1. QCD Thermodynamics Jean-Paul Blaizot, CNRS and ECT* RHIC Physics in the Context of the Standard Model RBRC June 21, 2006 www.ect.it

2. from the ideal gas to the « perfect liquid »

3. Ideal QGP Asymptotic freedom First predictions for existence of ideal quark matter (1975) Preparation of heavy ion program, and proposed « signatures », were (mostly) based on this simple picture

4. RHIC forces us to look into a region Where theory is hard -large energy density -Collective behavior -ideal hydro flows (low viscosity) -suppression of jets -etc Leading to the suggestion that matter created in nucleus-nucleus collisions at RHIC behaves as a « perfect liquid » or a « strongly coupled quark-gluon plasma » Some important findings at RHIC

5. Various regimes of QCD Perturbative QCD Non perturbative QCD Dense and hot matter

6. (S. Bethke, hep-ex/0211012) QCD Interactions Weaken at High Energy

7. Weak coupling, few particles Accurate calculations can be done Factorisation theorems Perturbative QCD

8. Effective theories (symmetries, low energy theorems), Intermediate concepts (condensates, constituent quarks, color strings, etc.) Non perturbative QCD No first principle calculations in terms of quarks and gluons except lattice QCD

9. Weak coupling, but many particles Calculations possible from 1st pciples QGP, CGC NB. At high T, genuine non perturbative physics remain in magnetic sector Dense and hot matter

10. T BB Hadronic matter Quark-Gluon Plasma Nuclei Colour superconductor The QCD phase diagram

11. (SU(3) lattice gauge calculation from Karsch et al, hep-lat/0106019) Thermodynamical functions go to SB limit as T becomes large

12. Region above Tc not well understood Degrees of freedom ? Bound states ? (Shuryak, Zahed, hep-ph/0403127) Heavy quark bd states appear to survive well above Tc (Asakawa,Hatsuda hep-ph/0308034) But charge(baryon,flavor) carriers seem to be quarks (Ejiri,Karsch,Redlich, hep-ph/0509051 - Gavai,Gupta hep-lat/0510044 ----) ……. Controversial issue Remnants of confinment ? Role of Z(3) symmetry and Polyakov loop Strong coupling ?

13. Super Yang Mills Cold atoms near a Feschbach resonance From Gavai,Gupta,Mukherjee, hep-latt/0506015 Analogies with other systems QCD

14. Weakly/strongly coupled plasmas

15. Kinetic energy >> interaction energy Ideal plasma 4 dimensionful parameters : e, n, T, m 1 dimensionless parameter : Non relativistic plasma Debye screening length Collective behavior Collisionless plasma

16. Ideal plasma (ultrarelativistic) n is no longer an independent parameter (Screening length controlled entirely by g) (quantum statistics)

17. QCD plasma 1/T 1/gT 1/g 2 T dimensionless gauge coupling electric screening magnetic screening interparticle distance (court. T. Hatsuda)

18. QCD plasma Dimensionless gauge coupling Thermal fluctuations Kinetic energy Interaction energy Hard Soft Ultrasof t Effective theory

19. Weak coupling techniques Effective theories- Dimensional reduction Skeleton expansion Insights from the functional renormalisation group -provide physical understanding of the regime of high temperature, and allow controlled extrapolations -not limited to perturbation theory; in fact weak coupling techniques can be used to study non perturbative phenomena (many degenerate degrees of freedom, strong fields) -present understanding of the transition from partonic w.f. (color glass) to matter produced in heavy ion collisions relies on weak coupling techniques

20. Perturbation theory is ill behaved A two naive conclusion: « weak coupling techniques are useless »

21. Similar difficulty in scalar theory The bad convergence of Pert. Th. is not related to non abelian features of QCD

22. DIMENSIONAL REDUCTION Integration over the hard modes In leading order Non perturbative contribution Integration over the soft modes

24. M. Laine, Y. Schr ö der, hep-ph/0503061 The effective coupling is not huge even close to Tc

25. Skeleton expansion Pressure in terms of dressed propagators (2PI formalism) Stationarity property Entropy is simple!

26. State of the art Compare Lattice – 2PI J.-P. B., E. Iancu, A. Rebhan: Phys.Rev.D63:065003,2001 F. Karsch, Nucl.Phys.A698:199-208,2002; G. Boyd et al., Nucl. Phys. B469, 419 (1996). from J.-P. B., E. Iancu, A. Rebhan: Nucl.Phys.A698:404-407,2002 pure-glue SU(3) Yang-Mills theory

27. Insights from the functional renormalization group (from weak to strong coupling) J.-P. B, A. Ipp, R. Mendez-Galain, N. Wschebor (work in progress)

28. Insight from the functional renormalization group = interpolating effective action Regulator depending on a continuous parameter k

29. Functional renormalization group (Exact) flow equation for the effective action q local potential approximation

31. From weak coupling To strong coupling

32. From weak coupling To strong coupling

33. Conclusions (1) A variety of weak coupling techniques converge to provide a simple pysical picture of the QGP for T>2.5 Tc The degrees of freedom are quark and gluon quasiparticles With effective masses due to thermal fluctuations and Weak residual interactions This physical picture is compatible with lattice data on thermodynamical functions

34. Conclusions (2) What happens to the quasiparticle picture near Tc is still not understood Does the concept of quasiparticle remain a useful concept ? Bound states ? Role of Z(3) symmetry ? The functional renormalisation group can provide useful insights on the transition from weak to strong coupling (e.g. it helps to undestand what happens when scale separation disappears)