1. 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

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

3. 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.

4. 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)

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

6. 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

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

8. 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)

9. 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)

10. 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

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

12. 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

13. 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

14. Lattice QCD results
F. Karsch ‘2001

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

16. 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

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

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

19. Suppression of away-side jetDf

20. Azimuthal anisotropy I
Single hadron

21. 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

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

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

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

25. 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)