(E802,E877, E917)SPS(NA49)RHIC(BRAHMS)

Fig. 1. Rapidity density of net protons(i.e. number of protons minus numberof antiprotons) measured at AGS, SPS,and RHIC (BRAHMS) for central col-lisions [19]. At RHIC, where the beamrapidity is y = 5.4, the full distributioncannot be measured with current experi-ments, but BRAHMS will be able to ex-tend its unique results to y=3.5 from themost recent high statistics Au+Au run,corresponding to measurements extend-ing to 2.3 degrees with respect to thebeam direction.

1 2 3 4 50

1

2

3

4

BRAHMS maximumBRAHMS estimateBRAHMS minimum

E917E802/E866NA49

0 1 2 3 4 50

20406080

100 dN/dy net-Baryons

y>

Rap

idity

loss

)

part

/(1

/2

[GeV

/cT

part

the blastwave approach.

Another powerful tool to study the thermodynamic properties of the source isthe analysis of the azimuthal momentum distribution of the emitted particlesrelative to the event plane (defined as the direction of the impact parame-ter). This distribution is usually parametrized as a series of terms dependingon cos(n( r)), where and r denote the azimuthal angles of the par-ticle and of the reaction plane, respectively. The coefficient (v1) to the n=1term measures the so-called directed flow and the coefficient (v2) to the n=2term measures the elliptic flow. Elliptic flow has been analyzed at RHIC [3439] and has been found to reach (for many hadron species) large (v2) valuesconsistent with the hydrodynamical limit and thus of equilibration. Modelcalculations suggest [4147] that the observed persistence of azimuthal mo-mentum anisotropy indicates that the system has reached local equilibriumvery quickly and that the equilibrium can only be established at the partoniclevel when the system is very dense and has many degrees of freedom. Thisexplanation presupposes however that there are many interactions and thusthat the dense partonic phase is strongly interacting.

The particle ratios observed at RHIC can be well described by concepts fromstatistical physics applied at the quark level, thus assuming thermodynamicalequilibrium. However this is only a necessary condition and not a sufficientcondition for equilibration. The observation of a strong elliptic flow at RHICand comparison to model calculation suggests that the system is strongly col-lective as must be the case for an equilibrated system.

6 High pT suppression. The smoking gun of QGP?

The discussion in the previous sections indicates that the conditions for par-ticle production in an interval |y| . 1.5 at RHIC are radically different thanfor reactions at lower energies. At RHIC the central zone is baryon poor, theconsidered rapidity interval appears to approximately exhibit the anticipatedboost invariant properties, the particle production is large and dominated bypair production and the energy density appears to exceed significantly theone required for QGP formation. The overall scenario is therefore consistentwith particle production from a color field, formation of a QGP and subse-quent hadronization. Correlation and flow studies suggest that the lifetimeof the system is short (< 10fm/c) and, for the first time, there is evidencesuggesting thermodynamic equilibrium already at the partonic level.

But, is this interpretation unique? And, can more mundane explanations basedon a purely hadronic scenario be excluded? In spite of the obvious difficultiesin reconciling the high initial energy density with hadronic volumes, a com-

16

prehensive answer to this question requires the observation of an effect thatis directly dependent on the partonic or hadronic nature of the formed highdensity zone.

6.1 High pT suppression at midrapidity: final state partonic energy loss?

Such an effect has recently been discovered at RHIC and is related to the sup-pression of the high transverse momentum component of hadron spectra incentral Au+Au collisions as compared to scaled momentum spectra from p+pcollisions [4851]. The effect, originally proposed by Bjorken, Gyulassy andothers [5255] is based on the expectation of a large energy loss of high mo-mentum partons, scattered in the initial stages of the collisions, in a mediumwith a high density of color charges [56]. According to QCD colored objectsmay lose energy by radiating gluons as bremsstrahlung. Due to the color chargeof the gluons, the energy loss is proportional to the square of the length of colormedium traversed. Such a mechanism would strongly degrade the energy ofleading partons resulting in a reduced transverse momentum of leading par-ticles in the jets that emerge after fragmentation into hadrons. The STARexperiment has shown that the topology of high pT hadron emission is consis-tent with jet emission, so that we may really speak about jet-suppression [57].

The two upper rows of fig. 11 show our measurements [48,58] of the so-callednuclear modification factors for unidentified charged hadrons from Au+Aucollisions at rapidities = 0 and 2.2. The nuclear modification factor is definedas:

RAA =d2NAA/dptd

< Nbin > d2NNN/dptd. (5)

It involves a scaling of measured nucleon-nucleon transverse momentum distri-butions by the calculated number of binary nucleon-nucleon collisions, Nbin. Inthe absence of medium effects, the nuclear collisions can, at high pT be viewedas a superposition of elementary hard nucleon-nucleon collisions. Consequentlywe expect RAA = 1 at high pT . At low pT , where the particle production fol-lows a scaling with the number of participants, the above definition of RAAleads to RAA < 1 for pT < 2GeV/c.

In fact, it is found that RAA > 1 for pT > 2GeV/c in nuclear reactions atlower energy. This enhancement, first observed by Cronin, is associated withmultiple scattering of partons [59,60].

Figure 11 demonstrates that, surprisingly, RAA < 1 also at high pT for centralcollisions at both pseudorapidities, while RAA 1 for more peripheral colli-sions. It is remarkable that the suppression observed at pT 4GeV/c is verylarge, amounting to a factor of 3 for central Au+Au collisions as compared to

17

[GeV/c]Tp1 2 3 4 5

(0-

10%)

AuA

uR

0.5

1=0

[GeV/c]Tp1 2 3 4 5

(40

-60%)

AuA

uR

0.5

1

[GeV/c]Tp1 2 3 4 5

CPR

0.5

1

[GeV/c]Tp1 2 3 4 5

=2.2

[GeV/c]Tp1 2 3 4 5

[GeV/c]Tp1 2 3 4 5

Fig. 11. Nuclear modification factors RAuAu as defined in the text,measured byBRAHMS for central (top row) and semi-peripheral (middle row) Au+Au collisionsat midrapidity (left) and forward pseudorapidity (right). Note the strong suppres-sion of the high pT component above pT > 2 GeV seen at both rapidities. Thelower row shows the factor Rcp, i.e. the ratio of the RAuAu for central and periph-eral collisions. This ratio has the property of being independent of the p+p referencespectrum [48].

p+p and a factor of more than 4 as compared to the more peripheral collisions.Such large suppression factors are observed at both pseudorapidities.

The very large suppression observed in central Au+Au collisions must bequantitatively understood and requires systematic modelling of the dynam-ics. At = 0 the particles are emitted at 90 degrees relative to the beamdirection, while at = 2.2 the angle is only about 12 degrees. In a naive geo-metrical picture of an absorbing medium with cylindrical symmetry aroundthe beam direction, the large suppression seen at forward angles suggests thatthe suppressing medium is extended also in the longitudinal direction. Sincethe observed high pT suppression is similar or even larger at forward rapid-ity as compared to midrapidity (see fig. 12) one might be tempted to infer alongitudinal extent of the dense medium which is approximately similar to itstransverse dimensions. However, the problem is more complicated, due to thesignificant transverse and in particular longitudinal expansion that occurs asthe leading parton propagates through the medium, effectively reducing thedensities of color charges seen. Also other high pT suppressing mechanisms

18

[GeV/c]Tp1 2 3 4 5

R

0.5

1

1.5 Au+Au

Fig. 12. Ratio R of the suppression factors Rcp at pseudorapidities = 0 and = 2.2 that are shown in figure 11. The figure suggest that high pT suppressionpersists (and is even more important) at forward rapidity than at = 0 [48].

may come into play at forward rapidities (see discussion on the Color GlassCondensate in the following chapter).

[GeV/c]Tp1 2 3 4 5

Nuc

lear

Mod

ifica

tion

Fact

or

0.5

1

1.5

d+Au (MB)Au+Au (0-10%)

=0

Fig. 13. Nuclear modification factors measured for central Au+Au collisions andminimum bias d+Au collisions at

sNN = 200GeV, evidencing the important high

pT suppression observed in central Au+Au collisions [48] which is absent in thed+Au reactions. The shaded band around the points indicates the systematic errors.The shaded box on the ordinate around unity shows the estimated uncertainty onthe value of Nbin.

It has been conjectured that the observed high pT suppression might be the re-sult of an entrance channel effect, for example as might arise from a limitationof the phase space available for parton collisions related to saturation effects[61] in the gluon distributions inside the swiftly moving colliding nucleons

19

(which have = 100). As a test of these ideas we have determined the nuclearmodification factor for d+Au minimum bias collisions at

sNN = 200GeV.

The resulting RdAu is shown in fig. 13 where it is also compared to the RAuAufor central collisions previously shown in fig. 11. No high pT jet suppressionis observed for d+Au [48,6365]. The RdAu distribution at y = 0 shows aCronin enhancement similar to that observed at lower energies [18,66,67]. AtpT 4GeV/c we find a ratio RdAu/RAuAu 4 5. These observations areconsistent with the smaller transverse dimensions of the overlap disk betweenthe d and the Au nuclei and also appear to rule out initial state effects as thecause of the observed high pT yield reduction observed in Au+Au collisions.

High pT suppression at forward rapidities may also be expected to arise fromthe possible Color Glass Condensate phase in the colliding nuclei (see thediscussion in the next section). There is little doubt that systematic studiesof the high pT jet energy loss as a function of the thickness of the absorbingmedium obtained by varying the angle of observation of high pT jets relativeto the event plane and the direction of the beams will be required in order tounderstand in detail the properties of the dense medium.

6.2 The flavor composition

[GeV/c]Tp0 1 2 3 4 5

pip

/

0

0.2

0.4

0.6

0.8

1

1.2

1.4 +pip/

[GeV/c]Tp1 2 3 4 5 0

0.2

0.4

0.6

0.8

1

1.2

1.4

pip /

-pi/ps = 200 GeV, 0-10%, y = 0Au+Au, (BRAHMS Preliminary)s = 63 GeVp+p

, gluon jet (DELPHI)-e+e

Fig. 14. Ratios of particle yields p/pi+ (left) and p/pi (right) measured at mid-ra-pidity for 0-10% central Au+Au collisions at

sNN = 200GeV. The error bars

show the statistical errors. The systematic errors are estimated to be smaller than8%. Data at

s = 63GeV for p+p collisions [69] are also shown (open circles). The

solid line in the right hand panel is the (p+ p)/(pi++ pi) ratio measured for gluonjets [70] in e+ + e collisions.

With its excellent particle identification capabilities BRAHMS can also studythe dependence of the high pT suppression on the type of particle. Prelimi-nary results [58,68] indicate that mesons (pions and kaons) experience highpT suppression while baryons (protons) do not. The reason for this differenceis at present not well understood.

The observed differences may be a consequence of baryons being more sensitiveto flow, because of their larger mass, than mesons. The flow contribution leads

20

[GeV/c]Tp0 0.5 1 1.5 2 2.5 3

-

pi/p0

0.2

0.4

0.6

0.8

1 = 0 ~ 2

BRAHMS Preliminary

Fig. 15. Comparison of the ratios yields of p/pi at rapidities y = 0 and y = 2.2.In spite of small statistics the data suggest that a forward rapidity the flow maybe weaker resulting in a derecreased yield of antiprotons relative to pions abovepT 2 GeV. BRAHMS preliminary [68]

a flatter transverse momentum spectrum for baryons than for mesons, thuspossibly compensating for a high pT suppression effect similar to that of themesons. It is also possible that the difference reflects details associated withthe fragmentation mechanism that leads to different degrees of suppressionof the high pT component for 2 and 3 valence quark systems. Finally thedifference may reflect the mechanism of recombination for 3 quarks relative tothat for 2 quarks in a medium with a high density of quarks.

Figure 14 shows a recent investigation by BRAHMS (ref. [68]) of the baryonto meson ratios at mid-rapidity p/pi+ and p/pi, as a function of pT for the0-10% most central Au+Au collisions at

sNN = 200 GeV. The ratios in-

crease rapidly at low pT and the yields of both protons and anti-protons arecomparable to the pion yields for pT > 2GeV/c. The corresponding ratios forpT > 2GeV/c observed in p + p collisions at

s = 62 GeV [69] and in gluon

jets produced in e+ + e collisions [70] are also shown. The increase of thep/pi+ and p/pi ratios at high pT , seen in central Au+Au collisions, relativeto the level seen in p + p and e+ + e indicates significant differences in theoverall description, either at the production or fragmentation level.

Figure 15 shows the comparison of BRAHMS data for the ratio of antiprotonsto negative pions at = 0 and 2.2. Although statistics at high transversemomentum are low there are indications that the ratio is smaller at the higherrapidity for pT > 2 GeV. Recent calculations based on a parton recombinationscenario [7173] with flow at the partonic level appear to be able to describethe data at midrapidity, while calculations omitting flow fall short of the dataalready at pT 1.5GeV .

The experimental and theoretical investigation of these questions is, however,still in its infancy. These issues can and will be addressed in depth throughthe analysis of the large data set collected by BRAHMS in the high luminosity

21

Au+Au run of year 2004.

6.3 High pT suppression at lower energy?

[GeV/c]Tp0.5 1 1.5 2 2.5 3 3.5 4

AA

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8 =62.4GeVNNsBRAHMS preliminary Au+Au, 0.9, 0-10% central )/2, - + h+(h

Fig. 16. Nuclear modification factor RAuAu measured by BRAHMS for chargedhadrons at = 0.95 for 0 10% central Au+Au collisions at snn = 62.4GeV [74].The dark shaded band indicates the systematic errors on the data, the lighter shadedband the combined estimated systematic error on the Au+Au data data and thep+p reference.

The short commissioning run for Au+Au collisions atsNN = 62.4GeV has

allowed us to carry out a first analysis of the high pT suppression of chargedhadrons at an energy of about 1/3 the maximum RHIC energy and about 3.5times the maximum SPS energy. Preliminary results are shown in figure 16for nuclear modification factor calculated for the sum of all charged hadronsmeasured at 45 degrees( = 0.9) with respect to the beam direction. The datahave been compared to reference spectra measured in

sNN = 63GeV p+p

collisions at the CERN-ISR. The figure shows that the high pT data are lesssuppressed at

sNN = 62.4GeV than at

sNN = 200GeV. This is consistent

with recent results from PHOBOS [75]. For comparison, at SPS energies nohigh pT suppression was observed (albeit a discussion has surfaced regardingthe accuracy of the reference spectra at that energy [62]). It thus seems thesuppression increases smoothly with energy.

The remarkable suppression of high pT jets at mid-rapidity seen at RHIC isan important signal that evidences the interaction of particles originating fromhard parton scatterings with the high energy density medium created in thecollisions. The quantitative understanding of the observed high pT suppression,as a function of energy, should be able to determine whether this suppressionoccurs at the partonic or hadronic level. This needs to be supplemented bydetailed studies of the flavor dependence of the suppression mechanism.

22

7 The color glass condensate: a model for the initial state of nuclei?

As part as the study of the high pT suppression in nucleus-nucleus collisionsBRAHMS has investigated the rapidity dependence of the nuclear modifica-tion factors as a function of rapidity ( = 0, 1, 2.2, 3.2) in d+Au collisions atsNN = 200GeV. As discussed in the previous section the measured nuclear

modification factors for d+Au are consistent with the absence of high pT sup-pression around midrapidity. This may be taken as direct evidence for the factthat the strong high pT suppression seen in Au+Au collisions around y = 0is not due to particular conditions of the colliding nuclei (initial state effects)[63,64,63] and [48].

[GeV/c]Tp1 2 3 4 5 6

d+A

uR

0

0.5

1

1.5

2 = 3.2 -h

[GeV/c]Tp1 2 3 4 5 6

d+A

uR

0

0.5

1

1.5

2 = 2.2 -h

[GeV/c]Tp1 2 3 4 5 6

d+A

uR

0

0.5

1

1.5

2 = 1

2-+h+h

[GeV/c]Tp1 2 3 4 5 6

d+A

uR

0

0.5

1

1.5

2 = 0

2-+h+h

Fig. 17. Evolution of the nuclear modification factors measured by BRAHMS forthe 10% most central d+Au collisions at

sNN = 200GeV, as a function of pseudo-

rapidity [76].

At forward rapidity in d+Au collisions, however, BRAHMS has observed [76]a marked high pT suppression starting already at = 1 (see Fig. 17) andincreasing smoothly in importance with increasing pseudorapidity (up to =3.2). It has been proposed that this effect at forward rapidity [77] is relatedto the initial conditions of the colliding d and Au nuclei, in particular to thepossible existence of the Color Glass Condensate (CGC).

The CGC is a description of the ground state of swiftly moving nuclei priorto collisions [78]. Due to the non Abelian nature of QCD, gluons self inter-act which results in nuclei containing a large number of lowx gluons (x isthe fraction of the longitudinal momentum carried by the parton) that ap-pears to diverge (grow) with decreasing x. There is however, a characteristicmomentum scale, termed the saturation scale, below which the gluon densitysaturates. This effect sets in when x becomes small and the associated gluonwave length ( 1

mpx) increases to nuclear dimensions. In such a regime gluons

may interact and form a coherent state reminiscent of a Bose-Einstein con-densate. Early indications for the formation of such non-linear QCD systemshave been found in lepton-hadron or lepton-nucleus collisions at HERA [79]and have been described by the so called Geometric Scaling model [80].

23

The density of gluons dNgd(ln(1/x))

1s

in such a saturated system is high, sinces, the strong interaction running coupling constant, decreases as the energyincreases. The system can therefore be described as a (semi)classical field, andtechniques borrowed from field theory can be employed to find the functionalform of the parton distributions in the initial state [82].

Saturation in the wave function sets in for gluons with transverse momentumQ2 < Q2s = A

13 (x0

x) A 13 ey. A value of 0.3 is estimated from fits to

HERA data [81]. The dependence of the saturation scale Qs on the atomicnumber of the target and rapidity suggests that saturation effects can be beststudied at RHIC with heavy nuclei at large rapidities, although larger beamenergy will also make it possible in the future to study low x phenomena innuclear collisions closer to midrapidty.

Collisions between heavy ions with energies E = 100AGeV may thereforeprovide a window to the study of lowx gluon distributions of swiftly movingnuclei. In particular, head-on collisions between deuterons and gold nuclei inwhich hadrons, produced mostly in quark-gluon collisions, are detected, closeto the beam direction but away from the direction of motion of the gold nuclei,allow the lowx components (mostly gluons) of the wave function of the goldnuclei to be probed.

[GeV/c]Tp1 2 3 4 5

CPR

0

0.5

1

1.5

2 = 3.2 -h

[GeV/c]Tp1 2 3 4 5

CPR

0

0.5

1

1.5

2 = 2.2 -h

[GeV/c]Tp1 2 3 4 5

CPR

0

0.5

1

1.5

2 = 1

2-+h+h

[GeV/c]Tp1 2 3 4 5

CPR

0

0.5

1

1.5

2

0-20%/60-80%30-50%/60-80%

= 02

-+h+h

Fig. 18. Central to peripheral ratios RCP as a function of pseudorapidity mea-sured by BRAHMS for d+Au collisions at the RHIC top energy [76]. The filledcircles represent the central-to-peripheral (0-20% over 60-80%) ratio. The open cir-cles the semicentral-to-peripheral (30-50% over 60-80%) ratio. The shaded bandaround unity indicates the uncertainty associated with the values of the number ofbinary collisions at the different centralities.

The centrality dependence of the nuclear modification factors provides ad-ditional information on the mechanism underlying the observed suppression.Fig. 18 shows the RCP factors, defined as the ratios of the nuclear spectrafor central (0-20%) and peripheral (60-80%) collisions (closed points) and forsemicentral (30-50%) and peripheral collisions(open points), suitably scaledby the corresponding number of binary collisions, versus pT and . There is asubstantial change in RCP as a function of . At = 0 the central-to-peripheralcollisions ratio is larger than the semicentral-to-peripheral ratios suggesting an

24

increased Cronin type multiple scattering effect in the more violent collisions.In contrast, the ratio of the most central collisions relative to the peripheral, ascompared to the semicentral-to-peripheral, is the most suppressed at forwardrapidities, suggesting a suppression mechanism that scales with the centralityof the collisions.

The observed suppression of yields in d+Au collisions (as compared to p+pcollisions) has been qualitatively predicted by various authors [8386], withinthe Color Glass Condensate scenario. Recently, a more quantitative calcula-tion has been carried out [87] which compares well with the data. Other au-thors [88,89] have estimated the nuclear modification factors based on a twocomponent model that includes a parametrization of perturbative QCD andstring breaking as a mechanism to account for soft coherent particle produc-tion using HIJING. HIJING uses the mechanism of gluon shadowing to reducethe number of gluon-gluon collisions and hence the multiplicity of charged par-ticles a lower pt. HIJING has been shown to give a good description of theoverall charged particle multiplicity in d+Au collisions. A similar approachwas followed by Barnafoldi et al. [90]. Vogt has used realistic parton distribu-tion functions and parametrizations of nuclear shadowing to give a reasonabledescription of the minimum bias data though not of the centrality depen-dence [91]. Guzey et al. have suggested that isospin effects may increase thesuppression [92]. Hwa et al. have reproduced the measured nuclear modifica-tion factors in calculations based on quark recombination in the final state[93].

The high pT -suppression in Au+Au collisions at large rapidites discussed ear-lier suggests that there may be two competing mechanisms responsible for theobserved high pT suppression in energetic Au+Au collisions, each active in itsparticular rapidity window. It has been proposed [8] that the high pT suppres-sion observed around midrapidity reflects the presence of an incoherent (hightemperature) state of quarks and gluons while the the high pT suppressionobserved at forward rapidities bears evidence of a dense coherent partonicstate. Clearly, additional analysis of recent high statistics data for Au +Aucollisions at high rapidites, as well as firmer theoretical predictions are neededto understand the quantitative role of gluon saturation effects in energeticnucleus-nucleus collisions.

The suppression of high pT particles seen at forward rapidities in nucleus-nucleus collisions is a novel and unexpected effect and may be related to a newcollective partonic state that describes nuclei at small x, and hence the initialconditions for the reaction in energetic nucleus-nucleus collisions.

25

8 Conclusions and perspectives

The results from the first round of RHIC experiments clearly show that studiesof high energy nucleus-nucleus collisions have moved to a qualitatively newphysics domain characterized by a high degree of reaction transparency leadingto the formation of a near baryon free central region. There is appreciableenergy loss of the colliding nuclei, so the conditions for the formation of avery high energy density zone with approximate balance between matter andantimatter, in an interval of |y| . 1.5 around midrapidity are present.

The indications are that the initial energy density is considerably larger than5 GeV/fm 3, i.e. well above the energy density at which it is difficult to conceiveof hadrons as isolated and well defined entities. Analysis within the frameworkof the statistical model of the relative abundances of many different particlescontaining the three lightest quark flavors suggest chemical equilibrium ata temperature in the vicinity of T=175 MeV and a near-zero light quarkchemical potential. The temperature thus determined for the chemical freeze-out compares well with the prediction for the critical temperature obtainedfrom lattice QCD calculations. The conditions necessary for the formation ofa dense system of quarks and gluons therefore appear to be present.

However, there are a number of features, early on considered as defining theconcept of the QGP, that do not appear to be realized in the current reactions,or at least have not (yet?) been identified in experiment. These are associatedwith the expectations that a QGP would be characterized by a vanishing in-teraction betweens quarks and exhibit the features of chiral symmetry restora-tion and, furthermore, that the system would exhibit a clear phase transitionbehavior. Likewise, it was originally expected that a QGP phase created innuclear collisions would be characterized by a long lifetime (up to 100 fm/c)and by the existence of a mixed phase exhibiting large fluctuations of charac-teristic parameters. In contrast, the present body of measurements comparedto theory suggest a short lifetime of the system, a large outward pressure, andsignificant interactions most likely at the parton level that result in a (seem-ingly) equilibrated system with fluid-like properties. Thus, the high densityphase that is observed, is not identical to the QGP with properties of an idealgas that was imagined a decade or two ago.

However, the central question is whether the properties of the matter as itis created in todays high energy nucleusnucleus collisions clearly bears theimprint of a system characterized by quark and gluon degrees of freedom overa range larger that the characteristic dimensions of the nucleon. We knowthat in nuclei the strong interaction is mediated by a color neutral objects(mesons). Is there experimental evidence that clearly demonstrates interac-tions based on the exchange of objects with color over distances larger than

26

those of conventional confined objects?

The best candidate for such an effect is clearly the suppression of high trans-verse momentum particles observed in central Au+Au collisions by the fourexperiments at RHIC. The remarkably large effect that is observed (a sup-pression by a factor of 3-5 as compared to peripheral and d+Au collisions)appears readily explainable by radiation losses due to the interaction of highpT partons with an extended medium (of transverse dimensions considerablylarger than nucleon dimensions) consisting of deconfined color charges. Cur-rent theoretical investigations, which recently have progressed to attempt firstunified descriptions of the reaction evolution, indicate that scenarios based oninteractions between hadronic objects cannot reproduce the magnitude of theobserved effect.

The interpretation of current data relies heavily on theoretical input and mod-elling, in particular on the apparent necessity to include partonic degrees offreedom in order to arrive at a consistent description of many of the phenomenaobserved in the experimental data. Seen from a purely experimental point ofview this situation is somewhat unsatisfying, but probably not unexpected, noravoidable, considering the complexity of the reaction and associated processes.

It is also clear that the unravelling of the physics of the matter state(s) ob-served at RHIC has just begun. In spite of the impressive advances that havebeen made in the last three years there are still many issues to be understoodin detail, such as the differences in the high pT suppression of baryons andmesons and the quantitative energy and rapidity dependence of the final andinitial state high pT suppression. Undoubtedly future measurements will shednew light on these and many other questions. We should not forget, however,that there are also significant challenges for theory. In the opening chaptersof this document we remarked on the requirement that scientific paradigmsmust be falsifiable. We have yet to see a fully self consistent calculation of theentire reaction evolution at RHIC that in an unambiguous way demonstratesthe impossibility of a hadronic description.

In conclusion, we find that the body of information obtained by BRAHMSand the other RHIC experiments in conjunction with the available theoret-ical studies is strongly suggestive of a high density system that cannot becharacterized solely by hadronic degrees of freedom but requires a partonicdescription. Indications are that such a partonic state is not characterized byvanishing interaction of its constituents, but rather by a relatively high degreeof coherence such as the one characterizing fluids. At the same time indica-tions of a coherent partonic state at low x in the colliding nuclei has beenfound.

There is no doubt that the experiments at RHIC have revealed a plethora of

27

new phenomena that for the most part have come as a surprise. In this sense itis clear that the matter that is created at RHIC differs from anything that hasbeen seen before. Its precise description must await our deeper understandingof this matter.

9 Acknowledgements

This work was supported by the Division of Nuclear Physics of the Officeof Science of the U.S. Department of Energy under contracts DE-AC02-98-CH10886, DE-FG03-93-ER40773, DE-FG03-96-ER40981, and DE-FG02-99-ER41121, the Danish Natural Science Research Council, the Research Councilof Norway, the Jagiellonian University Grants, the Korea Research FoundationGrant and the Romanian Ministry of Education and Research (5003/1999,6077/2000). We thank the staff of the Collider-Accelerator Division at BNLfor their excellent and dedicated work to deploy RHIC and their support tothe experiment.

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32

Formation of dense partonic matter in

relativistic nucleus-nucleus collisions at RHIC:

Experimental evaluation by the PHENIX

collaboration

K. Adcox be S.S. Adler e S. Afanasiev t C. Aidala e,j

N.N. Ajitanand aw Y. Akiba w,aq,ar A. Al-Jamel a J. Alexander aw

R. Amirikas n K. Aoki aa,aq L. Aphecetche az Y. Arai w

R. Armendariz a S.H. Aronson e R. Averbeck ay T.C. Awes am

R. Azmoun e,ay V. Babintsev q A. Baldisseri k K.N. Barish f

P.D. Barnes ad J. Barrette ag B. Bassalleck ak S. Bathe f,ah

S. Batsouli j V. Baublis ap F. Bauer f A. Bazilevsky e,q,ar

S. Belikov e,q,s F.G. Bellaiche am S.T. Belyaev z M.J. Bennett ad

Y. Berdnikov at S. Bhagavatula s M.T. Bjorndal j

J.G. Boissevain ad H. Borel k S. Borenstein ab S. Botelho au

M.L. Brooks ad D.S. Brown a N. Bruner ak D. Bucher ah

H. Buesching e,ah V. Bumazhnov q G. Bunce e,ar

J.M. Burward-Hoy ac,ad,ay S. Butsyk ap,ay X. Camard az

T.A. Carey ad J.-S. Chai u P. Chand d J. Chang f W.C. Chang b

L.L. Chavez ak S. Chernichenko q C.Y. Chi j J. Chiba w M. Chiu j

I.J. Choi bh J. Choi v R.K. Choudhury d T. Christ ay

T. Chujo e,bd,be M.S. Chung y,ad P. Chung aw V. Cianciolo am

C.R. Cleven o Y. Cobigo k B.A. Cole j M.P. Comets an

P. Constantin s M. Csanadm T. Csorgo x J.P. Cussonneau az

D. dEnterria j T. Dahms ay K. Das n G. David e F. Deakm

H. Delagrange az A. Denisov q A. Deshpande ar,ay E.J. Desmond e

A. Devismes ay O. Dietzsch au B.V. Dinesh d J.L. Drachenberg a

O. Drapier ab A. Drees ay A.K. Dubey bg R. du Rietz af

A. Durum q D. Dutta d V. Dzhordzhadze ba K. Ebisu aj

Y.V. Efremenko am J. Egdemir ay K. El Chenawi be

A. Enokizono p H. Enyo aa,aq,ar B. Espagnon an S. Esumi bd

L. Ewell e T. Ferdousi f D.E. Fields ak,ar C. Finck az F. Fleuret ab

S.L. Fokin z B. Forestier ae B.D. Fox ar Z. Fraenkel bg

Preprint submitted to Elsevier Science 21 March 2005

J.E. Frantz j A. Franz e A.D. Frawley n Y. Fukao aa,aq,ar

S.-Y. Fung f S. Gadrat ae S. Garpman af,1 F. Gastineau az

M. Germain az T.K. Ghosh be A. Glenn ba A.L. Godoi au

G. Gogiberidze ba M. Gonin ab J. Gosset k Y. Goto aq,ar

R. Granier de Cassagnac ab N. Grau s S.V. Greene be

M. Grosse Perdekamp r,ar T. Gunji h S.K. Gupta d W. Guryn e

H.-A. Gustafsson af T. Hachiya p,aq A. Hadjhenni az

J.S. Haggerty e M.N. Hagiwara a H. Hamagaki h A.G. Hansen ad

H. Hara aj H. Harada p E.P. Hartouni ac K. Haruna p M. Harvey e

E. Haslum af K. Hasuko aq R. Hayano h,bc N. Hayashi aq X. He o

M. Heffner ac T.K. Hemmick ay J.M. Heuser aq,ay M. Hibino bf

P. Hidas x H. Hiejima r J.C. Hill s D.S. Ho bh R. Hobbs ak

M. Holmes be W. Holzmann aw K. Homma p B. Hong y

A. Hoover a T. Horaguchi aq,ar,bb H.M. Hur u T. Ichihara aq,ar

V.V. Ikonnikov z K. Imai aa,aq M. Inaba bd M. Inuzuka h

M.S. Ippolitov z D. Isenhower a L. Isenhower a M. Ishihara aq,ar

T. Isobe h M. Issah aw A. Isupov t B.V. Jacak ar,ay W.Y. Jang y

Y. Jeong v J. Jia j,ay J. Jin j O. Jinnouchi aq,ar B.M. Johnson e

S.C. Johnson ac,ay K.S. Joo ai D. Jouan an F. Kajihara h,aq

S. Kametani h,bf N. Kamihara aq,bb M. Kaneta ar J.H. Kang bh

M. Kann ap S.S. Kapoor d K. Katou bf T. Kawabata h

T. Kawagishi bd A.V. Kazantsev z S. Kelly i,j B. Khachaturov bg

A. Khanzadeev ap J. Kikuchi bf D.H. Kim ai D.J. Kim bh

D.W. Kim v E. Kim av G.-B. Kim ab H.J. Kim bh S.Y. Kim bh

Y.-S. Kim u Y.G. Kim bh E. Kinney i W.W. Kinnison ad

A. Kissm E. Kistenev e A. Kiyomichi aq,bd K. Kiyoyama aj

C. Klein-Boesing ah S. Klinksiek ak H. Kobayashi aq,ar

L. Kochenda ap V. Kochetkov q D. Koehler ak T. Kohama p

R. Kohara p B. Komkov ap M. Konno bd M. Kopytine ay

D. Kotchetkov f A. Kozlov bg P.J. Kroon e C.H. Kuberg a,ad

G.J. Kunde ad N. Kurihara h K. Kurita aq,ar,as Y. Kuroki bd

M.J. Kweon y Y. Kwon bh G.S. Kyle a R. Lacey aw V. Ladygin t

J.G. Lajoie s J. Lauret aw Y. Le Bornec an A. Lebedev s,z

S. Leckey ay D.M. Lee ad M.K. Lee bh S. Lee v M.J. Leitch ad

M.A.L. Leite au X.H. Li f Z. Li g,aq D.J. Lim bh H. Lim av

34

A. Litvinenko t M.X. Liu ad X. Liu g Y. Liu an Z. Liu g

C.F. Maguire be J. Mahon e Y.I. Makdisi e A. Malakhov t

M.D. Malik ak V.I. Manko z Y. Mao g,ao,aq S.K. Mark ag

S. Markacs j G. Martinez az M.D. Marx ay A. Masaike aa

H. Masui bd F. Matathias ay T. Matsumoto h,bf M.C. McCain a,r

P.L. McGaughey ad E. Melnikov q M. Merschmeyer ah

F. Messer ay M. Messer e Y. Miake bd J. Milan aw T.E. Miller be

A. Milov ay,bg S. Mioduszewski e,ba R.E. Mischke ad G.C. Mishra o

J.T. Mitchell e A.K. Mohanty d D.P. Morrison e J.M. Moss ad

T.V. Moukhanova z F. Muhlbacher ay D. Mukhopadhyay be,bg

M. Muniruzzaman f J. Murata aq,ar,as S. Nagamiya w

Y. Nagasaka aj Y. Nagata bd J.L. Nagle i,j M. Naglis bg

Y. Nakada aa T. Nakamura p B.K. Nandi f M. Nara bd

J. Newby ac,ba M. Nguyen ay L. Nikkinen ag P. Nilsson af

S. Nishimura h B. Norman ad A.S. Nyanin z J. Nystrand af

E. OBrien e C.A. Ogilvie s H. Ohnishi e,p,aq I.D. Ojha c,be

H. Okada aa,aq K. Okada aq,ar O.O. Omiwade a M. Ono bd

V. Onuchin q A. Oskarsson af L. Osterman af I. Otterlund af

K. Oyama h,bc K. Ozawa h L. Paffrath e,1 D. Pal be,bg

A.P.T. Palounek ad V. Pantuev ay V. Papavassiliou a J. Park av

W.J. Park y A. Parmar ak S.F. Pate a H. Pei s T. Peitzmann ah

V. Penev t J.-C. Peng r,ad H. Pereira k V. Peresedov t

D.Yu. Peressounko z A.N. Petridis s A. Pierson ak

C. Pinkenburg e,aw R.P. Pisani e P. Pitukhin q F. Plasil am

M. Pollack ay,ba K. Pope ba M.L. Purschke e A.K. Purwar ay

H. Qu o J.M. Qualls a J. Rak s I. Ravinovich bg K.F. Read am,ba

M. Reuter ay K. Reygers ah V. Riabov ap,at Y. Riabov ap

G. Roche ae A. Romana ab M. Rosati s A.A. Rose be

S.S.E. Rosendahl af P. Rosnet ae P. Rukoyatkin t V.L. Rykov aq

S.S. Ryu bh M.E. Sadler a B. Sahlmueller ah N. Saito aa,aq,ar

A. Sakaguchi p T. Sakaguchi h,bf M. Sakai aj S. Sakai bd

H. Sako bd T. Sakuma aq,bb V. Samsonov ap L. Sanfratello ak

T.C. Sangster ac R. Santo ah H.D. Sato aa,aq S. Sato e,w,bd

S. Sawada w B.R. Schlei ad Y. Schutz az V. Semenov q R. Seto f

D. Sharma bg M.R. Shaw a,ad T.K. Shea e I. Shein q

35

T.-A. Shibata aq,bb K. Shigaki p,w T. Shiina ad M. Shimomura bd

Y.H. Shin bh T. Shohjoh bd K. Shoji aa,aq I.G. Sibiriak z

A. Sickles ay C.L. Silva au D. Silvermyr ad,af,am K.S. Sim y

J. Simon-Gillo ad C.P. Singh c V. Singh c M. Sivertz e S. Skutnik s

W.C. Smith a A. Soldatov q R.A. Soltz ac W.E. Sondheim ad

S.P. Sorensen am,ba I.V. Sourikova e F. Staley k P.W. Stankus am

N. Starinsky ag P. Steinberg j E. Stenlund af M. Stepanov a

A. Ster x S.P. Stoll e M. Sugioka aq,bb T. Sugitate p C. Suire an

J.P. Sullivan ad Y. Sumi p Z. Sun g M. Suzuki bd J. Sziklai x

T. Tabaru ar S. Takagi bd E.M. Takagui au A. Taketani aq,ar

M. Tamai bf K.H. Tanaka w Y. Tanaka aj K. Tanida aq,ar

E. Taniguchi aq,bb M.J. Tannenbaum e A. Taranenko aw

P. Tarjan J.D. Tepe a,ad J. Thomas ay J.H. Thomas ac

T.L. Thomas ak W. Tian g,ba M. Togawa aa,aq J. Tojo aa,aq

H. Torii aa,aq,ar R.S. Towell a,ad V-N. Tram ab I. Tserruya bg

Y. Tsuchimoto p,aq H. Tsuruoka bd A.A. Tsvetkov z S.K. Tuli c

H. Tydesjo af N. Tyurin q T.J. Uam ai T. Ushiroda aj H. Valle be

H.W. van Hecke ad C. Velissaris a J. Velkovska e,ay,be

M. Velkovsky ay R. Vertesi V. Veszpremi L. Villatte ba

A.A. Vinogradov z M.A. Volkov z A. Vorobyov ap

E. Vznuzdaev ap M. Wagner aa H. Wang f X.R. Wang o,a

Y. Watanabe aq,ar J. Wessels ah S.N. White e N. Willis an

D. Winter j C. Witzig e F.K. Wohn s C.L. Woody e M. Wysocki i

W. Xie f,ar,bg K. Yagi bd Y. Yang g A. Yanovich q S. Yokkaichi aq,ar

G.R. Young am I. Younus ak I.E. Yushmanov z W.A. Zajc j

O. Zaudkte ah C. Zhang j Z. Zhang ay S. Zhou g S.J. Zhou bg

J. Zimanyi x L. Zolin t X. Zong s (PHENIX Collaboration)

aAbilene Christian University, Abilene, TX 79699, USA

bInstitute of Physics, Academia Sinica, Taipei 11529, TaiwancDepartment of Physics, Banaras Hindu University, Varanasi 221005, India

dBhabha Atomic Research Centre, Bombay 400 085, IndiaeBrookhaven National Laboratory, Upton, NY 11973-5000, USAfUniversity of California - Riverside, Riverside, CA 92521, USA

gChina Institute of Atomic Energy (CIAE), Beijing, Peoples Republic of ChinahCenter for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1

36

Hongo, Bunkyo, Tokyo 113-0033, JapaniUniversity of Colorado, Boulder, CO 80309

jColumbia University, New York, NY 10027 and Nevis Laboratories, Irvington,NY 10533, USA

kDapnia, CEA Saclay, F-91191, Gif-sur-Yvette, FranceDebrecen University, H-4010 Debrecen, Egyetem ter 1, Hungary

mELTE, Eotvos Lorand University, H - 1117 Budapest, Pazmany P. s. 1/A,Hungary

nFlorida State University, Tallahassee, FL 32306, USAoGeorgia State University, Atlanta, GA 30303, USA

pHiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, JapanqInstitute for High Energy Physics (IHEP), Protvino, Russia

rUniversity of Illinois at Urbana-Champaign, Urbana, IL 61801sIowa State University, Ames, IA 50011, USA

tJoint Institute for Nuclear Research, 141980 Dubna, Moscow Region, RussiauKAERI, Cyclotron Application Laboratory, Seoul, South Korea

vKangnung National University, Kangnung 210-702, South KoreawKEK, High Energy Accelerator Research Organization, Tsukuba-shi, Ibaraki-ken

305-0801, JapanxKFKI Research Institute for Particle and Nuclear Physics (RMKI), H-1525

Budapest 114, POBox 49, HungaryyKorea University, Seoul, 136-701, Korea

zRussian Research Center Kurchatov Institute, Moscow, RussiaaaKyoto University, Kyoto 606, Japan

abLaboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route deSaclay, F-91128, Palaiseau, France

acLawrence Livermore National Laboratory, Livermore, CA 94550, USAadLos Alamos National Laboratory, Los Alamos, NM 87545, USA

aeLPC, Universite Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 AubiereCedex, France

afDepartment of Physics, Lund University, Box 118, SE-221 00 Lund, SwedenagMcGill University, Montreal, Quebec H3A 2T8, Canada

ahInstitut fur Kernphysik, University of Muenster, D-48149 Muenster, GermanyaiMyongji University, Yongin, Kyonggido 449-728, Korea

ajNagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, JapanakUniversity of New Mexico, Albuquerque, NM 87131, USAaNew Mexico State University, Las Cruces, NM 88003, USA

amOak Ridge National Laboratory, Oak Ridge, TN 37831, USA

37

anIPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, FranceaoPeking University, Beijing, Peoples Republic of China

apPNPI, Petersburg Nuclear Physics Institute, Gatchina, RussiaaqRIKEN (The Institute of Physical and Chemical Research), Wako, Saitama

351-0198, JAPANarRIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY

11973-5000, USAasPhysics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo

171-8501, JapanatSt. Petersburg State Technical University, St. Petersburg, Russia

auUniversidade de Sao Paulo, Instituto de Fsica, Caixa Postal 66318, Sao PauloCEP05315-970, Brazil

avSystem Electronics Laboratory, Seoul National University, Seoul, South KoreaawChemistry Department, Stony Brook University, Stony Brook, SUNY, NY

11794-3400, USAayDepartment of Physics and Astronomy, Stony Brook University, SUNY, Stony

Brook, NY 11794, USAazSUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universite de Nantes)

BP 20722 - 44307, Nantes, FrancebaUniversity of Tennessee, Knoxville, TN 37996, USA

bbDepartment of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, JapanbcUniversity of Tokyo, Tokyo, Japan

bdInstitute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, JapanbeVanderbilt University, Nashville, TN 37235, USA

bfWaseda University, Advanced Research Institute for Science and Engineering, 17Kikui-cho, Shinjuku-ku, Tokyo 162-0044, JapanbgWeizmann Institute, Rehovot 76100, Israel

bhYonsei University, IPAP, Seoul 120-749, Korea

Abstract

Extensive experimental data from high-energy nucleus-nucleus collisions were recordedusing the PHENIX detector at the Relativistic Heavy Ion Collider (RHIC). Thecomprehensive set of measurements from the first three years of RHIC operationincludes charged particle multiplicities, transverse energy, yield ratios and spectraof identified hadrons in a wide range of transverse momenta (pT ), elliptic flow,two-particle correlations, non-statistical fluctuations, and suppression of particleproduction at high pT . The results are examined with an emphasis on implicationsfor the formation of a new state of dense matter. We find that the state of mattercreated at RHIC cannot be described in terms of ordinary color neutral hadrons.

38

1 INTRODUCTION

1.1 Historical Introduction

A recurring theme in the history of physics is the desire to study matter underextreme conditions. The latter half of the twentieth century saw this quest ex-tended from ordinary atomic systems to those composed of nuclear matter.Even prior to the identification of Quantum Chromodynamics (QCD) as theunderlying theory of the strong interaction, there was considerable interest inthe fate of nuclear matter when subjected to density and temperature ex-tremes [13]. Particularly intriguing was the suggestion that new phases ofnuclear matter could be associated with a corresponding change in the struc-ture of the vacuum [4]. These considerations gained additional impetus withthe realizations that a) QCD was the correct theory of the strong interaction,b) the phenomena of quark confinement was a consequence of the nonpertur-bative structure of the vacuum and c) this vacuum structure is modified athigh temperatures and/or densities, suggesting that quarks and gluons undersuch conditions would be deconfined. Taken together, these facts suggest thatQCD is a fundamental theory of nature containing a phase transition that isaccessible to experimental investigation.

It is quite remarkable that this understanding was achieved very early in thedevelopment of QCD. Collins and Perry noted in 1975 [5] that the reductionof the coupling constant at small distances indicated that the dense nuclearmatter at the center of neutron stars would consist of deconfined quarks andgluons 2 . Their treatment focused on the high-density, low-temperature regimeof QCD, but they did note that similar arguments might apply to the hightemperatures present in the early universe. An extensive review by Shuryakin 1980 [7] is the first to have examined the high-temperature phase in detail,and is also notable for proposing the phrase quark-gluon plasma (QGP) todescribe the deconfined state:

When the energy density exceeds some typical hadronic value ( 1 GeV/fm3),matter no longer consists of separate hadrons (protons, neutrons, etc.), but

Email address: PHENIXSpokesperson: zajc@nevis.columbia.edu(W.A. Zajc).1 Deceased2 In fact, prior to the development of QCD the quark hypothesis raised seriousissues concerning the stability of neutron stars [6].

39

as their fundamental constituents, quarks and gluons. Because of the ap-parent analogy with similar phenomena in atomic physics we may call thisphase of matter the QCD (or quark-gluon) plasma.

Developing a quantitative understanding of the deconfining phase transitionin hadronic matter and of QGP properties has proven to be a challengingtask. While simple dimensional arguments suffice to identify both the criti-cal energy density C 1GeV/fm3 and the associated critical temperatureTC 170MeV, these values also imply that the transition occurs in a regimewhere the coupling constant is of order unity, thereby making perturbativedescriptions highly suspect.

Progress in understanding QCD in the extremely non-perturbative domainnear the critical temperature has relied on an essential contribution by Creutz[8], who showed that numerical implementations of Wilsons lattice formu-lation [9] could be used to study phase transition phenomena. This work,together with the continued exponential increases in computing power, stim-ulated the development of lattice QCD, which in turn has led to detailedinvestigations of the thermodynamic properties of quarks and gluons [10].

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

T/Tc

/T4 SB/T4

3 flavour2+1 flavour

2 flavour

Fig. 1. Lattice QCD results [11] for the energy density / T 4 as a function of thetemperature scaled by the critical temperature TC . Note the arrows on the rightside indicating the values for the Stefan-Boltzmann limit.

Lattice QCD predicts a phase transformation to a quark-gluon plasma at atemperature of approximately T 170MeV 1012 K, as shown in Fig. 1 [11].

40

This transition temperature corresponds to an energy density 1GeV/fm3,nearly an order of magnitude larger than that of normal nuclear matter. Asnoted above, this value is plausible based on dimensional grounds, since suchdensities correspond to the total overlap of several (light) hadrons within atypical hadron volume of 13 fm3. No plausible mechanism exists under whichhadrons could retain their in vacuo properties under these conditions. Latticecalculations also indicate that this significant change in the behavior of thesystem occurs over a small range in temperature (20 MeV), and suggest thatthe change of phase includes the restoration of approximate chiral symmetryresulting from greatly reduced or vanishing quark constituent masses.

Fig. 2. Theoretical phase diagram of nuclear matter for two massless quarks as afunction of temperature T and baryon chemical potential [12].

In the limit of massless noninteracting particles, each bosonic degree of free-dom contributes

2

30T 4 to the energy density; each fermionic degree of freedom

contributes 78this value. The corresponding Stefan-Boltzmann limits of the

energy density SB for the case of 2(3) active flavor quark-gluon plasma isthen

{2f 2s 2q 3c78+ 2s 8c}pi

2

30T 4 = 37

pi2

30T 4 (1)

SB =

{3f 2s 2q 3c78+ 2s 8c}pi

2

30T 4 = 47.5

pi2

30T 4 (2)

after summing over the appropriate flavor, spin, quark/antiquark and colorfactors for quarks and spin times color factors for gluons. The large numerical

41

coefficients (37 and 47.5) stand in stark contrast to the value of 3 expectedfor a hadron gas with temperature T < TC , in which case the degrees offreedom are dominated by the three pion species pi, pi0, pi+.

The exact order of this phase transition is not known. In a pure gauge the-ory containing only gluons the transition appears to be first order. However,inclusion of two light quarks (up and down) or three light quarks (adding thestrange quark) can change the transition from first order to second order toa smooth crossover. These results are obtained at zero net baryon density;dramatic changes in the nature of the transition and in the medium itself areexpected when the net baryon density becomes significant. A schematic versionof the phase diagram for an idealized form of nuclear matter with vanishinglight quark (up and down) masses and infinite strange quark mass is presentedin Fig. 2 [12]. For sufficiently large values of the baryon chemical potential this system exhibits a first order phase transition between hadronic matterand QGP, along with a tricritical point below which the transition becomessecond order. However, non-zero values of the light quark masses dramaticallyalter this simple picture: The second order phase transition denoted by thedashed line in Fig. 2 becomes a smooth crossover, and the tricritical pointcorrespondingly becomes a critical point designating the end of the first ordertransition found at higher values of . For example, recent calculations [13,14]indicate that the transition is a crossover for values of

quark and gluon degrees of freedom. This is supported by explicit calculationsof the spectrum of bound states above TC [22] which predict a rich structureof states that belies a description as a weakly interacting parton gas.

To emphasize this point, consider the standard measure of the degree of cou-pling in a classical plasma, obtained by comparing the relative magnitudes ofthe average kinetic and potential energies:

V (r)Ekin . (3)

In the case of the QCD plasma the mean inter-particle spacing should scaleas some numerical coefficient times 1/T . Naively, this gives a mean potentialenergy V (r) s(T )1/r s(T )T , leading to

s(T )T3T

s(T ). (4)

Any reasonable estimate for the numerical coefficients leads to > 1, which isthe condition for a strongly-coupled plasma. In reality, the screening presentat such densities (or equivalently, the generation of effective gluon masses)modifies the mean potential energy to V (r) g(T )T , which only increasesthe estimated value of [23]. Considerations such as these have led someauthors [24,25] to denote quark-gluon plasma in this regime as sQGP forstrongly interacting QGP.

It is worth noting that this state of affairs has been anticipated by manyauthors. Whether the argument was based on the divergence of perturbativeexpansions [26], on phenomenological descriptions of confinement [27], on thedevelopment of effective gluon masses from plasmon modes [28] or on generalprinciples [15], it is clear that the QGP near TC should not be regarded as anideal gas of quarks and gluons.

How high a temperature is needed not just to form a quark-gluon plasma, butto approach this weakly interacting plasma? A calculation of the pressureof hot matter within perturbative QCD [29] is shown in Fig. 3. The pressureresult oscillates significantly as one considers contributions of different orders.These oscillations are an indication that the expansion is not yielding reliableresults. However at temperatures approaching 1000 times of TC ( MS), theyappear to be converging toward the Stefan-Boltzmann limit (asymptoticallyfree partons). It is interesting that in considering the highest-order term, theresults are still nonconvergent though one seems to approach the lattice cal-culated pressure. Unlike the case of single parton-parton scattering at zerotemperature, the infrared problems of finite-temperature field theory preventfurther analytic progress even for very small values of the coupling constant

43

1 10 100 1000T/MS

_

0.0

0.5

1.0

1.5p/

p SB

g2

g3

g4

g5

g6(ln(1/g)+0.7)4d lattice

Fig. 3. Perturbative QCD results for the pressure as a function of temperature atvarious orders normalized to the Stefan-Boltzmann value pSB [29].

[2931].

The goal of relativistic heavy ion physics is the experimental study of thenature of QCD matter under conditions of extreme temperature. A great em-phasis has been placed on the discovery of the quark-gluon plasma, wherethe terminology quark-gluon plasma is used as a generic descriptor for asystem in which the degrees of freedom are no longer the color neutral hadronstates observed as isolated particles and resonances. This definition is lim-ited since high-energy proton-proton reactions cannot be described purely interms of color-neutral hadrons, but rather require analysis of the underlyingpartonic interactions. The hoped-for essential difference in heavy ion collisionsis the dominance of the partonic-level description for essentially all momentumscales and over nuclear size distances. Beyond this simple criterion, in order tocharacterize the produced system as a state of matter it is necessary to estab-lish that these non-hadronic degrees of freedom form a statistical ensemble,

44