Che-Ming KoTeaxs A&M University

Introduction: concepts and definitions

- Quark-gluon plasma (QGP)

- Heavy ion collisions (HIC)

Experiments and theory

- Signatures of QGP

- Experimental observations

Searching for the Quark-Gluon Plasma in Relativistic Heavy Ion Collisions

Largely based on slides by Vincenzo Greco

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~ 1 eV , t ~ 3.105 ys) “thermal freeze-out “

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

HIC can do it!BangBang

Freeze-out

Hadron Gas

Phase Transition

Plasma-phase

Pre-Equilibrium

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

Heuristic 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

Quantum ChromoDynamics

a

aaiiiia

a

n

ii FFmgAi

f

41

ψψψ2

γψ1

a a a abc b cF A A i f A A

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

which is broken in the vacuum.

UA(1) iral

Scale Invariance broken by quantum effects

Phase Transition in lattice QCDEnhancement of the degrees of freedom towards the QGP

42

1664

7

30Tn fgqq

Noninteracting massless partons

MeVT

fmGeV

c 15173

/7.0 3

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

QCD phase diagram

22)( CMSBANN Epps

From high regime

to high T regime

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

AGS

SPS

RHIC

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 they distributed?

• Only phenomenological descriptions available (pQCD

doesn’t work)

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

QGP

HARD minijets from first NN collisions Independent 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

1ln

2z

z

E py

E p

Additive like Galilean velocity

1/ 22 2

cosh , sinh

T T

T z T

m m p

E m y p m y

z

z

pppp

||||

ln21

)2/tan(ln

Angle with respect to beam axis

TTT pdyddN

ymm

pdddN

22

2

cosh1

CMLABLABjCMj yyy ///

PHOBOS

PHOBOS

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

v tanh

cosh

z

zy

tdz y dy

Particle streaming from origin

Some definitions I: radial collectiv flowsSlope of transverse momentum spectrumis due to folding temperature with radial collective expansion <T> from pressure.

2

T sl f T

TT sl f

T

1Non relativistic p , T T m v

2

1 vUltra relativistic p m, T T

1 v

m

Slopes for hadrons with different masses allow to separate thermal motionfrom 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 Fourier coeff. of particle transverse moment distribution

nn

TT

ndpdN

ddpdN

)cos(v21

Fourier decomposition of particle momentum distribution in x-y plane

22

22

2 2cosyx

yx

pp

ppv

Measure of the pressure gradient

Good probe of early pressure

Anisotropic flow vn

Sine terms vanish because of the symmetry in A+A collisions

Initial spatial

anisotropy

Anisotropicflows

Pressure gradient

anisotropy

x

Anisotropic flow

3

n T3n=1T T T T

d N dN 1 dNE 1 2v (p ,y)cos(n )

d p p dp d dy 2 p dp dy

Yield Mass Quantum Numbers

Temperature Chemical Potential

Statistical Model

Hydro adds radial flow & freeze-out hypersurfacefor describing the differential spectrum

Is there a dynamical evolution that leads to such values of temp. & abundances?

Yes, but what is Hydro?

Maximum entropy principle

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)

collprr IfUfm

p

t

f

Non-relativistically

)()( 4321

4

34121 2 3

2143

22 ppppWffffIcoll

Transport Model

),,(, tprf gq

Follows time evolution of particle distributionfrom initial non-equilibrium partonic phase

drift 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 (< 1 fm/c, ~ 10 GeV/fm3)

- very large v2

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

A deeper understanding of the system is certainly needed!

Signatures of quark-gluon plasma

Dilepton enhancement (Shuryak, 1978)

Strangeness enhancement (Meuller & Rafelski, 1982)

J/ψ suppression (Matsui & Satz, 1986)

Pion interferometry (Pratt; Bertsch, 1986)

Elliptic flow (Ollitrault, 1992)

Jet quenching (Gyulassy & Wang, 1992)

Net baryon and charge fluctuations (Jeon & Koch; Asakawa, Heinz & Muller, 2000)

Quark number scaling of hadron elliptic flows (Voloshin 2002)

……………

-

Dilepton spectrum at RHIC

MinBias Au-Au

thermal

• Low mass: thermal dominant (calculated by Rapp in kinetic model)• Inter. mass: charm decay

No signals for thermal dileptons yet

Strangeness Enhancement Basic Idea: Production threshold is lowered in QGP

MeVmQssgg

ssqqsQGP 3002502

Hadronic channels:

)530(

)670(

)71022(

MeVmmmmQKN

MeVmmmQKNNN

MeVmmQKK

NK

NK

K

Equilibration timescale? How much time do we have?

In the QGP:

)80(

)90(

)240(

)380(

MeVQ

MeVQKN

MeVQK

MeVQKNN

Decreasing threshold in a Resonance Gas

To be weighted with the abundances

npQCD calculation with quasi particle pictureand hard-thermal loop still gives t~5-10 fm/c

QGP Scenario Hadronic Scenario

How one calculates the Equilibration Time

Tnm

Kn

Tmpf

pdg

neq 2

1

2

3

3 12

)()2(

2

12211212 SSSSS

S vvgdt

d

gg

qqNNNg fsc 256

7222

12 Reaction dominated by gg

6 fm/c

(pQCD) Equilibration time in

QGP teq ~10 fm/c > tQGP

Hadronic matter teq ~ 30 fm/c

Similarly in hadronic casebut more channels

dduu

ssS

2

Experimental results

refwoundj

AAwoundj

jNY

NYE

/

/

e+e- collisionsSchwinger mechanism

Strangeness enhancement 1

Strangeness enhancement 2

J/ suppression In a QGP enviroment:In a QGP enviroment: • Color charge is subject to screening in QGP

qq interaction is weakened• Linear string term vanishes in the deconfined phase (T) 0 deconfinement

q

q

q,q,g distribution modified

Coulomb Yukawa

D

r

effeff err

V

=0 doesn’t mean no bound !

CTV /

CTr

Screening Effect

• Abelian

• Non Abelian (gauge boson self-interaction)

r

TgV cc

4

)(

4

2

One loop pQCD

112

1

3/263

TgTg

NN fcD

)(

2

)(

2

1 T

r

eff Der

T

rH

13.0 Tlatt

D0

)(

dr

rdE Bohr

eff

D r2.12.1

Bound state solution

Bound is not Tc !

MeVT eff

Bound 2109

2

84.0

MeV150

In HIC at √s ~ SPS, J/should be suppressed !

Lattice result for V channel (J/)

J/ (p 0) disappearsbetween 1.62Tc and 1.70Tc

A() 2()

Associated suppression of charmonium resonances ’c , …

as a “thermometer”, like spectral lines for stellar interiors

For light quarks rBohr ~ 4 fm >> D , dissociation is more effective but of course also recombination

B quark in similar condition at RHIC as Charmonium at SPS

J/J/ Initial productionInitial production

DissociationDissociationIn the plasmaIn the plasma

Recombine with Recombine with light quarkslight quarks

s

s

DscDdcuc

DscDdcuc

,

,

Suppression respect toSuppression respect to extrapolation from ppextrapolation from pp

NUCLEAR ABSORBTIONNUCLEAR ABSORBTION pre-equilibrium cc formation time and absorbtion by comoving hadrons

HADRONIC ABSORBTIONHADRONIC ABSORBTION rescattering after QGP formation

DYNAMICAL SUPPRESSIONDYNAMICAL SUPPRESSION (time scale, g+J/ cc,…)

pA (models)abs ~ 6 mb

DDhJ ,...),,(/

gluon-dissociation,inefficient for m≈ 2 mc

*

“quasifree” dissoc.[Grandchamp ’01]

Fireball dynamical evolution

Dynamical dissociation J/ + g c + c + X

• RHIC central: Ncc≈10-20,

• QCD lattice: J/’s to~2Tc

Regeneration in QGP / at Tc

J/ + g c + c + X→← -If c-quarks thermalize: )( eqNN

d

dN

[Grandchamp +Rapp ’03]

• dominated by regeneration • sensitive to: mc* , open-charm degeneracy

Charmonia in URHIC’s

RHIC SPS

Pion interferometry

STAR Au+Au @ 130 AGeV

)exp(1

)exp(1

)(

22

222222

invinv

llssoo

Rq

RqRqRq

qC

open: without Coulombsolid: with Coulomb

Au+Au @ 130 GeV

STAR

Ro/Rs~1 smaller than expected ~1.5

Source radii from hydrodynamic model

Fails to explain the extracted source sizes

Two-Pion Correlation Functions and source radii from AMPT

Lin, Ko & Pal, PRL 89, 152301 (2002)

Au+Au @ 130 AGeV

Need string melting and large parton scattering cross section which may bedue to quasi bound states in QGP and/or multiparton dynamics (gg↔ggg)

Emission Function from AMPT

• Shift in out direction (<xout> > 0)• Strong positive correlation between out position and emission time• Large halo due to resonance (ω) decay and explosion → non-Gaussian source

Jet quenching

Decrease of mini-jet hadrons (pT> 2 GeV) yield,because of in medium radiation.

Ok, what is a mini-jet? why it is quenched ?

hadrons

hadrons

leading particle

Jet: A localized collection of hadrons which come from a fragmenting parton

Parton Distribution Functions

Hard-scattering cross-section

Fragmentation Function

a

b

c

d

Fragmentation Function

High pT (> 2.0 GeV/c) hadron production in pp collisions

~

High pT Particle Production

Parton Distribution Functions

“Collinear factorization”

Hard-scattering cross-section

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

phad= z pc , z <1 energy needed to create quarks from vacuum

Jet Fragmentation-factorization

A Bab

c

p/ < 0.2

)(22 chc

c

c

cc

h

h zDpd

dNdz

pd

dN

ph= z pc , z <1 energy needed to create quarks from vacuum

2.0)(

)(

zD

zD

c

pc

B.A. Kniehl et al., NPB 582 (00) 514

a,b,c,d= g,u,d,s….

K, p ...

AB= pp (e+e)

Parton distribution after pp collision

)ˆˆˆδ()(ˆσ

π

ˆ

),(),( 222

utscdabtd

ds

QxfQxfdxdxpd

dNbab

ca

c

c

Bb

Aa

(+ phenomenological kT smearing due to vacuum radiation)

d

Intrinsic kT , Cronin Effect

Parton Distribution Functions

Shadowing, EMC Effect

Fragmentation Function leading

particle suppressed

Partonic Energy Loss

c

d

hadrons

a

b

Hard-scattering cross-section

c

ccch

c

c

bbBaaA

ba

bBbaAa

baabcd

ba

T

h

AB

z

QzD

z

zPd

cdabtd

d

QxSQxS

gg

QxfQxf

dddxdxABKpdyd

dN

),(

)(

)(ˆ

),(),(

)()(

),(),(

2*0

/

1

0

*

22

2

/

2

/

22

2

kk

kk

High pT Particle Production in A+A

Known from pp and pA

Known from pp and pA

)1/(* cc zz

)1(* cc pp

Non-Abelian gauge

Energy Loss

Static scattering centers assumedGluon multiple scattering

pi pf

ka

c

CCoolloorr makes a difference

cohform lkkv

xt

1

1/ coh

scatt

coh lN

22

ˆ Debyeqq

Transport coefficient

2ˆˆ LqELqNdx

dEcs

thickness

pi pfpfpi

k

~ Brehmstralung radiation in QED

× × ×

Medium Induced Radiation

Clearly similar Recursion Method is needed to go toward a large number of scatterings!

Ivan Vitev, LANL

2,1,1cM

Lμ

2log

μL

4

α32

g

)0( E

E

E

Non – abelian energy loss

Jet Quenching

EE

L/opacityLarge radiative energy loss

in a QGP medium

weak pT dependence of quenching

Jet distribution

E/E ~ 0.5

Quenching

Energy Loss and expanding QGP

00 /)(

2

2

)(

2ln),(

0

EdqL

out

eff

3/12/)()()( ggT

In the transverse plane

Quenching is angle dependent

nn

TT

ndpdN

ddpdN

)cos(v21

22

22

2 2cosyx

yx

pp

ppv

Probe the density

ddpNdN

ddpNdpR

T

NN

coll

T

AA

TAA/

/)(

2

2

<Ncoll>

nucleon-nucleon cross section

Nuclear Modification Factor:

AA

If R = 1 here, nothing newgoing on

Self-Analyzing (High pT) Probes of the Matter at RHIC

How to measure the quenching

Centrality Dependence

• Dramatically different and opposite centrality evolution of Au+Au experiment from d+Au control.

• Jet suppression is clearly a final state effect.

Au + Au Experiment d + Au Control

Consistent with L2 non-abelian plasma behavior Consistent with GeV (similar to hydro)

Is the plasma a QCD-QGP?

Baryon-Meson Puzzle

suppression: evidence of jet quenching before fragmentation

Fragmentation p/ Jet quenching should affect bothFragmentation is not the dominant

mechanism of hadronization at pT ~ 1-5 GeV !?

PHENIX,nucl-ex/0212014

PHENIX, nucl-ex/0304022

pionspions protonsprotons

Coalescence vs. Fragmentation

Coalescence: partons are already there $ to be close in phase space $

ph= n pT ,, n = 2 , 3 baryons from lower momenta

Fragmentation: Leading parton pT ph= z pT

according to a probability Dh(z)

z < 1, energy needed to create quarks from vacuum

Parton spectrum

B M

z

ppF

pppC

TT

TTT

)(

22)(

TpzF

C 4Even if eventually Fragm. takes over …

Coalescence

2

212

3

1

3

F3)Μ()()(V mqqpfpfpdpd

Pd

dNqq

m

Energy not conserved No confinement constraint

pd

dNpf q

q 3

FV

1)(

|Mqq->m|2 depends only on the phase space weighted by wave function (npQCD also encoded in the quark masses , mq=0.3 GeV, ms=0.475 GeV)

npQCD

yprobabilitcolorspingm

)(δ ),(,|,M 21

(3)32

21

2

qq ppPqrfrdgmPpp W

mmm

Our implementation

parametercoal

mmppxxf

px

px

W

m

./1

)()()(2

π9 2

21

2

21

22

21

2

Coalescence Formula

)(δ)...,...(),()π2(

σ 111

3

3

i2 iTTnnH

n

iiiq

ii

T

H ppppxxfpxfpd

dppd

dN

fH hadron Wigner function

221

221

2221

23

)()()()2(

π9mmppxxf px

pxM

x =p coalescence radius 221 )( pp

In the rest frame

fq invariant parton distribution function thermal (mq=0.3 GeV, ms=0.47 GeV)

with radial flow 0.5)+

quenched minijets (L

ET ~ 700 GeV

(r)~ 0.5 r/R T ~ 170 MeV

V ~ 900 fm-3

GeVfm-3)

5.0|| y

L/

T=170 MeV

P. Levai et al., NPA698(02)631

quenchedsoft hard

Distribution Function

REALITY: one spectrum with correlation kept also at pT < 2 GeV

Hadron from coalescence may have jet structure (away suppr.)

Pion & Proton spectra

V. Greco et al., PRL90 (03)202302 PRC68(03) 034904R. Fries et al., PRL90(03)202303 PRC68(03)44902R. C. Hwa et al., PRC66(02)025205

Au+Au @200AGeV (central)

ππρ

Proton enhancement due to coalescence!

Baryon/Meson ratio

Resonance decays Shrinking of baryon phase

space

Fragmentation not included for

Be careful , there are mass effects !

p

Momentum-space coalescence model

Including 4th order quark flow

q T 2,q T 4,q Tf (p ) 1 2v (p )cos(2 ) 2v (p )cos(4 )

Meson flow

Baryon flow

v

v

3

1+

3

1=

v

v ,

v

v

2

1+

4

1=

v

v ⇒ 2

2,q

4,q2

B2,

B4,22,q

4,q2

M2,

M4,

)v+v(2+1

v+v2= v,

)v+2(v+1

vv2+v2=v 2

4,q22,q

22,q4,q

M4,24,q

22,q

4,q2,q2,q

M2,

)vv+v+6(v+1

v3+vv6+v3+v3= v,

)vv+v+v(6+1

vv6+v3+vv6+v3=v

4,q22,q

24,q

22,q

34,q4,q

22,q

22,q4,q

B4,4,q

22,q

24,q

22,q

24,q2,q

32,q4,q2,q2,q

B2,

Kolb, Chen, Greco, & Ko, PRC 69 (2004) 051901

Wave function effects scaling breaking 10% q/m 5% b/m

wave function effect

Elliptic Flow from Coalescence

/3)(p3v)(pv

/2)(p2v)(pv

Tq2,TB2,

Tq2,TM2,

Enhancement of partonic vEnhancement of partonic v22Coalescence scalingCoalescence scaling

n

p

nT

2V1

Effect of Resonances on Elliptic Flow

K, , p … v2 not affected by resonances!

Pions from resonances

K & p

coal. moved towards data

nucl-th/0402020

*

w.f. + resonance decay

model ecoalescencquark naive in 2v v⇒ 1.2

v

v 2

2,q4,q22

4

Data can be described by a multiphase transport (AMPT) model

22,q4,q v v

Data

Parton cascade

Higher-order anisotropic flows

Back-to-Back Correlation

~8%

Away Side: quenching

has di-jet structure

Same Side: Indep. Fragm.

equal (?!) to pp

Coalescence from s-h leads to away side suppression,While same side is reduced if no further correlation …

trigger

Assoc.

Trigger is a particle at

4 GeV < pTrig < 6 GeV

Associated is a particle at

2 GeV < pT < pTrig

quenched

Unexpected: Appreciable charm flow

Does Charm quark thermalize?

v2 of D meson (single e) coalescence/fragmentation? energy loss?

pT Spectra and Yield of J/

From hard pp collision

D meson spectra

S. Batsouli,PLB557 (03) 26

PythiaHydro

D mesons

B mesons

Single electron does not resolve the two scenarios

Elliptic flow better probe of interaction

No B mes.

V. Greco , PLB595 (04) 202

D mesons

Charmed Elliptic Flow V2q from , p,

Coalescence can predict

v2D for v2c = 0 & v2c = v2q

V2 of electrons

VGCMKRR, PLB595 (04) 202

S. Kelly,QM04

Flow mass effect

Quenching

Quark gluon plasma was predicted to be a weakly

interacting gas of quarks and gluons

The matter created is not a firework of multiple minijets Strong Collective phenomena

Hydrodynamics describes well the bulk of the matter

Transport codes needs a quite large npQCD cross section

Charm quark interacts strongly in the plasma

Recent lattice QCD finds bound states of cc at T>Tc

Rethinking the QGP at Tc < T < 2Tc

“Strong” QGP

Summary

Most proposed QGP signatures are observed at RHIC.

Strangeness production is enhanced and is consistent with formation of hadronic matter at Tc.

Large elliptic flow requires large parton cross sections in transport model or earlier equilibration in hydrodynamic model.

HBT correlation is consistent with formation of strongly interacting partonic matter.

Jet quenching due to radiation requires initial matter with energy density order of magnitude higher than that of QCD at Tc.

Quark number scaling of elliptic flow of identified hadrons is consistent with hadronization via quark coalescence or recombination.

Studies are needed for electromagnetic probes and heavy flavor hadrons.

Theoretical models have played and will continue to play essential roles in understanding RHIC physics.

ConclusionsMatter with energy density too high for simple hadronic

phase ( > c from lattice)

Matter is approximately thermalized (T >Tc )

Jet quenching consistent with a hot and dense medium

described by the hydrodymic approach

Hadrons seem to have typical features of recombination

Strangeness enhancement consistent with grand canonical

ensemble

J/ Needed : - Thermal spectrum - Dilepton enhancement

A Lot of work to do …

Lattice QCD Effective field theory Transport theory (quantum, field condensate,…) pQCD

Scientific approach to an important part of the evolution of the primordial plasma can be achieved

Understanding of Non-Abelian Interaction !