arXiv:nucl-ex/0611012 v1 9 Nov 2006kperl/HIP/QGP_MATTER_revier_11_2006.pdf · • Parton structure...

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TOPICAL REVIEW

Quark-Gluon Matter

David d’EnterriaCERN, PH-EP, CH - 1211 Geneva 23, Switzerland

E-mail: e-mail:david.d’[email protected]

Abstract. A concise review of the experimental and phenomenological progress in high-energy heavy-ion physics over the past few years is presented. Emphasis is put onmeasurements at BNL-RHIC and CERN-SPS which provide information on fundamentalproperties of QCD matter at extreme values of temperature, density and low-x. The newopportunities accessible at the LHC, which may help clarifysome of the current open issues,are also outlined.

PACS numbers: 12.38.-t, 12.38.Mh, 13.85.-t, 13.87.Fh, 25.75.-q, 25.75.Nq

Submitted to:J. Phys. G: Nucl. Part. Phys.

Introduction

The study 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) has attracted an increasing experimental and theoreticalinterest during the last 20years. Indeed, QCD is not only a quantum field theory with an extremely rich dynamicalcontent (asymptotic freedom, infrared slavery, (approximate) chiral symmetry, non trivialvacuum topology, strong CP violation problem,UA(1) axial-vector anomaly, ...) butalso the only sector of the Standard Model whosecollectivebehaviour – phase diagram,phase transitions, thermalization of fundamental fields – is accessible to scrutiny in thelaboratory. The study of the many-body dynamics of high-density QCD covers a vast rangeof fundamental physics problems (Fig. 1):

• Deconfinement and chiral symmetry restoration: Lattice QCD calculations [1] predicta new form of matter at energy densities (well) aboveεcrit ≈ 1 GeV/fm3 consisting ofan extended volume of deconfined and bare-mass quarks and gluons: the Quark GluonPlasma (QGP) [2]. The scrutiny of this new state of matter – equation-of-state (EoS),order of the phase transition, transport properties, etc. –promises to shed light onbasic aspects of the strong interaction such as the nature ofconfinement, the mechanismof mass generation (chiral symmetry breaking, structure ofthe QCD vacuum) andhadronization, which still evade a thorough theoretical description [3] due to their highlynon-perturbative nature.

Quark-Gluon Matter 2

high temperaturequark gluon plasma (QGP)

large Nstrings

large densitycolour superconductivity

low densityhadronic matter

large N

color glass condensate

(CGC)

conformal phase

c

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nucleineutron stars corevacuum

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3 GeV3> ~ (-0.23)ψψ< GSI

AGS

tri-critical point

> >0ψψ<

orderst1

crossover

superconductorcolour

0.93 GeV

freeze-out line

gasFermiliquid

hadron

Figure 1. Left: The multiple facets of QCD (adapted from [4]). Right: QCD phasediagram in the temperature vs. baryochemical potential (T,µB) plane. The arrows indicatethe expected crossing through the deconfinement transitionduring the expansion phase inheavy-ion collisions at different accelerators. The dashed freeze-out curve indicates wherehadrochemical equilibrium is attained in the latest stage of the collision [5].

• Early universe cosmology: The quark-hadron phase transition took place some 10µsafter the Big-Bang and is believed to have been the most important event in the Universebetween the electro-weak (or SUSY) transition (τ ∼ 10−10 s) and nucleosynthesis (τ ∼200 s). Depending on the order of the transition‡, several cosmological implications havebeen postulated [6] such as the formation of strangelets andcold dark-matter (WIMP)clumps, or baryon fluctuations leading to inhomogeneous nucleosynthesis.

• Parton structure and evolution at small-x: HERA data [7] indicates that when probedat high energies, hadrons consist of a very dense system of gluons with small (Bjorken)momentumx = pparton/phadron. At low-x, the probability to emit an extra gluon is large,∝ αs ln(1/x), and gg fusion processes will eventually dominate the parton evolutionin the hadronic wavefunctions. At high virtualitiesQ2 and moderately lowx, suchevolution is described by linear DGLAP [8] or BFKL [9] equations, suitable for a diluteparton regime. Atx. 10−2 and below an energy-dependent “saturation momentum”Qs,hadrons are however more appropriately described as dense,saturated parton systemsin the context of the “Colour Glass Condensate” (CGC) [10] effective theory with thecorresponding non-linear JIMWLK evolution equations [11]. Since the growth of thegluon density depends on the transverse size of the hadron, saturation effects are expectedto set in earlier for ultrarelativistic heavy nuclei (for which Q2

s ∝ A1/3, with A the numberof nucleons) than for free nucleons.

• Gauge/String duality: Theoretical applications of the Anti-de-Sitter/Conformal-Field-Theory (AdS/CFT) correspondence provide results in strongly coupled (λ = g2Nc ≫ 1)SU(Nc) gauge theories in terms of a weakly-coupled dual gravity theory [12]. Recent

‡ The order itself is not exactly known: the transition, which is 1st-order in pure SU(3) gluodynamics and of afast cross-over type forNf = 2+1 quarks [1], is still sensitive to lattice extrapolations to the continuum limit.


applications of this formalism for QCD-like (N = 4 super Yang-Mills) theories haveled to the determination of transport properties of experimental relevance – such asthe QGP viscosity [13], the “jet quenching” parameter〈q〉 [14], or the heavy-quarkdiffusion coefficient [15] – from black hole thermodynamicscalculations. Such resultsprovide valuable insights ondynamicalproperties of strongly-coupled QCD that cannotbe directly treated by perturbative or lattice methods, andopen new phenomenologicaland experimental leads.

• Compact object astrophysics: At high baryon densities and not too high temperatures,the attractive force between (colour antisymmetric) quarks can lead to the formation ofbound〈qq〉 Cooper pairs. Cold dense matter is thus expected to behave asa coloursuperconductor with a non trivial quark pairing structure due to the combination of thevarious quantum numbers involved (spin, colour, flavour) [16]. This regime, currentlybeyond the direct reach of accelerator-based research, maybe realized in the core ofcompact stars (neutron, hybrid or other exotic stars) and, thus, open to study throughastronomical observation.

The only experimental means available so far to investigatethe (thermo)dynamics of a multi-parton system involves the use of large atomic nuclei collided at ultrarelativistic energies.Figure 2 left, shows the total center-of-mass energy available for particle production (i.e.subtracting the rest mass of the colliding hadrons) at different accelerators as a function ofthe first operation year (“Livingston plot”) [17]. The exponential increase in performancetranslates into an energy doubling every 2 (3) years for the ion (p, p) beams. Head-on collisions of heavy ions (AA) can produce extremely hot and dense QCD matter byconcentrating a substantial amount of energy (O(1 TeV) at mid-rapidities at the LHC, seeFig. 2 right) in anextendedcylindrical volumeV = πR2

Aτ0 ≈ 150 fm3 for a typical largenucleus with radiusRA = 6.5 fm, at thermalization times ofτ0 = 1 fm/c.

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Figure 2. Left: “Livingston plot” for (anti)proton and ion accelerators in the period 1960-2008 (adapted from [17]). Right: Measured transverse energy per unit rapidity atη = 0, andcorresponding Bjorken energy densityεBj(τ0 = 1 fm/c) [18], in central heavy-ion collisions atvarious c.m. energies [19, 20] fitted to a logarithmic parametrization.


The hot and dense systems produced in high-energyAAcollisions are not prepared under con-trolled thermodynamical conditions but they follow a dynamical trajectory along the phasediagram shown e.g. in Fig. 1, right. After the collision, thesystem (with a temperatureprofile decreasing from the center) expands with relativistic longitudinal (transverse) veloc-ities 〈β〉 ≈ 1.0(0.5) and cools at ratesT ∝ τ−1/n (e.g. n = 3 for a longitudinal-only expan-sion [18]). WhenT reachesTcrit ≈ 190 MeV, the quark matter undergoes a phase transi-tion into hadrons. The produced hadronic gas stops self-interacting collectively at freeze-outtimesτ ≈ 10 – 20 fm/c [21]. At the initial stages of the reaction (1 fm/c after impact), thecommonly used “Bjorken estimate” [18] gives energy densities attained at mid-rapidity ofεBj = dET/dη|η=0/(πR2

Aτ0) ≈ 5, 10 GeV/fm3 at RHIC and LHC (Fig. 2 right). Althoughthese values can only be considered as a lower limit since they are obtained in a simple 1+1Dexpansion scenario ignoring any effects from longitudinalwork, they are already about 5 and10 times larger, respectively, than the QCD critical energydensity for deconfinement. High-energy collisions in heavy-ion colliders provide therefore the appropriate conditions for thestudy of highly excited quark-gluon matter.

This review is organized as follows. Sections 1 introduces the experimental probes ofsubhadronic matter used in high-energyAA collisions. Section 2 briefly reviews theexperimental apparatus used in heavy-ion collisions at RHIC and SPS. In Section 3 varioushard QCD results from proton-proton collisions at RHIC are presented as the “free space”baseline to which one compares the heavy-ion (“QCD medium”)data. Sections 4–11 eachdiscuss a different physics observable in the context of thelatest experimental results availableat RHIC and SPS. Due to space limitations, the list of topics chosen covers but a fraction of thesubstantial amount of data collected in the last years. Those observables that provide directinformation on thepartonicphases of the reaction have been given preference over “soft” orbulk observables from the late hadronic stages. Thus, important results relative to the freeze-out phase of the collision – e.g. chemical and kinetic equilibrium from light (and especiallystrange [22, 23]) hadron abundances [24], “femtoscopy” measurements from HBT radii [25],or possible signatures of (prehadronic) divergent susceptibilities from final net charge and〈pT〉 fluctuations [26] – are not treated here. The selected experimental results are mostlyfrom the comprehensive reviews of the four RHIC experiments(PHENIX [27], STAR [28],PHOBOS [29], and BRAHMS [30]) fromAuAu, dAu and pp collisions up to a maximumcenter-of-mass energy of

√sNN = 200 GeV, as well as very recent results from NA60InIn

reactions at SPS (√

sNN = 17.3 GeV) [31].

1. Experimental probes of QCD matter

Direct information on the thermodynamical and transport properties of the strongly interactingmedium produced inAA collisions is commonly obtained by comparing the results for agiven observableΦAA to those measured in proton(deuteron)-nucleus (p(d)A, “cold QCDmatter”) and in proton-proton (pp, “QCD vacuum”) collisions as a function of c.m. energy,transverse momentum, rapidity, reaction centrality (impact parameterb), and particle type


(mass). Schematically:

RAA(√

sNN, pT ,y,m;b) =“hot/dense QCD medium”

“QCD vacuum”∝

ΦAA(√

sNN, pT ,y,m;b)

Φpp(√

s, pT ,y,m)(1)

Rp(d)A(√

sNN, pT ,y,m;b) =“cold QCD medium”

“QCD vacuum”’∝

Φp(d)A(√

sNN, pT ,y,m;b)

Φpp(√

sNN, pT ,y,m)(2)

The observedenhancementsand/orsuppressionsin the RAA,dA(√

sNN, pT ,y,m;b) ratios canthen be directly linked to the properties of the strongly interacting matter after accounting fora realistic modeling of the space-time evolution of theAA expansion process.

Among the observables whosesuppressionis expected to provide information on the producedsystem, we will discuss:

• The total particle multiplicity which, related via local parton-hadron duality [32] tothe number of initially produced partons, will be suppressed if the initial parton flux isreduced due to low-x saturation effects in the colliding nuclei [33] (Section 4).

• High-pT leading hadronsare expected to be produced in reduced yields due to medium-induced energy loss via gluonsstrahlung of the parent partons in a system with a largenumber density of colour charges [34, 35] (Sections 6 and 7).

• Dissociation of theheavy quarkonia bound states has long since proposed [36] as asensitive signature of Debye screening effects aboveTcrit (Section 10).

• The mass of light vector mesonsis expected to drop in some scenarios of chiralsymmetry restoration [37, 38] which directly link the in-medium meson mass to atemperature- (and baryon density-) dependent chiral condensate: m⋆

V ∝ mV · 〈qq〉(T)

(Section 11).

Likewise, the following observables discussed hereafter are expected to beenhancedin astrongly-interacting multi-parton system:

• The soft hadron spectra (pT < 2 GeV/c), both inclusive and relative to the reactionplane, are expected to be boosted due to the development of collective radial and elliptical(hydrodynamical) flows in the early partonic phases of the reaction [21, 39] (Section 5).

• Semihard (pT ≈ 2–5 GeV/c) yields and flows of baryonsare predicted to be enhanced inthe context of parton recombination models [40] which take into account modificationsof the hadronization process in a dense deconfined medium (Section 8).

• The measurement inAAcollisions of athermal photon excess over the expected promptγ yield [41] would provide direct access to the thermodynamical properties (temperature,EoS) of the produced system (Section 9).

Among all available experimental observables, particles with large transverse momentumpT and/or high mass (“hard probes”) [42, 43] are of crucial importance for several reasons(Fig. 3): (i) they originate from partonic scatterings withlarge momentum transferQ2

and thus are directly coupled to the fundamental QCD degreesof freedom; (ii) theirproduction time-scale is very short,τ ≈ 1/pT . 0.1 fm/c, allowing them to propagate through


Figure 3. Examples of hard probes whose modifications in high-energyAAcollisions providedirect information on properties of QCD matter such as the〈q〉 transport coefficient, the initialgluon rapidity densitydNg/dy, and the critical temperature and energy density.

(and be potentially affected by) the medium, (iii) their cross sections can be theoreticallypredicted using the perturbative QCD (pQCD) framework. Hard processes thus constituteexperimentally- and theoretically-controlled self-generated “tomographic” probes of thehottest and densest phases of the reaction. The pQCDfactorization theorem[44] allows oneto determine the production cross section of a given hard probe as the convolution of long-distance parton distribution (PDFs,fa/A) and fragmentation (FFs,Dc→h) functions and the(perturbatively computable up to a given order inαs) parton-parton scattering cross section:

dσhardAB→h = fa/A(x,Q2)⊗ fb/B(x,Q2)⊗dσhard

ab→c⊗Dc→h(z,Q2)+O(1/Q2) (3)

The validity of Eq. (3) holds on the possibility to separate long- and short-distance effects withindependent QCD time (length) scales as well as on the assumption of incoherentparton-parton scatterings. InAA collisions, the incoherence condition for hard processes implies:fa/A ≈ A · fa/N, i.e. that, in theabsenceof medium effects, the parton flux in a nucleusAshould be the same as that of a superposition ofA independent nucleons. Thus,

dσhardAB→h ≈ A ·B · fa/p(x,Q

2)⊗ fb/p(x,Q2)⊗dσhard

ab→c⊗Dc→h(z,Q2), (4)

and minimum-bias hard cross sections inAB collisions are expected to scale simply asdσhard

AA |MB = A ·B · dσhardpp . In the most general case, for a givenAB reaction with arbitrary

impact parameterb the yield can be obtained by multiplying the cross sections measuredin pp collisions with the ratio of the incident parton flux of the two nuclei: dNhard

AB (b) =

〈TAB(b)〉 · dσhardpp , whereTAB(b) (normalized toA ·B) is the nuclear overlap function atb

determined within a purely geometric Glauber eikonal modelusing the measured Woods-Saxon distribution for the colliding nuclei [45]. The standard method to quantify the effectsof the medium on the yield of a hard probe produced in aAA reaction is thus given by thenuclear modification factor:

RAA(pT ,y;b) =d2NAA/dydpT

〈TAA(b)〉 × d2σpp/dydpT, (5)


which measures the deviation ofAA at b from an incoherent superposition ofNN collisions.This normalization is usually known as “binary collision scaling”.

2. Experiments in high-energy heavy-ions physics

The Relativistic Heavy Ion Collider (RHIC) [46] at Brookhaven National Laboratory is a3.8-km circumference accelerator composed of two identical, quasi-circular rings of super-conducting magnets (∼400 dipoles and∼500 quadrupoles) with six crossing-points. Themachine, which started operation in 1999, can accelerate nuclei (protons) up to a maximumof 100 (250) GeV/c per nucleon. The center-of-mass energies inAA and p(d)A collisions,√

sNN = 200 GeV (√

s = 500 GeV forpp), are more than an order of magnitude larger thanthose at the CERN SPS (

√sNN = 17.3 GeV). The currently attained averageAA luminosities§,

〈L 〉 ≈ 4×1026 cm−2s−1 = 0.4 mb−1s−1 are twice the design luminosity thanks mainly toan improved vacuum system [47]. There are four dedicated experiments at RHIC: two largemulti-detector systems (PHENIX and STAR, Fig. 4) and two smaller specialized spectrome-tres (BRAHMS and PHOBOS).

BRAHMS [48] has two movable magnetic spectrometer arms withhadron identification(π,K, p) capabilities up to very large rapidities (ymax≈ 4 for charged pions). The two spec-trometers consist of a total of 5 tracking chambers and 5 dipole magnets (maximum field of1.7 T), plus 2 Time-Of-Flight systems and a Ring ImagingCerenkov Detector (RICH) forparticle identification. The angular coverage of the forward spectrometer (FS) goes from 2.3◦

< θ < 30◦ (solid angle of 0.8 msr) up to momenta of 35 GeV/c. The midrapidity spectrometer(MSR) covers 30◦ < θ < 95◦ (acceptance 6.5 msr). The PHOBOS experiment [49] is basedon silicon pad detectors and covers nearly the full solid angle (11 units of pseudorapidity) forcharged particles, featuring excellent global event characterization at RHIC. PHOBOS con-sists of 4 subsystems: a multiplicity array (“octagon”,|η|<3.2, and “rings”,|η|.5.4), a finelysegmented vertex detector, a two-arm magnetic spectrometer (with dipole magnet of strength1.5 Tm) at midrapidity including a time-of-flight wall, and several trigger detectors. Particleidentification (PID) is based on time-of-flight and energy loss in the silicon.

PHENIX [50] is a high interaction-rate experiment specifically designed to measure hardQCD probes such as highpT hadrons, directγ, lepton pairs, and heavy flavour. PHENIX(Fig. 4, left) achieves good mass and PID resolution, and small granularity by combining13 detector subsystems (∼350,000 channels) divided into: (i) 2 central arm spectrometers forelectron, photon and hadron measurement at mid-rapidity (|η|< 0.35,∆φ = π); (ii) 2 forward-backward spectrometers for muon detection (|η| = 1.15 - 2.25,∆φ = 2π); and (iii) 4 global(inner) detectors for trigger and centrality selection. Two types of electromagnetic calorime-ters, PbSc and PbGl, measureγ ande±. Additional electron identification is possible thanks tothe RICH detector. Charged hadrons are measured in the axialcentral magnetic field (strength

§ Note that the “equivalent-pp luminosity” for hard processes, obtained scaling by the number of nucleon-nucleon collisions, is a much larger value:〈L 〉pp−equiv= A2 · 〈L 〉AA = 15µb−1s−1.


Figure 4. The two large experiments at RHIC: PHENIX [50] (left) and STAR [51] (right).

1.15 Tm) by a drift chamber (DC) and 3 layers of MWPC’s with padreadout (PC). Hadronidentification (π±, K±, andp, p) is achieved by matching the reconstructed tracks to hits ina time-of-flight wall (TOF). Triggering is based on two Beam-Beam Counters (BBC,|η| =3.0 - 3.9) and the Zero Degree Calorimeters (ZDC, with|θ| < 2 mrad). PHENIX featuresa state-of-the-art DAQ system capable of recording∼300 MB/s to disk with event sizes of∼100 KB (i.e. event rates of∼3 kHz).

The STAR experiment [51] is based around a large-acceptanceTime Projection Chamber(TPC) inside a solenoidal magnet with radius 260 cm and maximum field strength 0.5 T(Fig. 4, right). The TPC with radius 200 cm and full azimuthalacceptance over|η| <1.4 pro-vides exceptional charged particle tracking and PID via ionization energy lossdE/dx in theTPC gas and reconstruction of secondary vertices for weaklydecaying particles. Additionaltracking is provided by inner silicon drift detectors at midrapidity and forward radial-driftTPCs at 2.5< |η| <4. Photons and electrons are measured in the Barrel and Endcap Electro-magnetic Calorimeters (EMC) covering -1.0< η <2.0 and fullφ. The large STAR coverageallows for multi-particle correlation studies, jet reconstruction inpp, and also measurement ofstrange and charm hadrons. Triggering is done with the ZDCs,forward scintillators (Beam-Beam counters), a barrel of scintillator slats surroundingthe TPC, and the EMC.

NA60 [52] is a high interaction-ratefixed-targetexperiment focused on the study of dimuon,vector meson and open charm production inpA andAA collisions at the CERN SPS. The17 m long muon spectrometer previously used by NA38 and NA50,is composed of 8 multi-wire proportional chambers, 4 scintillator trigger hodoscopes, and a toroidal magnet. Thisspectrometer is separated by a∼5 m long hadron absorber (mostly carbon) from the vertexregion, where a silicon tracker made of pixel detectors [53]placed in a 2.5 T dipole field,measures the produced charged particles. The matching between the muons and the vertextracks leads to an excellent dimuon mass resolution.


3. Benchmark channels in the vacuum and in cold QCD matter

Proton-proton collisions are the baseline free-space reference to which one compares theAA results in order to identify initial- or final-state effectswhich modify the expectationof equation (4) and can thus provide direct information on the underlying QCD medium.Figure 5 collects six differentpT -differential inclusive cross sections measured at RHIC inpp collisions at

√s = 200 GeV: jets [54], charged hadrons [55], neutral pions [56], direct

photons [57],D,B mesons (indirectly measured via their semileptonic electron decay) [58]all at central rapidities (y = 0), and negative hadrons at forward rapidities (η = 3.2) [59]. Themeasurements cover 9 orders of magnitude in cross section (from 10 mb down to 10 pb),and broad ranges in transverse momentum (from zero momentumfor D,B mesons up to∼45GeV/c, a half of the kinematical limit, for jets) and rapidity (from η = 0 up toη = 3.2 forh−

and even, not shown here,η = 3.8 forπ◦’s [60]). Whenever there is a concurrent measurementof the same observable by two or more RHIC experiments, the data are consistent with eachother (the only exception being the heavy-flavour electron cross sections, which are a factor2-3 larger in STAR [61] than in PHENIX [58]).

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Figure 5. Left: Compilation of hard cross sections inpp collisions at√

s = 200 GeV(10%-30% syst. uncertainties not shown for clarity purposes) measured by STAR [54, 55],PHENIX [56, 57, 58], and BRAHMS [59] compared to NLO [62, 63] and NLL [64] pQCDpredictions (yellow bands). Right: Nuclear modification factors forJ/ψ versus rapidity [70](top), and for high-pT π◦ at mid-rapidity [71] (bottom) in centraldAucollisions at

√sNN = 200

GeV compared to pQCD calculations [72, 73] with EKS98 [74] nuclear shadowing.

Standard next-to-leading-order (NLO) [62, 63] or resummednext-to-leading log (NLL) [64]perturbative QCD calculations with modern proton PDFs [65], hadron fragmentation func-tions [66, 67], and with varying factorization-renormalization scales (µ = pT/2−2pT) showan overall good agreement with the availablepp data at

√s= 200 GeV (yellow bands in Fig.


5, left). This is true even in the semi-hard rangepT ≈ 1−4 GeV/c, where a perturbative de-scription would be expected to give a poorer description of the spectra. These results indicatethat the hard QCD cross sections at RHIC energies are well under control both experimen-tally and theoretically in their full kinematic domain. This is at variance with measurementsat lower (fixed-target) energies where several data-theorydiscrepancies still remain [68, 69].

Not only the proton-proton hard cross sections are well under control theoretically at RHICbut the hard yields in deuteron-nucleus collisions do not show any significant deviationfrom the perturbative expectations. Figure 5 right, shows the nuclear modification factorsmeasured indAu collisions at

√sNN = 200 GeV forJ/ψ, RdAu(y) [70], and for leading

π◦, RdAu(pT) at y = 0 [71]. At mid-rapidity, the maximum deviation from theRdAu = 1expectation for hard processes without initial-state effects is of the order of∼20%. BothRdAu(y, pT) ratios are well accounted for by standard pQCD calculations[72, 73] that includeDGLAP-based parametrizations of nuclear shadowing [74] and/or a mild amount of initial-statepT broadening [75] to account for a modest “Cronin enhancement” [76]. These dataclearly confirm that at mid rapidities, the parton flux of the incident gold nucleus can bebasically obtained by geometric superposition of the nucleon PDFs, and that the nuclear(x,Q2) modifications of the PDFs are very modest. Since no final-state dense and hot systemis expected to be produced indAu collisions, such results indicate that any deviations fromRAA = 1 larger than∼20% potentially observed for hard probes inAuAucollisions (at centralrapidities) can only be due tofinal-state effects in the medium produced in the latter reactions.

4. Low-x gluon saturation: AA rapidity densities, and high-pT dA forward suppression

The bulk hadron multiplicities measured at mid-rapidity incentralAuAuat√

sNN = 200 GeVdNch/dη|η=0 ≈ 700, are comparatively lower than thedNch/dη|η=0 ≈ 1000 expectationsof “minijet” dominated scenarios [77], soft Regge models [78] (without accounting forstrong shadowing effects [79]), or extrapolations from an incoherent sum of proton-protoncollisions [80] (Fig. 6, left). However, Colour Glass Condensate (CGC) approaches [33, 81]which effectively take into account a reducedinitial number of scattering centers in the nuclearPDFs, fa/A(x,Q2) < A · fa/N(x,Q2), agree well with experimental data. In the saturationmodels non-linear effects become important and start to saturate the parton densities when thearea occupied by the partons becomes similar to that of the hadron,πR2. For a nucleus withA nucleons and total gluon distributionxG(x,Q2) this condition translates into the followingsaturation momentum [82, 83]:

Q2s(x) ≃ αs

1πR2 xG(x,Q2) ∼ A1/3x−λ ∼ A1/3(

√s)λ ∼ A1/3eλy, (6)

with λ ≈ 0.2–0.3 [33]. The mass number dependence implies that, at comparable energies,non-linear effects will beA1/3 ≈ 6 times larger in a heavy nucleus (A ∼ 200 for Au or Pb)than in a proton. Based on the general expression (6), CGC-based models can describe thecentrality and c.m. energy dependences of the bulkAA hadron production (Fig. 6, right).


0 500 1000500 1000 1500dNch/dy

HIJING (dNch/dη, b<3 fm)

HIJING+ZPC+ART (b=0 fm)

RQMD (b=3 fm)

UrQMD (b<3 fm)

VNI+UrQMD (b<1 fm)

HSD, VNI+HSD (b<2 fm)

NEXUS (b<2 fm)

DPM (Pb+Pb)

DPMJET (Pb+Pb, 3%)

SFM (5%)

LEXUS (5%)

EKRT saturation (b=0 fm)

Hydro+UrQMD (b=0 fm)

Fireball (~5%)

McLV (dN/dη, b=0 fm)

Au+Au200 GeV

Figure 6. Left: Data vs. models fordNch/dη|η=0 in centralAuAuat√

sNN = 200 GeV [29, 80](the saturation model prediction is identified as McLV [84]). Right: Energy- and centrality-(in terms of the number of nucleons participating in the collision, Npart) dependences ofdNch/dη|η=0 (normalized byNpart): PHOBOS data [29] versus the saturation prediction [81] .

The second manifestation of CGC-like effects in the RHIC data is the BRAHMS observationof suppressed yields of moderately high-pT hadrons (pT ≈ 2−4 GeV/c) in dAurelative toppcollisions at forward rapidities (η ≈ 3.2, Fig. 7) [59]. Hadron production at such small anglesis theoretically sensitive to partons in theAu nucleus withxmin

2 = (pT/√

sNN) exp(−η) ≈O(10−3) [73]. The observed nuclear modification factor,RdAu≈ 0.8, cannot be reproducedby pQCD calculations that include the sameleading-twistnuclear shadowing [73, 85, 86] thatdescribes thedAudata aty = 0 (Fig. 5, right) but can be described by CGC approaches thatparametrize theAunucleus as a saturated gluon wavefunction [87, 88, 89].

)c (GeV/T

p0 1 2 3 4 5

dAu

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

= 3.2)η = 200 GeV (NNs+X @ - h→d+Au

BRAHMS datapQCD+shadow [Guzey et al.]pQCD+shadow [Accardi]CGC [Tuchin et al.]CGC [Jalilian-Marian]

Figure 7. Nuclear modification factorRdAu(pT) for negative hadrons measured at forwardrapidities by BRAHMS indAuat

√sNN = 200 GeV [59] compared to predictions of leading-

twist shadowing pQCD [73, 85] (two upper curves) and CGC [87,88] (lower curves).

It is worth noting, however, that at RHIC energies the saturation momentum is in the transitionbetween the soft and hard regimes (Q2

s ≈ 2 GeV2) and that the results consistent with the CGC


predictions are in a kinematic range with relatively low momentum scales:〈pT〉 ∼ 0.5 GeVfor the bulk hadron multiplicities and〈pT〉 ∼ 2 GeV for forward inclusive hadron production.In such a kinematic range non-perturbative effects can blura simple interpretation based onpartonic degrees of freedom alone. Following Eq. (6), the relevance of low-x QCD effects willcertainly be enhanced at the LHC due to the increased: center-of-mass energy, nuclear radius(A1/3), and rapidity of the produced partons [75, 90]. At the LHC, the saturation momentumQ2

s ≈ 5 – 10 GeV2 [33] will be more clearly perturbative and the relevantx values inAA andpA collisions will be 30–70 times lower than at RHIC:x2 ≈ 10−3(10−5) at central (forward)rapidities for processes with a hard scalepT ∼10 GeV.

5. sQGP viscosity: Strong hydrodynamical flows and AdS/CFT connection

The bulk hadron production (pT . 2 GeV/c) in AuAu reactions at RHIC shows strongcollective effects known as radial and elliptic flows. First, the measured single hadronpT

spectra have an inverse slope parameter larger than that measured inpp collisions, increasingwith reaction centrality and with hadron mass as expected ifcollective expansion blue-shifts the hadron spectra. Phenomenological fits of the spectra to “blast wave” models(Teff = T + 〈βT〉2 ·m) yield transverse flow velocities〈βT〉 ≈ 0.6 [27]. Full hydrodynamicalcalculations which start with a partonic phase very shortlyafter impact (τ0 < 1 fm/c) developthe amount of collective radial flow needed to accurately reproduce all the measured hadronspectra (Fig. 8).

(GeV/c)Tp0 1 2 3 4 5

-2d

y) (

GeV

/c)

2 T d

pπ

N/(

2d

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

10

210

310

410

510 Au+Au (central) calculations:

[0-5%]-πHydro

-210× [0-5%]

-Hydro K

-410×Hydro p [0-5%]

0π[0-5%]*0.2, AA T×[NLO pQCD]

-2 10× -[0-5%]*0.2, KAA T×[NLO pQCD]

-4 10×[0-5%]*0.2, p AA T×[NLO pQCD]

Au+Au (central) data: [0-5%]-πPHENIX [0-10%]0πPHENIX

[5-10%]+πSTAR [0-15%]πPHOBOS [0-5%]-πBRAHMS

-2 10× [0-5%] +PHENIX K-2 10× [5-10%] +STAR K

-2 10× [0-5%] s0STAR K

-2 10×PHOBOS K [0-15%] -2 10× [0-5%] -BRAHMS K

-4 10×PHENIX p [0-5%] -4 10×STAR p [0-5%]

-4 10×PHOBOS p [0-15%] -4 10×BRAHMS p [0-10%]

Figure 8. Transverse momentum spectra for pions, kaons, and (anti)protons measured atRHIC belowpT ≈ 5. GeV/c in 0-10% centralAuAucollisions at

√sNN = 200 GeV compared

to hydrodynamics+pQCD calculations [91].

Secondly, the azimuthal distributionsdN/d∆φ of hadrons emitted relative to the reaction plane(∆φ = φ−ΦRP) show a strong harmonic modulation with a preferential “in-plane” emission in


[GeV/c]tp0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

) t(p

2v

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16 0-80%geoσ/σ200 GeV:

-π + +π

S0K

pp +

Λ + Λ

Cascade

Hydro curves Huovinen

= 130 MeV f = 165 MeV, TCT

Figure 9. Left: Spatial asymmetry with respect to the reaction plane of the produced “fireball”in non-central nucleus-nucleus collisions. Right: Measured elliptic flow parameterv2(pT)

belowpT = 2 GeV/c for a variety of hadrons [95] compared to hydrodynamic predictions [39].

non-central collisions. Such an azimuthal flow pattern is a truly collective effect (absent inppcollisions) consistent with an efficient translation of theinitial coordinate-space anisotropyin AA reactions with non-zero impact parameter (i.e. with a lens-shaped overlap zone, seeFig. 9 left) into a final “elliptical” asymmetry in momentum-space. Rescattering between theproduced particles drives collective motion along the pressure gradient, which is larger fordirections parallel to the smallest dimension of the lens. The strength of this asymmetryis quantified via the second Fourier coefficientv2(pT ,y) ≡ 〈cos(2∆φ)〉 of the azimuthaldecomposition of single inclusive hadron spectra with respect to the reaction plane [92]

Ed3Nd3p

=1

2πd2N

pT dpT dy

(

1+2∞

∑n=1

vncos[n(φ−ΦRP)]

)

. (7)

The largev2 ≈ 0.16 measured in the data (Fig. 9, right) indicates a strong degree of collectiv-ity (pressure gradients) building up in the first instants ofthe collision. Indeed, elliptic flowdevelops in the initial phase of the reaction and quickly self-quenches beyondτ ≈ 5 fm/c asthe original spatial eccentricity disappears [93]. Two additional experimental observationssupport the existence of an efficient hydrodynamical response with very short thermalizationtimes. First, not only light hadrons but also decaye± from D,B mesons show momentumanisotropies withv2 as large as 10% [94]. The fact that the heavyc andb quarks participatein the common flow of the medium is clearly suggestive of a robust collective response dur-ing the earlypartonicphase. In addition, thev2 values measured for different centralities, atdifferent center-of-mass energies (200 and 62 GeV) and for different colliding systems (AuAuandCuCu) are found to show simple scaling laws with the reaction eccentricity [96, 97] alsoin agreement with hydrodynamics expectations.

These results have attracted much attention for several reasons. First, the strongv2 seen inthe data is not consistent with the much lower values,v2 . 6%, expected by transport modelsof hadronic matter [98] or for a partonic system rescattering with perturbative cross sections


)-2 (fmη/dch

) dNT

(1/A0 5 10 15 20 25 30

part

ε/ 2v

0.04

0.1

0.2

0.3

0.4hydro limit (QGP-EoS)

hydro limit (H-EoS)

STAR AuAu-200 GeVPHOBOS AuAu-200 GeVSTAR AuAu-130 GeVSTAR AuAu-62.4 GeV

STAR CuCu-200 GeVPHOBOS CuCu-200 GeVSTAR CuCu-62.4 GeVPHOBOS CuCu-62.4 GeV

NA49 AuAu-17.3 GeV

NA49 AuAu-8.8 GeV

BNL-E877 -5.0 GeV

Figure 10. Elliptic flow (normalized by the participant eccentricity [96]) v2/ε as a functionof the hadron rapidity densitydNch/dη|η=0 normalized by the reaction overlap areaA⊥,measured at SPS [102, 96] and RHIC [103, 96] compared to the “hydrodynamical limit”expectations for a fully thermalized system with QGP or hadron EoS [106, 93]. Adaptedfrom [103, 96] (10% errors have been added to approx. accountfor v2, ε syst. uncertainties).

(σgg≈ 3 mb) [99]. The magnitude, and thepT and hadron mass dependences of the radial andelliptic flows belowpT ≈ 2 GeV/c are, however, well described byidealhydrodynamics mod-els whose space-time evolution starts with a realistic QGP Equation of State (EoS) with initialenergy densitiesε0 ≈ 30 GeV/fm3 at thermalization timesτ0 ≈ 0.6 fm/c [21, 39, 100, 101](Fig. 9). Second, such a degree of accord between relativistic hydrodynamics and the data wasabsent at lower CERN-SPS energies [102]. Fig. 10 shows the particle-density dependence ofthev2 parameter (scaled by the eccentricity of the reactionε to remove centrality-dependentgeometrical effects) measured in semicentral collisions at different c.m. energies. The factthat SPS data lie below the “hydrodynamical limit” curves [106, 93] estimated for a QGP orhadronic system completely thermalized, suggests that equilibration is only partially achievedat the top SPS energy [102]. RHICv2 data in the range

√sNN ≈ 62 – 200 GeV [103, 104, 96]

are, however, close to the full thermalization expectations. Third, inclusion of viscous (i.e.“internal friction”) corrections to the ideal fluid dynamics equations spoils the reproductionof v2(pT), especially abovepT ≈ 1 GeV/c where even a modest viscosity bringsv2 towardszero [107]. Estimates of the maximum amount of viscosity allowed by thev2(pT) data [108]give a value for the dimensionless viscosity/entropy ratioclose to the conjectured univer-sal lower bound,η/s = ~/(4π), obtained from AdS/CFT calculations [13]. Similarly, ap-proaches [109, 110] that describe simultaneously the largev2(pT) and quenching factors ofheavy-flavoure± require small heavy-quark diffusion coefficients (3< 2πT D < 6) whichcorrespond to very small shear viscosities, 1< 4π(η/s) < 2 and/or thermalization times.

The fast (local) thermalization times, the robust collective flow generated in the first instants ofthe reaction, and the good agreement of the data withideal relativistic hydrodynamics modelswhich assume a fluid evolution with zero viscosity (i.e. withnegligible internal shear stress),have been presented as evidences that the matter formed at RHIC is a strongly interacting


QGP (sQGP) [111, 112, 113, 114, 115]. This new state of matterwith liquid-like properties,e.g. a Coulomb coupling parameterΓ =

⟨

Epot⟩

/〈Ekin〉 ∼ g2(41/3T)/(3T) ∼ 3 for g2 ∼ 4−6at T ≈ 200 MeV [116], challenges the anticipated paradigm [2] of a weakly interacting gasof relativistic partons (withΓ ≪ 1), lending support to the application of strongly-coupled-gauge/weakly-coupled-gravity duality techniques [13, 14, 15] to compute relevant sQGP pa-rameters.

It is worth noting, however, that very recent lattice results predict a QCD transitiontemperature,Tc ≈ 190 MeV [117], which is∼30–40 MeV larger than the freeze-outtemperature extracted from observed particle yields in heavy ion experiments (dotted-dashedcurve in Fig. 1) [5, 24]. Thus, an intermediate regime between the QCD transition and freeze-out could exist during which the system created in heavy ion collisions persists in a verydense hadronic phase. At LHC energies the contribution fromthe QGP phase to the collectiveparticle flow(s) will be much larger than at RHIC or SPS and, therefore, thev2 will be lessdependent on the details of the late hadronic phase. The measurement of the differentialelliptic flow properties inAA collisions at the LHC will be of primary importance to confirmor not the sQGP interpretation as well as to search for a possible weakening of thev2 indicativeof the existence of a weakly interacting QGP phase at higher temperatures than those of theliquid-like state found at RHIC [116, 108].

6. Parton number density and〈q〉 transport coefficient: High-pT hadron suppression

Among the most exciting results of the RHIC physics programme is the observed strongsuppression of high-pT leading hadron spectra in centralAA [118] consistent with the pre-dicted attenuation of the parent quark and gluon jets in a dense QCD medium (“jet quench-ing”) [119, 120]. AbovepT ≈ 5 GeV/c, neutral mesons (π◦, η) [121] and inclusive chargedhadrons [55] all show a common factor of∼5 suppression compared to an incoherent su-perposition ofpp collisions (Fig. 11, left). Such a significant suppression was not observedat SPS where, after reevaluating thepp baseline spectrum [122, 123], the central-AA me-son spectra show aRAA around unity (Fig. 12, right) probably due to the cancellation of a∼50% final-state suppression by initial-state Cronin broadening [122, 124, 125]. At RHIC,theRAA≈ 1 perturbative expectation which holds for other hard probes such as “colour blind”photons [126] – and for high-pT hadrons indAu reactions (Fig. 5, right) – is badly broken(RAA ≈ 0.2) in centralAuAucollisions. This strongly supports the picture of partonicenergyloss infinal-stateinteractions within the dense matter produced in the reaction.

The dominant contribution to the energy loss is believed to be of non-Abelian radiative nature(gluonsstrahlung) as described in the GLV [127, 128] and BDMPS [34, 129] formalisms. Inthe GLV approach, the initial gluon densitydNg/dyof the expanding plasma (with transverseareaA⊥ and lengthL) can be estimated from the measured energy loss∆E via:

∆E ∝ α3SCR

1A⊥

dNg

dyL . (8)


)c (GeV/T

p0 2 4 6 8 10 12 14 16 18 20

AA

R

-110

1

10

Au+Au - 200 GeV (central collisions):* [PHENIX Preliminary]γ [PHENIX], γDirect

[STAR]±Inclusive h [PHENIX preliminary]0π

[PHENIX]η/dy = 1100)

gGLV parton energy loss (dN

Au+Au - 200 GeV (central collisions):* [PHENIX Preliminary]γ [PHENIX], γDirect

[STAR]±Inclusive h [PHENIX preliminary]0π

[PHENIX]η/dy = 1100)

gGLV parton energy loss (dN

)c (GeV/T

p0 2 4 6 8 10 12 14 16 18 20

AA

R

-110

1

10

pT (GeV/c)2 4 6 8 10

AA

R

1

0.1 Au+Au (0-5%)

STAR charged hadrons pT > 6 GeV/c

I: DGLV R (c+b)

II: BDMPS (c+b)

III: DGLV R+EL (c+b)

IV: Hees/Rapp EL (c+b)

V: BDMPS (c only)

Figure 11. Nuclear modification factorRAA(pT) for γ, π◦, η [121], γ⋆ [94], andh± [55] (left)and for “non-photonic”e± from D,B mesons [61] (right) in centralAuAuat

√sNN = 200 GeV

compared to various parton energy loss model predictions [128, 130, 133, 110].

In the BDMPS framework, the transport coefficient‖ 〈q〉, characterizing the squared averagemomentum transfer of the hard parton per unit distance, can be derived from the averageenergy loss according to:

〈∆E〉 ∝ αSCR〈q〉L2. (9)

From the general Eqs. (8) and (9), very large initial gluon rapidity densities,dNg/dy≈ 1100± 300 [128], or equivalently, transport coefficients〈q〉 ≈ 11 ± 3 GeV2/fm [131, 132, 133,134], are required in order to explain the observed amount ofhadron suppression at RHIC.The corresponding values for SPS aredNg/dy≈ 400± 100 and〈q〉≈ 3.5± 1 GeV2/fm [135].

Most of the empirical properties of the quenching factor forlight-flavour hadrons – magnitude,pT-, centrality-,

√sNN- dependences of the suppression – are in quantitative agreement

with the predictions of non-Abelian parton energy loss models (Fig. 12). However, thefact that the high-pT e± from semi-leptonicD and B decays is as suppressed as the lighthadrons in centralAuAu (Fig. 11, right) [136, 61] is in apparent conflict with the robust∆EQ < ∆Eq < ∆Eg prediction of radiative energy loss models. Since the gluonsstrahlungprobability of quarks and gluons is completely determined by the gauge structure (Casimirfactors) of SU(3), the color octet gluons (which fragment predominantly intolight hadrons)are expected to lose energy atCA/CF = 9/4 times the rate of quarks. In addition, massivec,bquarks are expected to lose less energy than light ones due totheir suppressed small-anglegluon radiation already in the vacuum (“dead-cone” effect)[137]. In order to reproduce thehigh-pT open charm/bottom suppression, jet quenching models require either initial gluonrapidity densities (dNg/dy≈ 3000) [130] inconsistent with the total hadron multiplicities,dNg/dy≈ 1.8dNch/dη|η=0 [135] or with thedNg/dy needed to describe the quenched lighthadron spectra, or they need a smaller relative contribution of B relative toD mesons than

‖ Technically, the ˆq parameter can be identified with the coefficient in the exponential of an adjoint Wilson loop

averaged over the medium length:⟨

WA(C)⟩

≡ exp[

(−1/4√

2)qL−L2]

[14].


(GeV)s 0 20 40 60 80 100 120 140 160 180 200 220

= 4

GeV

/c)

T (

pA

A R

0.1

0.2

0.3

0.40.5

1

2

= 4 GeV/c:TSuppression at p

+X 0-7% central [WA98]0π →Pb+Pb

+X 0-5% central [CERES]±π →Pb+Au

+X 0-8% central [WA80]0π →S+Au

+X 0-10% central [PHENIX]0π →Au+Au

X.N.Wang jet quenching:

= 9/4q E∆/g E∆Non-Abelian energy loss:

q E∆ = g E∆"Non-QCD" energy loss:

NN

Figure 12. Left: Centrality dependence ofRAA(pT > 7 GeV/c) for π◦ in AuAuandCuCucollisions at

√sNN = 200 GeV compared to the BDMPS-based PQM model [131, 134] for

different values of the〈q〉 coefficient. Right: Excitation function of the nuclear modificationfactor,RAA(

√sNN), for π◦ in centralAA reactions at a fixedpT = 4 GeV/c [135], compared to

predictions of a jet-quenching model with canonical non-Abelian (solid line) energy loss [138].

theoretically expected in the measured decay electronpT range [133]. This discrepancy¶ maypoint to an additional contribution from elastic (i.e. non-radiative) energy loss [139, 140] forheavy-quarks [130] which was considered negligible so far [120]. The unique possibility atthe LHC to fully reconstruct jets [141], to tag them with prompt γ [142] or Z [143] and tocarry out detailed studies in thec, b quark sector [144, 145] will be very valuable to clarifythe response of strongly interacting matter to fast heavy-quarks, and will provide accurateinformation on the transport properties of QCD matter [14, 15].

7. Propagation of collective perturbations in QCD matter: Distorted di-jet correlations

Full jet reconstruction inAA collisions with standard jet algorithms [146] is unpractical atRHIC energies due to low cross-sections for high-ET jets and the overwhelming backgroundof soft particles in the underlying event (only above∼30 GeV are jets above the background).Instead, jet-like correlations at RHIC are conventionallymeasured on a statistical basis byselecting high-pT trigger particles and measuring the azimuthal (∆φ = φ−φtrig) and rapidity(∆η = η−ηtrig) distributions ofassociatedhadrons (pT,assoc< pT,trig) relative to the trigger:

C(∆φ,∆η) =1

Ntrig

d2Npair

d∆φd∆η. (10)

Combinatorial background contributions, corrections forfinite pair acceptance, and thesuperimposed effects of global azimuthal modulations (elliptic flow) are taken into accountwith different techniques [147, 148, 149, 150]. Inpp or dAucollisions, a dijet signal appearsas two distinct back-to-back Gaussian-like peaks around∆φ = 0 (near-side) and∆φ = π (away-side) (dAupanel in Fig. 13). At variance with this standard dijet topology in the QCD vacuum,

¶ Note, however, that the theoretical and experimental control of the pp→ D,B+ X reference (Fig. 5, left) isnot as good as for the light hadron spectra [133].


early STAR results for semihard jets in centralAuAu reactions [147] showed a completedisappearance of the opposite side peak for 3< pT,assoc< 4 < pT,trig < 6 GeV/c whilethe near-side correlation remained unchanged (Fig. 13, leftmost panel). Such a monojet-liketopology confirmed a jet-quenching picture where a 2→ 2 hard scattering takes place near thesurface of the system with the trigger parton being unaffected and the away-side parton losingenergy while traversing a medium opaque to coloured probes.For risingpT,trig, the away-sideparton is seen to increasingly “punchthrough” the medium [147], although the azimuthally-opposite correlation strength is still significantly reduced compared todAu(Fig. 13).

Figure 13. Angular correlations of high-pT charged hadron pairs measured in: 0-5% centralAuAuevents in variousptrig

T and passocT (GeV/c) ranges (left), and indAu and 0-5%-central

AuAufor fixed ptrigT = 8 – 15 GeV/c and twopassoc

T ranges [151] (right).

The estimated energy loss, Eqs. (8) and (9), of the quenched partons is very large, up to∆Eloss ≈ 3 GeV/fm for a 10 GeV parton [134] and most of the (mini)jets, apart from thoseclose to the surface, dump a significant fraction of their energy and momentum in a cell ofabout 1 fm3 in the rest frame of the medium. Since energy and momentum areconserved, thefragments of the quenched parton are either shifted to lowerenergy (pT <2 GeV/c) and/orscattered into a broadened angular distribution. Both softening and broadening of the away-side distribution are seen in the data [148] when thepT threshold of the away-side associatedhadrons islowered. Fig. 14 shows the dihadron azimuthal correlationsdNpair/d∆φ in centralAuAucollisions for pT,assoc= 1 – 2.5 GeV/c [149, 152]. In this semi-hard range, the away-side hemisphere shows a very unconventional angular distribution with a “dip” at∆φ ≈ π withtwo neighbouring local maxima at∆φ ≈ π± 1.1. Such a non-Gaussian “volcano”-like profilehas been explained as due to the preferential emission of energy from the quenched partonat a finite angle with respect to the jet axis. This could happen in a purely radiative energyloss scenario [153] but more intriguing explanations for the conical-like pattern have beenput forward based on the dissipation of the lost energy into acollective mode of the mediumwhich generates a wake of lower energy gluons with Mach- [154, 155, 156] orCerenkov-


Figure 14.Azimuthal distributions of semihard hadrons (pT,assoc= 1 – 2.5 GeV/c) relative to ahigherpT trigger hadron measured at RHIC. Left: PHENIX data in central (top) and peripheral(bottom)AuAu [149] (the arrows indicate the local maxima in the away-sidehemisphere).Right: STAR data in centralAuAu(squares) anddAu(circles) [152].

like [156, 157, 158] angular emissions. In the Mach-cone scenario, thespeed of sound+ ofthe traversed matter,c2

s = ∂P/∂ε, can be determined from the characteristic supersonic angleof the emitted secondaries: cos(θM) = 〈cs〉, whereθM is the Mach shock wave angle and〈cs〉the time-averaged value of the speed of sound of the medium traversed by the parton. Theresulting preferential emission of secondary partons fromthe plasma at afixedangleθM ≈ 1.1,yields a value〈cs〉≈ 0.45 which is larger than that of a hadron-resonance gas (cs≈ 0.35) [159],and not far from that of a deconfined QGP∗ (cs = 1/

√3). Experimental confirmation of the

Mach-cone picture or other alternative emission mechanisms for the associated particles inthe quenched jet requires more detailed differential studies [160] such as the ongoing analysisof three- and many-particle azimuthal correlations [161, 162].

8. Bulk hadronization: Enhanced baryon yields/flows at intermediate pT

The increasingly suppressed production of mesons abovepT ≈ 2 GeV/c in centralAuAureactions at RHIC contrasts with the simultaneousunsuppressed p, p [163, 164, 165] andΛ, Λ [166] yields in the rangepT ≈ 2 – 4 GeV/c. The intermediate-pT range inAuAureactionsfeatures an anomalous baryon/meson∼ 0.8 ratio which is roughly four times higher than inmore elementarypp or e+e− interactions (Fig. 15, left). Semihard (anti)protons showanenhancement with respect to the “xT scaling” expectation for the ratio of perturbative crosssections at different c.m. energies [167], whereasxT scaling holds forall hadrons (mesons)

+ The speed of sound is a simple proportionality constant relating the fluid pressure and energy density:P= c2s ε.

∗ Note that although lattice calculations indicate that there are∼30% deviations from the ideal-gas limit in thes(T),P(T) andε(T) dependences up to very highT’s [1], the ideal-gas relationε ≈ 3P (as well as other ratios ofthermodynamical potentials) approximately holds above∼ 2Tc.


measured inpp (AuAu) collisions at RHIC [164, 167, 168]. Only abovepT ≈ 6 GeV/c [165](Fig. 15, left) the meson/baryon ratio is again consistent with the expected yields obtainedfrom universal fragmentation functions. Not only their spectra are enhanced, but atpT =2 GeV/c the v2 elliptic flow parameter of baryons exceeds that of mesons (vmeson

2 ≈ 0.16,see Fig. 9, right) and keeps increasing up topT ∼ 4 GeV/c when it finally saturates atvbaryons

2 ≈ 0.22 [169, 170]. All those observations clearly indicate that standard hadronproduction via (mini)jet fragmentation is not sufficient toexplain the RHIC data for baryonsat transverse momenta of a few GeV/c.

0 2 4 6 8 10 12

Rati

os

-110

1

+π(a)p/ 0-12% Au+Au60-80% Au+Aud+Au

0 2 4 6 8 10 12

-π/p(b) )-π++π)/(p:(p+-e+eHwa:RecombinationFries:Coalescence+Jet

)-π++π)/(p:(p+-e+eHwa:RecombinationFries:Coalescence+Jet

(GeV/c)T

Transverse Momentum p (GeV)q/nT[m - m]0 1 2 3

q/n

2v

0

0.05

0.1

0.15 (PHENIX)-π + +π

(PHENIX)0π (PHENIX)- + K+K

(STAR)S0K (STAR)φ

(PHENIX)pp + (STAR)Λ + Λ (STAR)

+Ξ + -Ξ

d (PHENIX Preliminary)

Figure 15. Left: Proton/pion indAuandAuAucollisions at√

sNN = 200 GeV [165] comparedto the ratio in light quark fragmentation ine+e− at

√s= 91.2 GeV (dotted-dashed line) and to

parton coalescence predictions [40]. Right: Elliptic flow parameterv2 for all hadrons at RHICnormalized by the number of constituent quarks of each species (nq = 2,3 for mesons,baryons)vsthe transverse kinetic energyKET = mT −mnormalized also bynq [97, 171].

The observed baryon nuclear modification factors close to unity, the high baryon/meson ratios,and their large elliptic flow have lent support to the existence of an extra mechanism ofbaryon production inAuAu based on quark coalescence in a dense partonic medium [40].Recombination models compute the spectrum of hadrons as a convolution of Wignerfunctions with single parton thermal distributions leading to an exponential distributionwhich dominates over the standard power-law fragmentationregime belowpT ∼ 6 GeV/c.Coalescence models can thus reproduce the enhanced baryon production and predict alsothat the elliptic flow of any hadron species should follow theunderlying partonic flow scaledby the numbern of (recombined) constituent quarks in the hadron:v2(pT) = nvq

2(pT/n),n = 2,3 for mesons and baryons, respectively [172]. Such a quark-scaling law for the ellipticflow is confirmed by the data [169, 170]. Figure 15 right, showsa recent variation of thequark-number scaling law forv2 that uses the transverse kinetic energy (KET = mT −m,

mT =√

p2T +m2) rather than thepT and seems to account perfectly for the scaledv2 of all

measured species also in the soft hydrodynamical regime below pT ∼2 GeV/c [97, 171]. Theoverall success of valence quark coalescence models to explain hadron production in the semi-hard regime highlights the role ofthermalizeddegrees of freedom in the produced system withpartonic(as opposed to hadronic) quantum numbers.


9. Temperature and equation-of-state (EoS): Thermal photons

In order to describe the transient systems produced inAA collisions in terms ofthermodynamicalvariables (T, ε, s, etc.) linked by an EoS which can be compared to latticeQCD expectations, it is a prerequisite to establish that theunderlying degrees of freedomform, at some stage of the reaction, a statistical ensemble.Proving thatlocal♯ thermalizationhas been attained in the course of the collision is thus a crucial issue both experimentallyand theoretically [173]. The large elliptic flow signal observed in the data strongly supportsthe idea of fast thermalization as discussed in Section 5. The identification of real and/orvirtual γ radiation from the produced “fireball” with properties consistent with a thermaldistribution would in addition allow us to determine the underlying temperature and EoS of thesystem. Hydrodynamical [39] and parton transport [174] calculations indicate that the samecascade of secondary parton-parton collisions that drivesthe system towards equilibrationin the first tenths of fm/c results in an identifiable emission of thermal radiation above theprompt perturbative yield inAA reactions in a windowpT ≈ 1 – 3 GeV/c. The preliminaryγ spectrum measured in centralAuAu by PHENIX [94, 175] is consistent with the sumof such perturbative (prompt) plus thermal (secondary) contributions (Fig. 16). Differenthydrodynamical calculations of thermal photon production[91, 176, 177, 178, 179] canreproduce the PHENIX data assuming the formation of a radiating QGP with temperaturesaround 2·Tcrit (T0 = 400 – 600 MeV, corresponding to average temperatures〈T0〉 ≈ 350 MeVover the source profile ) at timesτ0 = 2RA/γ ≈ 0.2 fm/c right after the two colliding nucleipass-through each other.

(GeV/c)T

p0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

-2dy

) (G

eV/c

)2 T

dp

πN

/(2 d

-710

-610

-510

-410

-310

-210

-110

1

10

210

310= 200 GeVNNs+X at (*)γ →Direct photons: Au+Au

[0-10% central]γPHENIX

[0-20% central]*γPHENIX

: Prompt + Hydro [DdE-Peressou.]γTotal [0-10%]

AA T×: NLO pQCD γPrompt

=0.15 fm/c0τ = 590 MeV, 0D.d’Enterria-D.Peressounko. T

=0.17 fm/c0τ = 580 MeV, 0S.Rasanen et al. T

=0.20 fm/c0τ = 450-600 MeV, 0D.K.Srivastava. T

=0.20 fm/c0τ = 400 MeV, 0J.Alam et al. T

=0.33 fm/c0τ = 370 MeV, 0S.Turbide et al. T

Figure 16. Direct photon spectrum measured by PHENIX [126] in centralAuAucollisions at√sNN = 200 GeV compared to NLO pQCD [63] and different hydrodynamics predictions [91]

including a QGP phase with〈T0〉 = 350-600 MeV.

♯ Note that, by simple causality arguments,globalequilibrium in a finite system with radiusRA ≈ 7 fm can onlyoccur for time-scalesτ & 7 fm/c.


After subtracting the promptγ component from the inclusive direct photon spectrum, the localinverse slope parameterTeff in the rangepT ≈ 2 – 4 GeV/c can be used as a relatively goodproxy of the initial medium temperature [91]. The combination of Teff with another globalobservable directly related to the entropy densitys would therefore allow one to determinethe effective number of degrees of freedomg of the system via the Stefan-Boltzmann ratiog ∝ s/T3. Since the final charged particle rapidity densitydNch/dη|η=0 is directly correlatedwith the initial entropy density of the system, by empirically studying the evolution ofgeff ∝ dNch/dη|η=0/T3

eff versusTeff in different AA centralities one can effectively study theevolution of the number of degrees of freedom and look for anythreshold behaviour relatedto the sudden increase at the transition temperature and/ora flattening ofgeff for temperaturesaboveTcrit. Such an approach has been tested in the context of a 2D+1 hydrodynamical modelwhich effectively reproduces the hadron and photon data at RHIC [91]. We found that onecan clearly distinguish between the equation of state of a weakly interacting QGP and that ofa system with hadron-resonance-gas-like EoS (i.e. with rapidly rising number of mass stateswith T). However, direct evidence of the parton-hadron phase change itself as a jump ingeff

aroundTeff ∼ Tcrit can only be potentially visible inAuAu reactions atlower center-of-massenergies (

√sNN ≈ 20 – 65 GeV) [180]. At the LHC, the expected temperaturesO(1 GeV)

reached in centralPbPbwill also produce a significant thermal photon signal up topT ≈ 6GeV/c [181] which can be used to determine the thermodynamical conditions in theplateauregime of thes/T3 EoS, closer to the ideal-gas limit than at RHIC.

10. Critical temperature and energy density: AnomalousJ/ψ suppression

The study of heavy-quark bound states in high-energyAA collisions has been long sinceproposed as a sensitive probe of the thermodynamical properties of the produced medium [36].Analysis of quarkonia correlators and potentials in finite-T lattice QCD indicate that thedifferent charmonium and bottomonium states dissociate attemperatures for which the colour(Debye) screening radius of the medium falls below their correspondingQQ binding radius.Recent lattice analyses of the quarkonia spectral functions [182] indicate that the ground states(J/ψ andϒ) survive at least up toT ≈ 2Tcrit whereas the less boundedχc andψ′ melt nearTcrit.Experimental confirmation of such a threshold-like dissociation pattern would provide a directmeans to determine the transition temperature reached in the system and their comparisonto ab initio lattice QCD predictions. A significant amount of experimental data onJ/ψproduction in differentp(d)A andAAcollisions has been collected at SPS [183, 184, 185] andRHIC [186]. The corresponding nuclear modification factorscompiled in [187] are shown inFig. 17 as a function ofNpart. The surprisingly similar amount ofJ/ψ suppression observedat SPS and RHIC energies (with expected temperature differences of a factor of∼2) has beeninterpreted in a sequential-dissociation scenario [188] where theJ/ψ survives up toT ≈ 2Tcrit

in agreement with the lattice predictions, and the observedsuppression at both c.m. energiesis just due to the absence of (30% and 10%) feed-down decay contributions fromχ(1P) andψ′(2S) resonances which melt already atT ≈ Tcrit. The confirmation of such an interpretationwould set an upper limit ofT . 2Tcrit ≈ 400 MeV for the temperatures reached at RHIC.


0

0.2

0.4

0.6

0.8

1

1.2

1 10 102

Npart

[ψ/N

coll (A

B)] /

[ψ/N

coll (p

p)]

PHENIX d-Au y=0 (preliminary)

PHENIX Au-Au y=0 (preliminary)

NA38 S-U 200 GeV

NA50 Pb-Pb 158 GeV

NA60 In-In 158 GeV (preliminary)

Figure 17. J/ψ nuclear modification factor versus centrality [187] (givenby the number ofparticipant nucleons in the collision) measured inAA andp(d)A collisions at SPS [183, 184,185] and RHIC [70, 186].

Other explanations of the comparatively low depletion ofJ/ψ yields at RHIC have beenput forward based on a much stronger directJ/ψ suppression (at temperatures close toTc) combined withcc pairs regeneration from the abundant charm quarks†† in the densemedium [189]. The LHC measurements will be crucial to resolve this issue. A stronglysuppressedJ/ψ yield in PbPbat 5.5 TeV – where the expected initial temperatures will bewell above 2Tcrit – would support the sequential-screening scenario, whereas recombinationmodels predict a strong enhancement due to the larger density of cc pairs in the medium. Inaddition, the abundant production of theϒ(1s,2s,3s) states at LHC energies will open up aunique opportunity to study the threshold dissociation behaviour of the whole bottomoniumfamily. Theϒ is expected to survive up to 4·Tcrit and, therefore,direct suppression of thebbground state would be indicative of medium temperatures around 1 GeV at the LHC.

11. Chiral symmetry restoration: In-medium vector mesons

In-medium modifications of the spectral function (mass, width) of the light vector mesons(ρ, ω, andφ) have been proposed as a promising signature of the (approximate) restorationof chiral symmetry in theu,d,s quark sector [37, 38]. In the QCD vacuum the spontaneousbreaking of chiral symmetry manifests itself in the hadron spectrum through the mass-splittingof “chiral partners” i.e. between states of opposite paritybut equal quantum numbers. Chiralsymmetry breaking leads, in the mesonic sector, to the non-degeneracy of the pseudo-/scalar(π − σ) and axial-/vector (a1 − ρ) channels. For temperatures above the chiral transition,massless left- and right-handed quarks will decouple and one expects to observe a gradualdisappearance of the mass-splitting, leading to a shift of the masses of vector mesons andtheir chiral partners. Theρ meson is an excellent candidate for the experimental study of in-

††10 charm pairs are produced on average in a centralAuAucollision at the top RHIC energy.


medium spectral functions inAAcollisions due to (i) its short lifetime (τ0 = 1.3 fm/c) allowingit to decay before regaining its vacuum spectral shape, and (ii) its (rare but detectable) dileptondecay branching ratio (Γl+l− ≈ 5 ·10−5) which is unaffected by final-state interactions withthe surrounding environment.

0 0.2 0.4 0.6 0.8 1 1.2 1.40

500

1000

1500

2000

2500

3000

3500In-In SemiCentral

Tall p

2dN

/dM

per

20

MeV

/c

)2M (GeV/c

Rapp/WambachBrown/Rho

ρcockt.DD

ρVacuum

(dashed)(dashed)

Figure 18. “Excess” invariantµ+µ− mass spectrum in semi-centralInIn collisions at√

sNN

= 17.3 GeV [31] compared to the expectedρ line shape in different theoretical scenarios:vacuumρ, collisional broadening [37, 190], and mass drop [38].

The NA60 experiment has recently studied a high-statisticssample of low mass muon pairsin InIn collisions at

√sNN = 17.3 GeV [31]. The measuredρ spectrum, after subtraction of all

other sources of opposite-sign muon pairs, is peaked at the nominal (free) mass (mρ = 0.77GeV/c2) but its width is substantially broadened for increasing centralities (Fig. 18). Theρspectral shape is better reproduced by models which consider in-medium width broadeningdue to interactions in a hot and densehadronicmedium close to the expected phase boundary(T ∼ 190 MeV) [190], than by a long-standing prediction based on adownwards mass-shiftcoupled directly to the melting of the chiral condensate [38]. Such a result sets new constraintson the realization of chiral symmetry in QCD matter. At RHIC energies, the factor of twolarger temperatures reached compared to SPS prefigure that theρ should exhibit a completely“melted” line-shape if, as expected from the lattice, the chiral and deconfinement transitionsoccur at the sameTcrit. The ρ measurement in the dielectron channel will be possible inPHENIX with the recently installed hadron-blind-detector[191] which will allow to suppressby two orders of magnitude the large combinatorial background arising from light-mesonDalitz decays and photon conversions, while preserving 50%of the signal.

Summary

High-energy collisions of heavy ions provide the only existing method today to explore em-pirically the phase diagram of QCD at extreme values of temperature, density and low-x.


We have reviewed the experimental and phenomenological progress in nucleus-nucleus col-lisions at BNL-RHIC (

√sNN ≈ 20 – 200 GeV) and CERN-SPS (

√sNN ≈ 20 GeV) in recent

years with a particular emphasis on the modifications suffered by different hard probes inthe QCD medium that is produced, compared to baseline measurements in proton-proton orproton(deuteron)-nucleus collisions. The observed modifications allow us to obtain direct in-formation on fundamental (thermo)dynamical properties ofstrongly interacting matter.

The reducedAuAuhadron multiplicities and the depleted yields of semihard hadrons (pT ≈1 – 4 GeV/c) at forward rapidities indAucollisions indicate that the initial conditions of thenuclei accelerated at RHIC energies are consistent with colour-glass-condensate approachesthat model the hadronic parton distributions as a low-x saturated gluon wavefunction evolvingaccording to non-linear QCD equations. These new data – complementary to the rich HERAresults on the partonic structure of the proton – shed new light on the asymptotic limit ofQCD, a physics topic not only appealing in its own right but anessential ingredient for anyserious attempt to compute a large variety of hadron-, photon- and neutrino- scattering crosssections at very high energies.

The robust radial and elliptic flows seen for all identified hadron species up topT ≈ 2 GeV/cin AuAureactions at

√sNN = 200 GeV are remarkably well described byideal relativistic hy-

drodynamics calculations which model the expanding systemstarting with a realistic QGPequation-of-state with initial energy densitiesε0 ≈ 30 GeV/fm3 at thermalization timesτ0 ≈0.6 fm/c. Detailed hydro-data comparisons for various differential observables – in particularthe elliptic flow parameterv2(pT) for different light and heavy hadron species – indicate thatthe system exhibits very small viscosities (i.e. very shortmean free paths) and, thus,liquid-like properties at variance with the anticipated QGP paradigm of a weakly interacting gasof relativistic partons. In the intermediatepT ≈ 2 – 4 GeV/c range, baryons have enhancedyields and flows compared to mesons pointing to a novel channel for hadronization based onconstituent-quark coalescence in a dense partonic medium.The existence of a new mecha-nism of hadron formation in heavy-ion reactions at transverse momenta of a few GeV/c, apartfrom standard parton fragmentation, offers new ways to probe the space-time dynamics ofconfinement in different QCD environments.

In the high-pT sector, leading hadrons (but not colour-blind promptγ) are suppressed byup to a factor of∼5 in the rangepT ≈ 4 – 20 GeV/c compared to perturbatively-scaledproton-proton spectra. This result is in agreement with non-Abelian energy loss models thatassume that the produced partons traverse a medium with verylarge parton rapidity densi-ties dNg/dy≈ 1100 and transport coefficients〈q〉 ≈ 10 GeV2/fm. The energy lost by thequenched parton in the medium shows up in a very unconventional conical-like azimuthalprofile of secondary hadrons (pT ≈ 1 – 3 GeV/c) in the away-side hemisphere of high-pT

trigger hadrons. Interpretations of this preferential azimuthal emission at∆φ ≈ π± 1.1, ascaused by the generation of a Mach-cone boom by a supersonic parton propagating throughthe dense system, yield average speeds of sound〈cs〉 = cos(θM) = 0.45 not far from those


expected from lattice QCD for deconfined quark-gluon matter.

In the electromagnetic sector, preliminary real and virtual γ spectra in centralAuAu in therangepT ≈ 1 – 14 GeV/c can be described as the sum of a perturbative (prompt) photoncontribution plus a secondary component of thermal origin.Hydrodynamics calculations canreproduce the data assuming the formation of a radiating QGPwith average temperatures2Tcrit ≈ 350 MeV. Such temperature values seem to be consistent with the observation that theamount ofJ/ψ suppression at RHIC and SPS is about the same as expected fromlattice-basedcalculations that predict a survival of thecc ground state up toT ≈ 2Tcrit but a “melting” of theχc andψ′ (which feed-down at a∼40% level to theJ/ψ) nearTcrit. At the CERN SPS, recentNA60 results on theρ spectral function in centralInIn collisions at

√sNN = 17.3 GeV indicate

that the width of the vector meson is substantially broadened in the medium. Theoretical cal-culations indicate that most of the broadening can be accounted for by collisional effects in ahot and dense hadronic medium with initial temperatures close toTcrit ≈175 MeV (note thatsuch a result is also consistent with the observed hadron abundances at SPS which indicatethat the system reaches chemical equilibrium at temperatures around 160 MeV).

The overall scenario taking form from the wealth of recent experimental data suggests, on theone hand, that heavy-ion collisions at RHIC energies produce a strongly interacting liquid-likeQGP with very large initial parton rapidity densitiesdNg/dy≈ 1100, temperatures 2Tcrit ≈350 MeV and very low shear viscosities. On the other hand, systems produced at SPS seemto be only partially thermalized – according to the lower measured collective anisotropic flowcompared to RHIC –, have initialdNg/dy≈ 400 and temperatures around the phase boundaryat Tcrit ≈ 175 MeV. However, it is fair to acknowledge that among the existing signals thereis yet no incontrovertible “textbook” figureproving the formation of a thermalised extendedmedium consisting of deconfined and chirally symmetric quarks and gluons. One such evi-dence would be a direct empirical observation of a jump in thenumber of effective degreesof freedom at the phase change as expected by EoS calculations in the lattice. Since RHICtop energies seem to produce systems at twiceTcrit and SPS data point to conditions just at thepredicted phase change, the expected jump is likely to be observed (e.g. via precise studiesof the correlation of thermal photon slopes with the global hadron multiplicities) in a nextphase of RHIC running at intermediate energies (

√sNN ≈ 20 – 62 GeV) and high luminosi-

ties. Likewise, confirmation of the concurrent chiral and deconfinement transitions in QCDmatter will require e.g. precise measurements of theρ spectral shape (and, ideally, that of itschiral partnera1) at RHIC energies. Lower-energy runs at RHIC, as well as at the projectedCBM facility [192], will access also the region of large baryon densities around the QCDcritical point. Finding signs of the tri-critical point at relatively high temperatures would in-dicate that the smooth cross-over changes to a first order phase transition at higher baryondensities, a result of relevance for the conditions prevailing in the core of neutron (and othercompact) stars. Direct validation of the strongly-coupledinterpretation of the medium formedat RHIC and potential observation of the anticipatedweaklyinteracting quark-gluon plasmarequire key measurements inPbPbat 5.5 TeV at CERN-LHC where the initial temperatures


O(1 GeV) will be large enough to observe the direct melting of ground-state quarkonia reso-nances, and where the longer duration of the QGP phase and themuch abundant productionof other hard probes (in particular parton energy loss results for fully reconstructed,γ- or Z-tagged, and flavour-identified jets) thermal photons,v2 flow parameter, etc. will likely resultin indisputable probes of the deconfined medium much less dependent on details of the laterhadronic phase.

The experimental advances in the last years have been paralleled by significant progressesin the theoretical description of high-density QCD matter.Lattice methods are increasinglymore refined and powerful to describe not only the infrared collective dynamics (EoS, criti-cal parameters) but also the in-medium correlators (quarkonia). Effective field theories havebeen developed in specific domains such as the Colour-Glass-Condensate which effectivelydescribes the high-energy (low-x) limit of QCD. Perturbative calculations have substantiallyimproved the description of the interaction of hard probes with hot and dense quark-gluonmatter. Last but not least, duality approaches based on the application of AdS/CFT cor-respondence between weakly coupled gravity and strongly coupled QCD-like systems, areproviding new powerful insights on dynamical properties that cannot be directly treated byeither perturbation theory or lattice methods while simultaneously opening novel directionsfor phenomenological studies and experimental searches.

The impressive experimental and theoretical advances triggered by the wealth of high-statistics, high-quality data collected in ultrarelativistic nucleus-nucleus collisions at RHICand SPS, have significantly expanded the knowledge of many-body QCD at extremeconditions of temperature, density and low-x. Those studies – which will be substantiallyextended in the upcoming LHC (and likely RHIC-II) nucleus-nucleus and proton-nucleusprogramme – go beyond the strict realm of the strong interaction and shed light on a vastramification of fundamental physics problems. Knowledge ofthe collective behaviour ofmany-parton systems is of primary importance not only to address basic aspects of the stronginteraction such as the nature of confinement or the mechanism of mass generation via chiralsymmetry breaking, but to ascertain the high-energy limit of all scattering cross sectionsinvolving hadronic objects, the inner structure of compactstellar objects, or the evolutionof the early universe between the electroweak transition and primordial nucleosynthesis.

Acknowledgments

Special thanks due to F. Antinori, N. Armesto, W. Busza, A. deRoeck, D. Denegri,J. Harris, B. Jacak, P. Jacobs, C. Lourenco, G. Rolandi, C. Salgado, J. Schukraft, Y. Schutz,W. Wyslouch, and B. Zajc for a careful reading of the manuscript, informative discussions anduseful suggestions. This work is supported by the 6th EU Framework Programme contractMEIF-CT-2005-025073.


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