---
abstract: 'The Relativistic Heavy Ion Collider (RHIC) was built to re-create and study in the laboratory the extremely hot and dense matter that filled our entire universe during its first few microseconds. Its operation since June 2000 has been extremely successful, and the four large RHIC experiments have produced an impressive body of data which indeed provide compelling evidence for the formation of thermally equilibrated matter at unprecedented temperatures and energy densities – a “quark-gluon plasma (QGP)”. A surprise has been the discovery that this plasma behaves like an almost perfect fluid, with extremely low viscosity. Theorists had expected a weakly interacting gas of quarks and gluons, but instead we seem to have created a strongly coupled plasma liquid. The experimental evidence strongly relies on a feature called “elliptic flow” in off-central collisions, with additional support from other observations. This article explains how we probe the strongly coupled QGP, describes the ideas and measurements which led to the conclusion that the QGP is an almost perfect liquid, and shows how they tie relativistic heavy-ion physics into other burgeoning fields of modern physics, such as strongly coupled Coulomb plasmas, ultracold systems of trapped atoms, and superstring theory.'
address:
- '$^1$Department of Physics, The Ohio State University, Columbus, OH 43210, USA'
- '$^2$CERN, Physics Department, Theory Division, CH-1211 Geneva 23, Switzerland'
author:
- 'Ulrich Heinz$^{1,2}$'
title: 'The strongly coupled quark-gluon plasma created at RHIC '
---

Introduction: what is a QGP, and how to create it {#sec1}
=================================================

Initially, the Universe didn’t look at all like it does today: until about 10$\mu$s after the Big Bang, it was too hot and dense to allow quarks and gluons to form hadrons, and the entire Universe was filled with a thermalized plasma of deconfined quarks, antiquarks, gluons and leptons (and other, heavier particles at even earlier times) – a Quark-Gluon Plasma (QGP). After hadronization of this QGP, it took another 3 minutes until the first small nuclei were formed from protons and neutrons (primordial nucleosynthesis and chemical freeze-out), another 400,000 years until atomic nuclei and electrons could combine to form electrically neutral atoms, thereby making the Universe transparent and liberating the Cosmic Microwave Background (kinetic decoupling of photons and thermal freeze-out), and another 13 billion years or so for creatures to evolve with sufficient intelligence to contemplate all of this.

With high-energy nuclear collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory or at the Large Hadron Collider (LHC) at CERN, one attempts to recreate the conditions of the Early Universe in the laboratory, by heating nuclear matter back up to temperatures above the quark-gluon deconfinement temperature. The hot and dense fireballs created in these collisions undergo thermalization, cooling by expansion, hadronization, chemical and thermal freeze-out in a pattern that strongly resembles the evolution of the Universe after the Big Bang. For this reason heavy-ion collisions are often called “Little Bangs”. A major difference is, however, the much smaller size of the Little Bang and its much (by about 18 orders of magnitude) faster dynamical evolution when compared with the Big Bang. This complicates the theoretical analysis of the experimental observations.

The main stages of the Little Bang are: 1.) Two disk-like nuclei approach each other, Lorentz contracted along the beam direction by a factor $\gamma=E_\mathrm{beam}/M$ (where $E_\mathrm{beam}$ is the beam energy per nucleon and $M=0.94$GeV is the nucleon mass, such that $\gamma\approx
110$ for heavy ions at RHIC and $\approx 3000$ at the LHC at their respective top energies). 2.) After impact, hard collisions which large momentum transfer $Q \gg 1$GeV between quarks, antiquarks or gluons (partons) inside the nucleons of the two nuclei produce secondary partons with large transverse momenta $p_T$ at early times $\sim 1/Q \sim 1/p_T$. 3.) Soft collisions with small momentum exchange $Q\lesssim 1$GeV produce many more particles somewhat later and thermalize the QGP after about 1fm/$c$. The resulting thermalized QGP fluid expands hydrodynamically and cools approximately adiabatically. 4.) The QGP converts to a gas of hadrons; the hadrons continue to interact quasi-elastically, further accelerating the expansion and cooling of the fireball until thermal freeze-out. The chemical composition of the hadron gas is fixed during the hadronization process and remains basically unchanged afterwards. After thermal decoupling, unstable hadrons decay and the stable decay products stream freely towards the detector.

By studying the behaviour of the matter created in the Little Bangs we can explore the phase structure and phase diagram of strongly interacting matter. Where the proton-proton collision program at the LHC aims at an understanding of the elementary degrees of freedom and fundamental forces at the shortest distances, the heavy-ion program focusses on the condensed matter aspects of bulk material whose constituents interact with each other through these forces. The difference between this kind of condensed matter physics and the traditional one is that in our case the fundamental interaction is mediated by the strong rather than the electromagnetic force. The coupling strength of the strong interaction gets bigger rather than smaller at large distances, leading us to expect a completely new type of phase structure. Indeed, strongly interacting matter appears to behave like a liquid (“quark soup”) at high temperature and like a gas (“hadron resonance gas”) at low temperature, contrary to intuition. On the other hand, the QGP state, with its unconfined color charges, has similarities with electrodynamic plasmas whose dynamical behaviour is controlled by the presence of unconfined electric charges. For example, both feature Debye screening of (color) electric fields. The main differences are QGP temperatures that are about a factor 1000 higher, and particle densities that are about a factor $10^9$ larger, than their counterparts in the hottest and densest electrodynamic plasmas. Accordingly, quark-gluon plasmas are intrinsically relativistic, and magnetic fields play everywhere an equally important role as electric fields. The nonlinear effects resulting from the non-Abelian structure of the strong interaction manifest themselves most importantly in the magnetic sector.

The equilibrium properties of a QGP with small net baryon density can be computed from first principles using Lattice QCD. Such calculations exhibit a smooth but rapid cross-over phase transition from a QGP above $T_c$ to a hadron gas below $T_c$ around critical temperature $T_c= 173\pm15$MeV, corresponding to a critical energy density $e_c\simeq 0.7$GeV/fm$^3$. For $T\gtrsim2\,T_c$, the QGP features an equation of state $p(e)$ corresponding to an ideal gas of massless partons, $p\approx\frac{1}{3}e$, with sound speed $c_s=
\sqrt{\frac{\partial p}{\partial e}}=\sqrt{\frac{1}{3}}$. But both the normalized energy density $e/T^4$ and pressure $p/T^4$ remain about 15-20% below the corresponding Boltzmann limits for a non-interacting massless parton gas. At face value, this relatively small deviation from the ideal gas appears to support the idea (long held by theorists before the RHIC era) that, because of “asymptotic freedom” (the QCD coupling “constant” decreases logarithmically with increasing energy), the QGP is a weakly interacting system of quarks, antiquarks and gluons that can be treated perturbatively. However, RHIC experiments proved this expectation to be quite wrong. Instead the QGP was found to behave like an almost perfect liquid, requiring it to be a [*strongly coupled plasma*]{}.

This experimental surprise is based on three key observations: 1.) [**Large elliptic flow:**]{} The anisotropic collective flow of the fireball matter measured in non-central heavy-ion collisions is huge and essentially exhausts the upper theoretical limit predicted by ideal fluid dynamics. 2.) [**Heavy quark collective flow:**]{} Even heavy charm and bottom quarks are observed to be dragged along by the collective expansion of the fireball and exhibit large elliptic flow. 3.) [**Jet quenching:**]{} Fast partons plowing through the dense fireball matter, even if they are very heavy such as charm and bottom quarks, lose large amounts of energy, leading to a strong suppression of hadrons with large $p_T$ when compared with expectations based on a naive extrapolation of proton-proton collision data, and the quenching of hadronic jets.

As I will try to explain in the rest of this review, none of these three observations can be understood without assuming some sort of strong coupling among the plasma constituents. Further, I will show that there is rather compelling evidence that we are indeed dealing with a “plasma” state where color charges are deconfined. The strongly-coupled nature of the QGP manifests itself in its collectivity and its transport properties, seen in non-equilibrium situations such as those generated in heavy-ion collisions. It is much more difficult to extract directly from its bulk equilibrium properties which are studied in lattice QCD.

Statements made and conclusions drawn in this overview are based on a large body of experimental data and comparisons with models for the dynamical evolution of heavy-ion collisions. Unfortunately, the assigned space does not permit me to show these here. For the most important plots and a comprehensive list of references I refer the interested reader to recent reviews by Müller and Nagle [@Muller:2006ee] and by Shuryak [@Shuryak:2008eq]. For some newer developments I will provide references to the original papers.

Collective flow – the “Bang” {#sec2}
============================

The primary observables in heavy-ion collisions are (i) hadron momentum spectra and yield ratios, from which we can extract the chemical composition, temperature, and collective flow pattern (including anisotropies) of the fireball when it finally decouples, (ii) the energy distributions of hard direct probes such as jets created by hadronizing fast partons, hadrons containing heavy charm and bottom quarks, and directly emitted electromagnetic radiation, from which we can extract information on the fireball temperature and density at earlier times before it decouples, and (iii) two-particle momentum correlations from which we can extract space-time information about the size and shape of the fireball at decoupling (hadron correlations) or at earlier times (photon correlations). Except for photon correlations which are hard to measure, good experimental data exist now for all of these observables. To learn about the existence and properties of the quark-hadron phase transition itself one needs to study event-by-event fluctuations around the statistical average of the event ensemble; this subject is still in its infancy, both experimentally and theoretically.

I will first discuss the collective flow patterns observed in heavy-ion collisions at RHIC. Collective flow is driven by pressure gradients and thus provides access to the equation of state $p(e)$ ($p$ is the thermodynamic pressure, $e$ is the energy density, and the net baryon density $n_B$ is small enough at RHIC energies that its influence on the EOS can be neglected). The key equation is $${\dot u}^\mu=\frac{\nabla^\mu p}{e+p} = \frac{c_s^2}{1+c_s^2}
             \frac{\nabla^\mu e}{e},$$ valid for ideal fluids, which shows that the acceleration of the fluid is controlled by the speed of sound $c_s=\sqrt{\frac{\partial p}{\partial e}}$ (reflecting the stiffness of the EOS $p(e)$) which determines the fluid’s reaction to the normalized pressure or energy density gradients. (The dot in ${\dot u}^\mu \equiv (u\cdot\partial)u^\mu$ denotes the time derivative in the fluid’s local rest frame (LRF), and $\nabla^\mu$ is the spatial gradient in that frame. For non-ideal (viscous) fluids, additional terms appear on the r.h.s., depending on spatial velocity gradients in the LRF multiplied by transport coefficients (shear and bulk viscosity).)

Lattice QCD data show that $c_s^2$ decreases from about $\frac{1}{3}$ at $T>2T_c$ by almost a factor 10 close to $T_c$, rising again to around $0.16-0.2$ in the hadron gas (HG) phase below $T_c$. The finally observed collective flow transverse to the beam direction reflects a (weighted) average of the history of $c_s^2(T)$ along the cooling trajectory explored by the fireball medium. Different aspects of the final flow pattern weight this history differently. Whereas the azimuthally averaged “radial flow” receives contributions from all expansion stages, due to persistent (normalized) pressure gradients between the fireball interior and the outside vacuum, flow anisotropies, in particular the strong “elliptic flow” seen in non-central collisions, are generated mostly during the hot early collision stages. They are driven by spatial anisotropies of the pressure gradients due to the initial spatial deformation of the nuclear reaction zone (see Fig. 1),

but this deformation decreases with time as a result of anisotropic flow, since the matter accelerates more rapidly, due to larger pressure gradients, in the direction where the fireball was initially shorter. With the disappearance of pressure gradient anisotropies the driving force for flow anisotropies vanishes, and due to this “self-quenching” effect the elliptic flow saturates early. If the fireball expansion starts at sufficiently high initial temperature, it is possible that all elliptic flow is generated before the matter reaches $T_c$ and hadronizes. In this case (which we expect to be realized in heavy-ion collisions at the LHC) elliptic flow is a clean probe of the EOS of the QGP phase.

Elliptic flow is measured as the second Fourier coefficient of the azimuthal angle distribution of the final hadrons in the transverse plane: $$v_2(y,p_T;b) = \langle \cos(2\phi_p)\rangle
= \frac{\int d\phi_p \cos(2\phi_p) \frac{dN}{dy\,p_T\,dp_T\,d\phi_p}(b)}
       {\int d\phi_p               \frac{dN}{dy\,p_T\,dp_T\,d\phi_p}(b)}.$$ Here $y=\frac{1}{2}\ln[(E+p_L)/(E-p_L)]$ is the rapidity of the particles, and $b$ the impact parameter of the collision. Each particle species has its own elliptic flow coefficient, characterizing the elliptic azimuthal deformation of its momentum distribution. $v_2$ has been measured as a function of transverse momentum $p_T$ for a variety of hadron species with different masses, ranging from the pion ($m_\pi=140$MeV) to the $\Omega$ hyperon ($m_\Omega=1672$MeV). For some hadron species $v_2$ has been measured out to $p_T>10$GeV where the spectrum has decayed by more than 7 orders of magnitude from the yield measured at low $p_T$! More than 99% of all hadrons have $p_T<2$GeV; in this domain the data show excellent agreement with ideal fluid dynamical predictions, including the hydrodynamically predicted rest mass dependence of $v_2$ (at the same $p_T$, heavier hadrons show less elliptic flow). Ideal fluid dynamics thus gives a good description of the collective behaviour of the bulk of the fireball matter.

It must be emphasized that the ideal hydrodynamic prediction of $v_2(p_T)$ is essentially parameter free: All model parameters (initial conditions and decoupling temperature) are fixed in central collisions where $v_2=0$, and the only non-trivial input for non-central collisions is the initial geometric source eccentricity as a function of impact parameter. Originally, one computed this eccentricity from a geometric Glauber model, and in this case one finds that the experimental data fully exhaust the theoretical prediction from ideal fluid dynamics, leaving very little room for viscosity which would reduce the theoretical value for the elliptic flow. This is the cornerstone of the “perfect fluid” paradigm for the QGP that has emerged from the RHIC data. However, recently suggested alternate models for the initial state, for example the Color Glass Condensate (CGC) model, can give initial eccentricities that are up to 30% larger than the Glauber model values. Furthermore, the first ideal fluid calculations used an incorrect chemical composition during the late hadronic stage of the collision; once corrected, this increased the theoretical prediction for $v_2(p_T)$ for pions by another 30% or so. If both of these effects are included, the measured $v_2(p_T)$ reaches only about 2/3 of the ideal fluid limit, opening some room for viscous effects in the fireball fluid.

At RHIC energies, not all of the flow anisotropy is created before hadronization, especially in noncentral collisions and away from midrapidity where the initial temperatures are not as high as in central collisions near midrapidity. Recent studies which treat this late hadronic stage microscopically rather than as an ideal fluid have exhibited large viscous effects in the hadron gas phase [@Hirano:2005xf]. If these are taken into account in the theoretical description, one finds that they reduce the elliptic flow and compensate for the $\sim 30\%$ increase of $v_2$ due to non-equilibrium hadron chemistry mentioned above. With Glauber initial conditions one is thus again left with almost no room for QGP viscosity, whereas CGC initial conditions allow the QGP fluid to have some non-zero viscosity.[^1]

Recent theoretical progress in the formulation and simulation of relativistic hydrodynamics for [*viscous*]{} fluids (see [@Heinz:2008qm] for a summary) has provided us with a tool that permits us to answer the question how large the QGP viscosity might be. This breakthrough is based on second-order Israel-Stewart theory and variations thereof which avoids longstanding problems of violations of causality in relativistic Navier-Stokes theory which includes only first-order gradients of the local thermodynamic variables. This is still largely work in progress, and published results based on this approach do not yet include all the physical ingredients known to be relevant for a quantitative prediction of elliptic flow. Nonetheless, a first heroic effort has been made by Luzum and Romatschke [@Luzum:2008cw] to use this new approach to limit the shear viscosity to entropy ratio $\eta/s$ from experimental elliptic flow data. Their work does not include non-equilibrium chemistry in the late hadronic stage (which would increase the calculated $v_2$), nor does it subtract effects from increased viscosity during that stage (which would reduce $v_2$). These two effects work against each other, and it may therefore not be too presumptuous to try to extract an upper limit for $\eta/s$ from their results, shown in Fig. 8 of Ref. [@Luzum:2008cw]. Even with all the uncertainties shown in that Figure (Glauber vs. CGC and a claimed 20% uncertainty in the normalization of the experimental data), it looks like $\frac{\eta}{s}>3 \left(\frac{\eta}{s}\right)_\mathrm{min}$ (where $\left(\frac{\eta}{s}\right)_\mathrm{min}=\frac{1}{4\pi}\approx
0.08$ is a conjectured absolute lower limit on the specific shear viscosity for [*any*]{} fluid, derived for strongly coupled conformally invariant supersymmetric field theories using the AdS/CFT correspondence [@Kovtun:2004de]) is difficult to accomodate. (The authors quote a conservative upper limit of $\eta/s<0.5$.) Since all known classical fluids have $\eta/s >> 1$ at all temperatures, even at their boiling points where $\eta/s$ typically reaches a minimum [@Kovtun:2004de], this makes the QGP the most perfect fluid of any studied so far in the laboratory. (Recent studies indicate that ultracold atoms in the unitary limit (infinite scattering length) may come in a close second [@Rupak:2007vp].)

Primordial hadrosynthesis – measuring $T_c$ {#sec3}
===========================================

The observed hadron yields (better: hadron yield ratios, from which the hard to measure fireball volume drops out) tell us about the chemical composition of the fireball when it finally decouples. It turns out that the hadron yield ratios measured in Au+Au collisions at RHIC can be described extremely well using a thermal model with just two parameters: a chemical decoupling temperature $T_\mathrm{chem}=163\pm4$MeV and a small baryon chemical $\mu_B=24\pm4$MeV. In central and semi-central collisions the phase space for strange quarks is fully saturated – if one generalizes the thermal fit to include a strangeness saturation factor $\gamma_s$ one finds $\gamma_s=0.99\pm0.07$. In peripheral collisions with less than 150 participating nucleons, $\gamma_s$ is found to drop, approaching a value around 0.5 in $pp$ collisions, reflecting the well-known strangeness suppression in such collisions. This suppression is completely removed in central Au+Au collisions. In contrast to $\gamma_s$, the chemical decoupling temperature $T_\mathrm{chem}$ is found to be completely independent of collision centrality. So, at freeze-out, all Au+Au collisions are well described by a thermalized hadron resonance gas in [*relative*]{} chemical equilibrium with respect to all types of inelastic, identity-changing hadronic reactions, as long as the total number of strange valence quark-antiquark pairs (which in peripheral collisions is suppressed below its [*absolute*]{} equilibrium value) is conserved.

Two aspects of this observation are, at first sight, puzzling: (i) The measured chemical decoupling temperature is, within errors, consistent with the critical temperature for hadronization of a QGP predicted by lattice QCD. If hadrons formed at $T_c$ and then stopped interacting inelastically with each other at $T_\mathrm{chem}\approx T_c$, how was there ever enough time in the continuously expanding and cooling fireball for their abundances to reach chemical equilibrium? (ii) If chemical equilibrium among the hadrons is controlled by inelastic scattering between them, the decoupling of hadron abundances is controlled by a competition between the microscopic inelastic scattering rate and the macroscopic hydrodynamic expansion rate. Since the expansion rate depends on the fireball radius and thereby on the impact parameter of the Au+Au collision, the chemical decoupling temperature (which controls the density and thus the scattering rate) should also depend on collision centrality [@Heinz:2007in]. How can the measured $T_\mathrm{chem}$ then be independent of centrality?

There is only one explanation that resolves both puzzles simultaneously: The hadrons are born into a maximum entropy state by complicated quark-gluon dynamics during hadronization, and after completion of this process the hadronic phase is so dilute that inelastic hadronic collisions (other than resonance scattering that only affects the particles’momenta but not the abundances of finally observed stable decay products) can no longer compete with dilution by expansion, freezing the chemical composition. This maximum entropy state cannot be distinguished from the chemical equilibrium state with the same temperature and chemical potential that would eventually be reached by microscopic inelastic scattering if the fireball medium were held in box. The measured temperature $T_\mathrm{chem}=T_c$ is, however, not established by hadronic scattering processes, but characterizes the energy density at which the quarks and gluons coalesce into hadrons, independent of the local expansion rate of the fluid in which this happens. The microscopic dynamics itself that leads to the observed maximum entropy state is not describable in terms of well-defined hadronic degrees of freedom but involves effective degrees of freedom which control the microscopic physics of the hadronization phase transition.

The absence of inelastic hadronic scattering processes after completion of hadronization is fortunate since it opens a window onto the phase transition itself, allowing us to measure $T_c$ through the hadron yields in spite of the fact that the hadrons continue to scatter quasi-elastically, maintaining approximate thermal (but not chemical!) equilibrium for the momentum distributions down to much lower thermal decoupling temperatures around 100MeV. This “kinetic decoupling temperature” can be extracted from the measured momentum distributions and [*is*]{} found to depend on collision centrality, as predicted by hydrodynamics [@Heinz:2007in].

JET: Jet Emission Tomography of the QGP {#sec5}
=======================================

As explained so far, RHIC collisions show strong evidence for fast thermalization of the momenta of the fireball constituents throughout at least the earlier part of the fireball expansion (until hadronization) and for chemical equilibrium at hadronization. After hadronization, chemical equilibrium is immediately broken at $T_c$, and thermal equilibration becomes gradually less efficient until the momenta finally decouple, too, a $T_\mathrm{therm}\sim 100\,\mathrm{MeV} < T_\mathrm{chem}$.

What causes the fast thermalization during the early expansion stage? We can use fast partons, created in primary collisions between quarks or gluons from the two nuclei, to probe the early dense stage of the medium. Such hard partons, emitted with high transverse momenta $p_T$, fragment into a spray of hadrons in the direction of the parton, forming what’s called a [*jet*]{}. The rate for creating such jets can be factored into a hard parton-parton cross section, described by perturbative QCD, a soft structure function describing the probability to find a parton to scatter off inside a nucleon within the colliding nuclei, and a soft fragmentation function describing the fragmentation of the scattered parton into hadrons. The structure and fragmentation functions are universal and can be measured in deep-inelastic $ep$ scattering (DIS) and in $pp$ collisions. Nuclear modifications of the structure function can be measured in DIS of electrons on nuclei. Jets thus form a calibrated, selfgenerated probe which can used to explore the fireball medium tomographically. The medium will affect the hard parton along the path from its production point to where it exits the fireball. If the parton is sufficiently energetic, it will exit the medium before it can begin to fragment into hadrons. The difference in jet production rates or, more generally, in the rates for producing high-$p_T$ hadrons from jet fragmentation in Au+Au and $pp$ collisions can be calculated in terms of the density of scatterers in the medium, multiplied with a perturbatively calculable cross section (if the parton has sufficiently high energy to justify a perturbative approach), and integrated along the path of the jet. This integrated product of density times cross section characterizes the opacity of the medium. Since the probe is colored and interacts through color exchange, it is sensitive to density of color charges resolvable at the scale of its Compton wave length; that density will be higher in a color-deconfined QGP than in a cold nucleus where quarks and gluons are hidden away inside the nucleons.

The procedure is similar to the familiar Positron Emission Tomography (PET) in medicine – therefore I call it “JET”. The main difference is that the positron emitting source used in PET is injected externally into the medium to be probed while the jets used in heavy-ion collisions are created internally together with the medium.

One of the first results from RHIC, right after the discovery of strong elliptic flow, was the experimental confirmation of the theoretical prediction that QGP formation should result in a strong suppression of high-$p_T$ hadrons compared to appropriately scaled $pp$ collisions. The observed suppression amounts to a factor 5-6, almost independent of $p_T$ in the region $4<p_T<15$GeV/$c$. This is close to $A^{1/3}$ for $A\sim 200$ and suggests a surface/volume effect, i.e. that high-$p_T$ hadrons are predominantly emitted from the firball surface while fast partons created in the fireball interior lose so much energy before exiting that they no longer contribute to high-$p_T$ hadron production. Indeed, angular correlations between a high-$p_T$ leading hadron selected from the collision and other energetic hadrons, indicative of a fragmenting jet, strongly support such a picture: Whereas in $pp$ and d+Au collisions, where fast sideward-moving partons escape from the narrow “fireball medium” almost instantaneously (if one can even use the notion of a “medium” in that case), one observes two such correlation peaks, separated by $180^\circ$ and corresponding to the pair of hard partons created back-to-back in the primary hard scattering, one sees only one such peak in central Au+Au collisions, in the direction of the fast trigger haddron. This can be understood if one assumes that the trigger hadron stems from the fragmentation of the outgoing partner of a hard parton pair created near the surface of the fireball, which exits the medium soon after creation, while its inward-travelling partner at $180^\circ$ loses most of its energy before exiting the fireball on the other side and no longer contributes energetic hadrons correlated with the trigger hadron. Still, the energy initially carried by that partner should show up near $180^\circ$ relative to the trigger hadron, and it does: While the away-side correlations of energetic hadrons with the trigger one are [*depleted*]{}, the away-side correlations between “soft” hadrons ($p_T<1.5$GeV/$c$) and the trigger hadron are [*enhanced*]{}. The energy lost by the fast parton travelling away from the trigger hadron and through the medium re-appears in the form of additional soft hadrons, with a distribution of transverse momenta similar to that of the medium itself: As the Au+Au collisions become more central, the average transverse momenta $\langle p_T\rangle$ of the extra hadrons emitted into the away-side hemisphere are observed to approach the $\langle p_T\rangle$ of the entire collision event.

In non-central collisions, the fireball created in the collision is deformed like an egg. Its orientation can be determined from the elliptic flow of the soft hadrons discussed in Sec. \[sec2\]. In this case, the overall fireball size is smaller than in central Au+Au collisions, and the observed away-side suppression of jet-like angular correlations is less complete. (Indeed, even in central Au+Au collisions, the away-side angular correlations among hard hadrons begin to reappear when the energy of the trigger hadron is increased beyond 10GeV or so; this is apparently too high for the inward-traveling partner to lose all of its initial energy.) But the suppression that is observed is stronger if the trigger is emitted perpendicular to the reaction plane (and its partner thus must travel through the fire-egg along its long direction) than when it moves within the reaction plane (i.e. its partner passes through the fire-egg along its short direction).

Fast partons moving through a QGP collide with its constituents, causing them to lose energy via both elastic collisions and collision-induced gluon radiation. For very energetic partons radiative energy loss is expected to dominate, so first model comparisons with the data included only radiative energy loss. From such calculations it was concluded that the observed suppression of hard particles required densities of scatterers that were consistent with and independently confirmed estimates of the initial energy densities extracted from the successful hydrodynamical models that describe the measured elliptic flow of soft hadrons. On a more quantitative level, radiative energy loss models soon started, however, to develop difficulties. They could not reproduce the observed large difference in away-side jet quenching between the in-plane and out-of-plane emission directions. Decay electrons from weak decays of hadrons containing charm and bottom quarks and pointing back to these hadrons were observed to feature strong elliptic flow (indicating that even these heavy quarks (“boulders in the stream”) are dragged along by the anisotropically expanding QGP liquid) and large energy loss, almost as large as that observed for hadrons containing only light quarks. The inclusion of elastic collisional energy loss and recent refinements in the calculation of radiative energy loss have reduced the disagreement between theory and experiment, but some significant tension remains. This has recently generated lively theoretical activity aiming to compute heavy quark drag and diffusion coefficients for strongly coupled quantum field theories, using gravity duals and the AdS/CFT correspondence (see [@Shuryak:2008eq] for a review and references).

What happens to all the energy lost by fast partons plowing through a QGP? There is some experimental evidence (and it appears to be getting stronger with recent 3-particle correlation measurements) that the soft partons emitted into the away-side hemisphere relative to a hard trigger particle emerge in the shape of a conical structure. This could signal a Mach shock cone, generated by the supersonically moving fast parton as it barrels through the perfect QGP liquid. Interestingly, the perhaps most convincing theoretical approach that actually generates something like the observed structures in the angular and 3-particle correlations on the away-side of the trigger jet again is based on models using gravity duals and the AdS/CFT connection [@Chesler:2007sv]. Clearly this needs more work, but the implications are intriguing.

Outlook {#sec6}
=======

On a qualitative level, the new RHIC paradigm, which states that the QGP is a strongly coupled plasma exhibiting almost perfect liquid behaviour and strong color opacity (even for the heaviest colored probes such as charm and bottom quarks), has solid experimental and theoretical support. The microscopic origins of the strong coupling observed in the collective dynamical behaviour of the QGP remain, however, to be clarified. Theorists are approaching this question from three angles: perturbative QCD based on an expansion in $\alpha_s\ll 1$, lattice QCD with $\alpha_s$ adjusted to reproduce the measured hadron mass spectrum, and strong-coupling methods for the limit $\alpha_s\gg 1$, based on the AdS/CFT correspondence which states that properties of certain strongly coupled field theories can be calculated by solving Einstein’s equations in appropriately curved space-times called “gravity duals”. Quantitatively precise and reliable results from either approach are expected to still require much hard work. An overview over some of the ongoing theoretical activities in this direction can be found in [@Shuryak:2008eq].

However, even without a complete quantitative theoretical understanding of the QGP transport coefficients, the body of experimental heavy-ion collision data is already very rich, and it is expected to further grow at a staggering rate with the completion of the RHIC II upgrade and the turn-on of the LHC. With the continued development of increasingly sophisticated models for the fireball expansion dynamics and its ultimate decoupling into non-interacting hadrons, the time is ripe for a comprehensive attack on the problem of extracting precise values for the QGP transport coefficients from a phenomenological description of the experimental data. This program has already started and produced first preliminary results as reported here; its outcome will yield valuable constraints and guidance for the theorists aiming for a first-principles based theoretical understanding of the QGP and its properties.

[**Acknowledgement:**]{} This work was supported by the U.S. Department of Energy under Contract DE-FG02-01ER41190. I am grateful to my students and postdocs who joined me in this research for so many years and helped develop a coherent picture of the complex dynamics of heavy-ion collisions.

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[^1]: An important aspect of the hydrodynamical simulations that describe the experimental data well is that they require short thermalization times, of order 1fm/$c$. This is true in particular for Glauber initial conditions where one simply doesn’t get enough elliptic flow to describe the data if one doesn’t initiate the hydrodynamic expansion before 1fm/$c$ (where the clock starts at nuclear impact). Short thermalization times and the validity of an ideal fluid picture are, of course, two sides of the same consistent picture. For CGC initial conditions, assuming similarly short thermalization times, the experimental $v_2$ data do not saturate the ideal fluid prediction. In this case one can either start the ideal fluid dynamic expansion later, or endow the fluid with some non-zero viscosity, or both. Again, these are two sides of the same consistent picture, which now invokes non-zero mean free paths for the plasma constituents, leading to incomplete local thermalization.
