QCD Thermodynamics

Jean-Paul Blaizot, CNRS and ECT*

RHIC Physics in the Context of the Standard Model

RBRCJune 21, 2006

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from the ideal gasto the « perfect liquid »

Ideal QGP

Asymptotic freedom

First predictions for existence ofideal quark matter (1975)

Preparation of heavy ion program, and proposed « signatures », were (mostly)based on this simple picture

€

α s =g2

4π≈

2π

b0 ln μ /ΛQCD( )

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μ ≈2πT( )

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

(S. Bethke, hep-ex/0211012)

QCD Interactions Weaken at High Energy

Weak coupling, few particles

Accurate calculations can be done

Factorisation theorems

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 gluonsexcept lattice QCD

Weak coupling, but many particlesCalculations possible from 1st pciplesQGP, CGC

NB. At high T, genuine non perturbative physics remain in magnetic sector

Dense and hot matter

T

μB

Hadronic matter

Quark-Gluon Plasma

Nuclei

Colour superconductor

The QCD phase diagram

(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

Degrees of freedom ?

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Tc ≤ T ≤ 2.5Tc

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 issueRemnants 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

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S

S0

=3

4+

45

32ς (3)

1

λ3 / 2

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λ ≡g2Nc( )

Analogies with other systems

QCD

Weakly/strongly coupled plasmas

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T >>e2

r0≈ e2n1/ 3

Kinetic energy >> interaction energy

Ideal plasma

4 dimensionful parameters : e, n, T, m

1 dimensionless parameter :

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g = e n1/ 3 /T

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T >> e2n1/ 3 ⇔ g <<1

Non relativistic plasma

Debye screening length

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λ =T

ne2≈r0g

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g <<1⇒ λ >> r0 Collective behaviorCollisionless plasma

Ideal plasma (ultrarelativistic)

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T >>m n is no longer an independent parameter

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n ≈T

h

⎛

⎝ ⎜

⎞

⎠ ⎟3

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r0 ≈h

T

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g→e

h

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λ ≈r0g

≈h

gT(Screening length controlled entirely by g)

(quantum statistics)

QCD plasma

1/T

1/gT

1/g2T€

gdimensionless gauge coupling

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1

T<<

1

gT<<

1

g2Telectric screening

magnetic screening

interparticle distance

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(g <<1)€

(T >> Tc )

(court. T. Hatsuda)

QCD plasma

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gDimensionless gauge coupling

Thermal fluctuations

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A2

κT≈ κT

Kinetic energy

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∂κT ≈ κT

Interaction energy

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g A2

κT≈ g κT

Hard

Soft

Ultrasoft

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κ ≈1

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κ ≈g

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κ ≈g2

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T

€

gT

€

g3 / 2T

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gT

€

g2T

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g2T

Effective theory

Weak coupling techniques

Effective theories- Dimensional reduction

Skeleton expansion

Insights from the functional renormalisation group

-provide physical understanding of the regime of hightemperature, 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

Perturbation theory is ill behaved

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

Similar difficulty in scalar theory

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

DIMENSIONAL REDUCTION

Integration over the hard modes

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(gT ≤ ΛE ≤ T)

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Di =∂i − igEAi

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gE ≈ g T

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mE ≈ gT

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λE ≈ g4TIn leading order

Non perturbative contribution

Integration over the soft modes

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(g2T ≤ ΛM ≤ gT)

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M. Laine, Y. Schröder, hep-ph/0503061

The effective coupling is not huge even close to Tc

Skeleton expansionPressure in terms of dressed propagators (2PI formalism)

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P[G]

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S =dP

dT=dP

dT G

Stationarity property

Entropy is simple!

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δPδG

= 0

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 functionalrenormalization 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

From weak coupling

To strong 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 quasiparticlesWith effective masses due to thermal fluctuations andWeak residual interactions

This physical picture is compatible with lattice data on thermodynamical functions

Conclusions (2)

What happens to the quasiparticle picture near Tc is stillnot 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)