Search for the Quark-Gluon Plasma in Heavy Ion Collision

V. Greco

Outline

Introduction: definitons & concepts - Quark-Gluon Plasma (QGP) - Heavy-Ion-Collisions (HIC)

Theory and Experiments - probes of QGP in HIC - what we have found till now!

Introduction I Goals of the Ultra-RHIC program: Production of high energy density matter better understanding of the origin of the masses of ordinary nuclei Produce matter where confinement -> deconf QGP and hadronization Structure of the nucleon how quantum numbers arise (charge spin, baryon number)

Big Bang

• Hadronization (T~ 0.2 GeV, t~ 10-2s)

• Quark and gluons

• Atomic nuclei (T~100 KeV, t ~200s) “chemical freeze-out”

• but matter opaqueopaque to e.m. radiation

• e. m. decouple (T~ 1eV , t ~ 3.105 ys) “thermal freeze-out “

We’ll never see what happened t < 3 .105 ys (hidden behind the curtain of the cosmic microwave background)

HIC can do it!BangBang

Little Bang

22)( CMSBANN Epps

From high regime

to high T regime

We do not observe hadronic systems with T> 170 MeV (Hagerdon prediction)

AGS

SPS

RHIC

Freeze-out

Hadron Gas

Phase Transition

Plasma-phase

Pre-Equilibrium

Different stages of the Little Bang

finite t

NN “Elastic”

44 R

CB

V

EP H

H

HRP 0

4

0

3

3 30)(

)2(Tgpfppd

g

V

Etot

Bag Model (cosm. cost.)

Euristic QGP phase transition

Pressure exceeds the Bag pressure -> quark liberation

Extension to finite

B1/4 ~ 210 MeV Tc~ 145 MeVBT 42

90

37 4/1

4/1

23790

BTc

Free massless gas)(8

7qqgtot gggg

fscqqg NNNggg ,16

Phase TransitionDef.Def. Phase transition of order n-th means the n-th derivative of the free energy F is discontinous

V

TF TF

I order

2

2

T

FCV

II order

Cross over Not a mixed phase, but a continous modification of the matter between the two phases

Mixed phaseMixed phase

Critical behaviorCritical behavior

Quantum ChromoDynamics

a

aaiiiia

a

n

ii FFmgAi

f

41

ψψψ2

γψ1

cbabcaaa AAfiAAF

Similar to QED, but much richer structureSimilar to QED, but much richer structure: SU(3) gauge symmetry in color space Approximate Chiral Symmetry in the light sector

broken in the vacuum.

UA(1) iral

Scale Invariance broken by quantum effects

Confinement Chiral Symmetry Restoration

Chiral Symmetry

Eight goldstone Bosons

() Absence of parity doublets

)1()1()3()3()3( AVVAC UUSUSUSU

RL

i

RL

jjRLe ,,

,

)1( 5, RL QCD is nearly invariant under rotation among u,d,s

associate Axial and Vector currents are conserved

Constituent quark masses explicit breaking of chiral simmetry

MeVqq 3)250(

a

f

P-S V-A splitting In the physical vacuum

Mas

s (M

eV)

Lattice QCDQCD can be solved in a discretized space !

)(exp)ˆ,( nAtignnU aa

)(ψ n

It is less trivial than it seems, Ex.: fermion action, determinant

,,3

0)()()(ALxddi

a exDxDxADZ

FFxdnFgiaTr

gnUTr

gS a

pp pclosed

4022

22 4

1)(exp

2

1)(

2

1Gluon field Continuum limit

Lattice QCD is the algorithm to evaluate Z in theSpace-time -> static at finite temperature

Ti /1 HiHt ee

Dynamics -> Statistics

time dim. regulate the temperature

,,4

)()()( ALxdia exDxDxADZ

Lattice QCD

CPU time is very large quark loops is very time consuming

(mq=∞ no quark loops = “quenched approximation”) lattice spacing a 0 baryon chemical potential

ProspectivesQuark –gluon plasma properties (vs density and temperature) Hadron properties (mass, spin, ) vacuum QCD structure (istantons ..) CKM matrix elements (f,fk,fc,fB)

Limitations No real time processes Scattering Non equilibrium Physical understanding

Effective models are always necessary !!!

0 0 ),( dtxAigeTrL

)0,0,0,1(2

)( xyigyJa

a

)(2

)()( 0

3

int xAigyAyJydH aa

aa

-static quark-only gluon dynamics

Polyakov Loop

tconfinemen

HL

int0

int0 0 ),( HdtxAig eTreTrL

If quark mass is not infinite and quark loops are present L is not really an order parameter !

Lattice QCD

Chiral CondensatePolyakov Loop

• Coincident transitions: deconfinement and chiral symmetry restoration it is seen to hold also vs quark mass

Phase Transition to Quark-Gluon PlasmaEnhancement of the degrees of freedom towards the QGP

42

1664

7

30Tn fgqq

Quantum-massless non interacting

MeVT

fmGeV

c 15173

/7.0 3

Gap in the energy density(I0 order or cross over ?)

Definitions and concepts in HIC

Kinematics

Observables

Language of experimentalist

The RHIC Experiments

STAR

Au+Au

Soft and Hard

• Small momentum transfer • Bulk particle production

– How ? How many ? How are distributed?

• Only phenomenological descriptions available (pQCD

doesn’t work)

SOFT (npQCD) string fragmentation in e+epp … or(pT<2 GeV) string melting in AA (AMPT, HIJING, NEXUS…)

QGP

HARD minijets from first NN collisions Indipendent Fragmentation : pQCD + phenomenologyphenomenology

99% of particles

Collision Geometry - “Centrality”

0 N_part 394

15 fm b 0 fm

Spectators

Participants

For a given b, Glauber model predicts Npart and Nbinary

S. Modiuswescki

Kinematical observables

z

zz pE

pEy

ln21 Additive like Galilean velocity

zTzT

TT

ympymE

pmm

sinh,cosh

2/122

z

z

pppp

||||

ln21

)2/tan(ln

Angle respect z beam axis

TTT pdyddN

ymm

pdddN

22

2

cosh1

CMLABLABjCMj yyy ///

Transverse mass

Rapidity -pseudorapidity

Energy Density

Energy density a la Bjorken:

dydE

τπR1

Aε T

2T

T dz

dE

fm/c 14.0τ

fm/c 1τ

7A 1.18R

RHIC

SPS

1/3

fm

dET/dy ~ 720 GeV

Estimate for RHIC:

38~6.0 GeV/fmfm/c

Time estimate from hydro:

Tinitial ~ 300-350 MeV

5.0|| y

dyydz

yt

zzz

cosh

tanhv

Particle streaming from origin

Collective Flow I: RadialObservable in the spectra, that have a slope due to temperature folded with Radial flow expansion <T> due to the pressure.

T

TfslT

2

TfslT

v1

v1TT,mpicRelativistUltra

vm2

1TT,p icRelativistNon

m

Slope for hadrons with different masses allow to separate thermal from collective flow

Absence

Tf ~ (120 ± 10) MeV

<T> ~ (0.5 ± 0.05)

Collective flow II: Elliptic Flow

Anisotropic Flowx

yz

px

py

v2 is the 2nd harmonic Fourier coeff.of the distribution of particles.

nn

TT

ndpdN

ddpdN

)cos(v21

Perform a Fourier decomposition of the momentum space particle distributions in the x-y plane

22

22

2 2cosyx

yx

pp

ppv

Measure of the Pressure gradient

Good probe of early pressure

Yield Mass Quantum Numbers

Temperature Chemical Potential

Statistical Model

Hydro add radial flow, freeze-out hypersurfacefor describing the differential spectrum

There is a dynamical evolution that Leads to such values of Temp. & abundances?

Yes, but what is Hydro?

Maximum entropy principle

Maximum Entropy Principle

k V

ffffxpdd

S )1ln()1(ln)2( 3

33

i

ii fEdE

i

ii fBdB

i

ii fsdS

All processes costrained by the conservation laws

Maximizing S with this constraintsthe solution is the statistical thermal equilibrium

The apparent “equilibrium” is not achieved kinetically but statistically !

HYDRODYNAMICS

0)(

0)(

xj

xT

B

Local conservation Laws

)()()(

)()()()()()(

xuxnxj

gxpxuxuxpxexT

BB

5 partial diff. eq. for 6 fields (p,e,n,u)+ Equation of State p(e,nB)

No details about collision dynamics (mean free path 0)

Follow distribution function time evolutionFollow distribution function time evolution: Initial non-equilibrium gluon phase

final chemical and thermal equlibrated system How hydrodynamical behavior is reached Relevance of npQCD cross section Description of the QCD field dynamics

Another level of Knoweledge

collprr IfUfm

p

t

f

Non-relativistically

)()( 4321

4

34121 2 3

2143

22 ppppWffffIcoll

Transport Theory

),,(, tprf gq

Follow distribution function time evolutionFrom the initial non-equilibrium gluon phase

drifting mean field collision

To be treated:- Multiparticle collision (elastic and inelastic)- Quantum transport theory (off-shell effect, … )- Mean field or condensate dynamics

...213222 collcollcoll IIIfp

Relativistically

at High density

ggggg ggg

Sp

ectr

a st

ill

app

ear

ther

mal

Elliptic Flow Hydro Transport

rapidity rapidity

• Chemical equilibrium with a limiting Tc ~170MeV

• Thermal equilibrium with collective behavior

- Tth ~120 MeV and <>~ 0.5

• Early thermalization (< 1fm/c, ~ 10 GeV)

- very large v2

We have not just crashed 400 balls to get fireworks, but we have created a transient state of plasma

A deeper and dynamical knowledge of the system is still pending!

Outline II

Probes of QGP in HICProbes of QGP in HIC

What we have find till now! strangeness enhancement jet quenching coalescence J/ suppression

What we have learned ?

Binary Collisions

Participants

b (fm)N

Glauber model