# Presentation: 190585

##          QCD Thermodynamics 

**Jean-Paul Blaizot, CNRS and ECT***

- RHIC Physics
- in the Context of the Standard Model
- RBRC
- June 21, 2006

- www.ect.it

**Notes:**
Necessity to develop tools to calculate QGP at high temperature (signals?)
Weak coupling calculations do not reduce to perturbation theory.

**from the ideal gas**
**to the « perfect liquid »**

**Notes:**
''weakly or strongly coupled QGP''

## 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 **

## 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**

## Various regimes of QCD

- Perturbative QCD

- Non perturbative QCD

- Dense and hot  matter

## QCD Interactions Weaken at High Energy

- (S. Bethke, hep-ex/0211012)

**QCD Interactions Weaken at High Energy**

## Perturbative QCD

**Accurate calculations can be done**
**Factorisation theorems**

**Perturbative QCD**

## Non perturbative QCD

**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**

## Dense and hot  matter

**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**

## The QCD phase diagram

- B

**Hadronic matter**

**Quark-Gluon Plasma**

- Nuclei

**The QCD phase diagram**

## Thermodynamical functions go to SB limit as T becomes large

- (SU(3) lattice gauge calculation from Karsch et al,  hep-lat/0106019)

**Thermodynamical functions go to SB limit as T becomes large**

## Region above Tc not well understood

**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 ?**

## Strong coupling ?

**Super Yang Mills**

**Cold atoms near a Feschbach resonance**

- From Gavai,Gupta,Mukherjee, hep-latt/0506015

**Analogies with other systems**

**QCD**

## Weakly/strongly 

- coupled plasmas

**Notes:**
''weakly or strongly coupled QGP''

## Ideal plasma

**Ideal plasma**

**4 dimensionful parameters** : *e, n, T, m*

**1 dimensionless parameter :**

**Non relativistic plasma**

**Debye screening length****	**

**Collective behavior**
**Collisionless plasma**

## Ideal plasma (ultrarelativistic)

* **n* **is no longer an independent parameter**

**(Screening length controlled **
**entirely by g)**

**(quantum **
**    ****statistics)**

## QCD plasma

**dimensionless gauge coupling**

**electric **
** ****screening**

**magnetic **
** ****screening**

**interparticle **
** ****distance**

**(court. T. Hatsuda)**

## QCD plasma

**Dimensionless gauge coupling**

**Thermal fluctuations**

**Kinetic energy**

**Interaction energy**

**Hard**

**Soft**

**Ultrasoft**

**Effective theory**

## 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**

**Notes:**
''weakly or strongly coupled QGP''

## Perturbation theory is ill behaved

**Perturbation theory is ill behaved**

**A two naive conclusion: **
**« weak coupling techniques are useless »**

**Notes:**
Origin  of the difficulty : weak coupling but many degrees of freedom.

## Similar difficulty in scalar theory

**Similar difficulty in scalar theory**

**The bad convergence of Pert. Th. is not related to non abelian features of QCD**

**Notes:**
The difficulty, the one that is evidenced in the previous plot, has nothing to do with non abelian gauge theories

## DIMENSIONAL REDUCTION

**Integration over the hard modes**

**In leading order**

**Non perturbative contribution**

**Integration over the soft modes**

## Slide 23

## The effective coupling is not huge even close to Tc

- M. Laine, Y. Schröder, hep-ph/0503061

**The effective coupling is not huge even close to Tc**

## Skeleton expansion

**Pressure in terms of dressed propagators**** (2PI formalism)**** **

**Stationarity property**

**Entropy is simple!**

## 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

## Insights from the functional

- renormalization group
- (from weak to strong coupling)

- J.-P. B, A. Ipp, R. Mendez-Galain, N. Wschebor
-  (work in progress)

## Insight from the functional renormalization group

**= ****interpolating effective action**

**Regulator depending on a continuous parameter k**

## Functional renormalization group

**(Exact) flow equation for the effective action**

- q

**local potential approximation**

## Slide 30

## From weak coupling

**From weak coupling**

**To strong coupling**

## From weak coupling

**From weak coupling**

**To strong coupling**

## 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**** **_ _

## 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)**