QCD and Heavy-ion Collisions 王新年 Let me first thank the local organizers, 相对论重离子碰撞与低能强子物理讨论会 威海, 2004年 8 月报3-7 日 LBNL

Heavy-ion Collisions RHIC BNL Au+Au up to 200 GeV/n

QCD Theory (approx.)Chiral symmetry and its spontaneous breaking Goldstone boson and chiral condensate Scale and UA(1) anomaly SU(3) gauge symmetry (non-Abelian) Confinement at long distance Asymptotic freedom at short distance …. The Quantum Chromodynamics theory that governs the strong interaction is extremely simple in its mathematical form. Its Largeriangian has many symmetries that give rise to interesting physical consequences on one hand but also make it extremely difficult to solve the theory on the other.

Chiral Symmetry Chirality of massless quarks: Chiral symmetry: Or alternatively: Conserved currents: Two conserved currents. The combination of them give vector and axial vector cuurents Uv transform vector currents among themselves, while U_A transform between vector and axial vector currents Spontaneously broken: Goldstone bosons (p,K,h)

Chiral symmetry restoration Restoration at high temperature F. Karsch ‘2001 Brown-Rho postulation:

UA(1) Anomaly U(1) and UA(1) Symmetry: (Classically) conserved current: Spontaneous chiral symmetry breaking  9th Goldstone boson (h0) A0m not a conserved current UA(1) is broken in quantum theory: Chiral anomaly UA(1) charge is not conserved for topologically nontrivial vacuum and <FF~> is not zero. Alder&Jackiw Topological susceptibility

Partial restoration of UA(1) Z. Huang & XNW UA(1) restored phase could lead to false vacuum Massive parity violation Kharzeev & Pisarski

Running of as(Q) SU(3) Gauge Symmetry Non-abelian interaction S Bethke J.Phys. G26 (2000) R27 Anti-screening of color It is therefore possible to use perturbative method to calculate physical observables. It is has been extremely successful in many cases, Asymptotic freedom Gross,Wilczek;Politzer (73)

Ideal Gas Approximation Leading orders in perturbation (Kapusta) Failure of simple perturbation: (non-convergenceg g~1) (Arnold & Zhai ’94) Expand contributions from soft modes k~ gT in terms of g. This also prompts one to try to calculate the EOS for a quark gluon gas. P=Tlog(Z/V)

Resummation of HTL Resummation of Hard Thermal Loops (Braaten & Pisarski) Effective theory integrating out “hard” (k~T) loops Resummation of HTP (Weldon’94) = + … Debye mass

Quasi-partciles & Self-consistent Resummation Quasi-particles with dispersion given by HTL Self-consistent resummation: Dyson’s equation Phi- thermal dynamic potential

Scale Anomaly Scale invariance (massless quarks) QCD interaction  renormalization of g(l) Break scale invariance  scale anomaly Classically conserved dilation current Bag constant Gluon condensate

QCD Phase transition Ideal quark and gluon gas P T4 Tc4 e T4 Tc4 Massless pion gas First order phase transition: P Tc4 T4 P=Tlog(Z/V) Apparently, this model is too simplistic, it ignore strong interaction close to Tc, other hadron mass could decrease which will also contribute to the pressure e T4 Tc4

Lattice QCD results F. Karsch ‘2001

Confinement-deconfinement SU(3) non-Abelian gauge interaction  confinement Heavy quark potential: Karsch, Laermann and Peikert 2001 J/Y suppression

QGP in AA Collision? Criteria: ? QGP Expanding, short-lived, small volume QGP Criteria: High density: e>>ec Large volume: V>>l (mean-free-path) Long life-time: t>>l Local thermal equilibration (interaction): approximately parton degrees of freedom Debye screening of strong interaction: deconfinement

Energy Loss & Jet Quenching BDPM Gyulassy Vitev Levai Wang & Wang Wiedemann; Zakharov Asymptotic form of parton energy loss

Single hadron suppression NLO calc. H.-Z. Zhang

Suppression of away-side jet Df

Azimuthal anisotropy I Single hadron

dE/dx and gluon density at RHIC From RHIC data of Au+Au Collisions GeV for E=10 GeV Energy density is about 100 times that of that in cold nuclear matter Initial Density about 30 times of that in a Cold Au Nucleus Consistent with estimate of initial condition

Elliptic Flow Coordinate space: initial asymmetry Hydro-dynamics calc. Pressure gradient diff Hydro-dynamics calc. py px Momentum space: final asymmetry

Early Thermalization U. Heinz Constraint on thermalization time nucl-th/0407067 Constraint on thermalization time

Flavor of Jet Quenching Parton recombination -> Partonic degrees of freedom

Summary Heavy-ion collisions can test many properties of QCD Deconfinement phase transition Chiral symmetry restoration Current RHIC data indicate formation of QGP High energy density 20 GeV/fm (t0=1 fm/c) from jet quenching, dN/dy, radial flow Jet quenching  Strong parton interaction thermalization v2  early thermalization Parton recombination  partonic matter More experimental studies to come Heavy-quark energy loss (B.-W. Zhang)