1. Towards understanding the Quark-Gluon Plasma
Theoretical overview:
Towards understanding the
Quark-Gluon Plasma
November 14, 2006
Jean-Paul Blaizot, CNRS and ECT*

2. Fundamental questions
What is the form of matter at « extreme » temperature or density?
What is the wave function of a hadron, a nucleus, at asymptotically high energy?
SIMPLICITY emerges in asymptotic situations
QCD matters !

3. Shifts of paradigms
Some form of a quark-gluon plasma is produced in ultra-relativistic nucleus-nucleus collisions
From the « ideal gas » to the « perfect liquid » (weakly or strongly coupled plasma)?

4. Some form of a quark-gluon plasma is
produced in ultra-relativistic nucleus-nucleus collisions
Large energy density achieved
Collective behaviour observed
Jet energy loss in matter
Hints of gluon saturation
« Perfect liquid », « sQGP »

5. From the « ideal gas » to the « perfect liquid »
''weakly or strongly coupled QGP''

6. Ideal QGP Asymptotic freedom At high temperature and/or density
matter is « simple »
Most « signatures » based on
this simple picture

7. Thermodynamical functions go to SB limit as T becomes large
Pressure SB
Resummed Pert. Th.
(SU(3) lattice gauge calculation from Karsch et al, hep-lat/ )

8. The QCD phase diagram B T Quark-Gluon Plasma Hadronic matter Colour
192MeV ?
Quark-Gluon Plasma
Hadronic matter
Colour
superconductor
Nuclei B

9. Theory near Tc is difficult
Degrees of freedom?
Remnants of confinement?
Strong coupling?
Voir expose d’ E. Shuryak (Signatures of strongly coupled QGP)
… present experiments are
Probing this region…

10. sQGP ?
Experimental evidence for « liquid » rather than « gaseous » behavior
Perturbation theory is ill behaved
''weakly or strongly coupled QGP''
New techniques to address strong
coupling problems

11. Weakly or strongly coupled ?
Interaction energy<<Kinetic energy ?
In the qgp, whether the degrees of freedom are weakly or strongly coupled depends on their momentum k
Compare k with g x <fluctuations>
Hard modes (k~T) dominate thermodynamics ; Pert. Th. OK
Soft modes (k~gT) represent subleading contributions,
require resummations
Ultra-soft modes (k~g^2 T) remain strongly coupled

12. The effective coupling is not huge even close to Tc
(from M. Laine, Y. Schröder, hep-ph/ )
Effective coupling in dimensionally reduced theory
Resummations are
successful
(from J.-P. B., E. Iancu, A. Rebhan: Nucl.Phys.A698: ,2002)
Pure-glue SU(3) Yang-Mills theory

13. Perturbative QCD Weak coupling, few particles
Accurate calculations can be done
Factorisation theorems
(PHENIX, hep-ex/ )

14. Dense and hot matter
Coupling may be weak, but many particles, or strong fields.
If coupling weak, Calculations possible from 1st principles: QGP, CGC

15. AdS/CFT Duality N=4 Supersymmetric SU(Nc) Yang-Mills theory
Is dual to string theory on AdS5+S5
Duality:
- strong coupling in one theory is weak
coupling in the other
- weak coupling string theory is classical (super)gravity
Note : theory has conformal symmetry, the coupling
Constant does not run, different from QCD

16. Thermodynamics in ADS/CFT
Simple limit of the entropy density at strong coupling
QCD
However does not immediately
apply to QCD near Tc
(no conformal symmetry)
Cold

17. Many recent calculations
Transport coefficients, in particular the viscosity
Energy loss parameter
Photon production
Thermodynamics
Hydrodynamics
Etc

18. Early stages of nucleus-nucleus collisions
- Initial wave function
- Early thermalization
… other facets of high density QCD

19. High density partonic systems
Parton density grows as x decreases

20. The saturation scale
The growth of the gluon density is governed by non linear
evolution equations and eventually « saturates »
Whether a parton is in the saturated regime or not depends on its (transverse) momentum
(saturated regime)
(dilute regime)

21. beyond mean field (JIMWLK, BK)
Recent developments:
beyond mean field (JIMWLK, BK)
Important role of the fluctuations.
Interesting connection with problems in non equilibrium
statistical mechanics (reaction-diffusion phenomena)
(from C. Marquet, hep-ph/ )

22. Early stage of nucleus-nucleus collisions
Conventional picture (mean field): Qs sets the scale at
Which partons are set free, as well as their typical
transverse momentum
Role of fluctuations of Qs ?
Anisotropy of initial momentum distributions may lead to
plasma instabilities. Role in thermalization ?

23. Conclusions (1) Many exciting theoretical developments, new ideas
progress in lattice calculations, more precision, finite mu
analytical techniques are developing
theory of initial wave functions is rapidly progressing
emergence of new methods to handle Strong coupling

24. Conclusions (2) What is the physical picture ?
Above 3Tc the degrees of freedom are quark and gluon
quasiparticles With effective masses due to thermal
fluctuations and Weak residual interactions
Below 3Tc situation still unclear,
But not obviously describable by strong coupling physics
Note that our understanding of the early stages of the collisions
remains based on weak coupling assumptions