Ultra-relativistic heavy ion collisions Theoretical overview

ICPAQGP5, KOLKATA February 8, 2005

Jean-Paul Blaizot, CNRS and ECT*

Ultra-relativistic heavy ion collisions

Explore properties of matter under extreme conditons (density, temperature)

Study how QCD works in unusual conditions

Much focus on formation of « quark-gluon plasma »

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 extreme (asymptotic) situations

At high temperature and/or high density matter is « simple »

(S. Bethke, hep-ex/0211012)

QCD Interactions Weaken at High Energy

The quark-gluon plasma

(from F. Karsch, hep-lat/0106019)

Energy density

Temperature

Free gas limit

(from F. Kajantie et al, PRL86, PRD67)(from F. Karsch, hep-lat/0106019)

Weakly interacting quasiparticles

Weak coupling calculations provide adequate descriptionOf the thermodynamics at high temperature

SU(3) Pressure

Dimensional reduction€

(T ≥ 3Tc )

T

B

Hadronic matter

Quark-Gluon Plasma

Nuclei

Colour superconductor

The QCD phase diagram

Theory near Tc is difficult

Degrees of freedom?

Strong coupling?

Bound states?

… and present experiments may be Probing this region…

Speed of sounds decreases as one approaches Tc from above

(from R. Gavai and S. Gupta)(from F. Csikor et al, hep-lat/0401022)

Simple quasiparticle picture breaks down close to Tc

How does the wavefunction of a nucleus look like at

asymptotically high energy ?

High density partonic systems

Parton density grows as x decreases

The very early stages of nucleus-nucleus collisions

Physics of dense systems of quarks and gluons

Weak coupling but many active degrees of freedom

Non linear QCD effects become important when

€

∂A( )2

≈ g2 A4 ≈ g2 A2 2

Gluon saturation

Saturation scale

Non linear effects important when

(Gribov, Levin, Ryskin 83)

Large gluon densites at small x

i.e. at a characterisitic scale

€

∂A( )2

≈ g2 A2 2

€

A2 ≈xG(x,Q2)

πR2

€

Q2 ≈ g2 A2

€

Qs2 ≈ α s

xG(x,Q2)

πR2

€

kT ≤ Qs

€

kT ≥ Qs(saturated regime) (dilute regime)

The saturation scale

In a nucleus

The densities in the central rapidity of a nucleus-nucleus collision at RHIC are similar to those at HERA.

From fit to DIS (HERA)

At the LHC

At RHIC, smaller x can be reached in the forward rapidity region

€

Qs2(x) = Q0

2 x0

x

⎛

⎝ ⎜

⎞

⎠ ⎟λ

€

Q02 → Q0

2A1/ 3

Early stages of a nucleus-nucleus collision

Partons set free have typical tranverse momenta

They are set free at (proper) time

At that time €

kT ≈ Qs

€

τ ≈Qs−1

€

dN

dy≈ 2AxG(x,Qs)

€

dET

dy≈ 2QsAxG(x,Qs)

Phenomenology based on such arguments (refined) is reasonably successful at RHIC

High density partonic systems

Large occupation numbers

Classical fields

McLerran-Venugopalan, etc.

€

Qs2 ≈ α s

xG(x,Q2)

πR2

€

n ≈xG(x,Q2)

πR2

€

πQs

2n ≈

π

α s

€

2 /Qs

Non linear evolution equations

Balitsky-Kovchegov equationCOLOR GLASS CONDENSATE and JIMWLK(*) equation

(*) Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner

Experimental discoveries at RHIC

Large energy density achieved

Collective behaviour observed

Jet quenching and strong « final state » interactions

Hints of gluon saturation

And much more…(Focus on observables sensitive to initial state)

Large energy density

Moderate increase of multiplicity with beam energy

From Phenix

White paper

Bjorken energy density

€

εBj (1 fm /c) ≈ 5.5GeV / fm3

εBj (0.35 fm /c) ≈16GeV / fm3

εBj (0.14 fm /c) ≈ 40GeV / fm3

€

εBj (τ 0) =1

πR2τ 0

dET

dy

€

(τ 0 ≈1/mT )

(τ 0 ≈1/Qs)

Elliptic flow

Produced particles flow preferentiallyin the reaction plane

(J.-Y. Ollitrault, 1992)

€

εx =y 2 − x 2

y 2 + x 2

(P.F. Kolb, J. Sollfrank and U. Heinz, PRC 62 (2000) 054909)

€

V2 = cos(2ϕ )

(S. Voloshin and Y. Zhang, 1994)

Elliptic flow

(Phenix white paper)

Comparison with hydrodynamics

(From U. Heinz, nucl-th/0412094)

Strong conclusions drawn from comparison with hydrodynamical calculations:

- early thermalisation time - sensitivity to equation of state- low viscosity

€

dr v

dt= −

r ∇P

ε + P

€

dr v

dt≈ −

cs2

1+ cs2

r ∇ε

ε

€

dP

dε= cs

2

Euler equation Speed of sound

Some simple remarks (*)

(* R. Bhalerao, J-P B, N. Borghini, J.-Y. Ollitrault)

The overall energy density scale is irrelevant for collective flow

For constant speed of sound

€

v(τ )

cs

≈ cs(τ − τ 0) ×1

R

For constant speed of sound

€

V2 ≈ cs

€

V2 ≈ ε

The time scale for establishing elliptic flow is

€

R /cs

Argument for early thermalisation= based on delayed hydro expansion. Natural time scale is large:

€

R/c

Small thermalisation time unatural (?)

(ellipticity)

Good control parameter ? -initial energy density (no) -average number of collisions during the build up of elliptic flow (?)

€

R

λ≈

σ

S

dN

dy

⎛

⎝ ⎜

⎞

⎠ ⎟

(From NA49, nucl-ex/0303001)

Jet quenching and strong « final state » interactions

q

q

pp

AuAubinaryAuAuAA Yield

NYieldR

/ ⟩⟨=

Au-Au nucl-ex/0304022

Jet production in matter

(PHENIX, nucl-ex/0401001)

Control experiment: d-AU

STAR: Phys.Rev.Lett.91:072304,2003

Hints of gluon saturation

Solution of the BK equation, Albacete et al, hep-ph/0307179

y0

0.05

0.1

0.2

0.4

0.6

1

1.4

2

(Related analytical work by Iancu, Itakura, Triantafyllopoulos hep-ph/0403103)

Suppression can also be due to initial state effects (nuclear wave function probed at small x; color glass condensate)

QuickTime™ et undécompresseur TIFF (LZW)

sont requis pour visionner cette image.

(Kharzeev, Kovchegov, Tuchin, hep-ph/0405045)

SUMMARY-Strongly interacting matter is produced in high energy nucleus-nucleus collisions. Large « initial » energy density. Collective behaviour.

- Many (indirect) evidences that partonic degrees of freedom play an important role in the collision dynamics at RHIC

- Early stages of the collisions, and hence « initial state effects » are important at RHIC (and will be more so at LHC).

- Hints of saturation (color glass condensate) may be already present at RHIC. Phenomenology based on saturation ideas is reasonably successful at RHIC

- QCD has become a central reference in the analysis of the data