Introduction to the physics of the Quark-Gluon Plasma

and the relativistic heavy-ion collisions

Villa Gualino-Torino, 7-3-2011

Fermi Notes on Thermodynamics

QGPQGP

Matter under extreme conditions…

Eleven Science Questions for the New CenturyEleven Science Questions for the New CenturyNATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES…NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES…

No. 7 - What Are the New States of Matter at Exceedingly No. 7 - What Are the New States of Matter at Exceedingly High Density and Temperature? High Density and Temperature? QGP is at T QGP is at T>>10101212K and K and >>

10104040 cm cm-3-3

p

p

p,n,

1911 - Rutherford discovered the NucleusIn ’30 started the study of a new force:Nuclear Force between nucleons

Bashing nucleons with increasing energy …

It became clear that nucleons and more generally hadrons are made of

quarks exchanging gluons

Let’s start from 100 years ago …Let’s start from 100 years ago …

In 1974 the theory of the strong interactionwas written down and calledQuantum Chromodynamics

aaaiiii

aa

n

iiQCD FFmgAiL

f

4

1ψψψ

2γψ

1

cbabcaaa AAfiAAF

Quantum ChromodynamicsQuantum Chromodynamics

Similar to QED but 3 charges + gauge invarianceimply that the gauge field (gluons) self-interact:

- Asymptotic freedomAsymptotic freedom- ConfinementConfinement

electric charge

colour charge

Two regimes:Two regimes:

- Q>>QCD one can use perturbative QCD (pQCD)

- Q ~QCD , Q >QCD non perturbative methods :

lattice QCD (lQCD) and effective lagrangian approach

Several arguments already in the ’70-’80 leadto think that at some temperature and/ordensity quarks “can roam freely in a medium”-> QGP

Quark-Gluon PlasmaQuark-Gluon Plasma

Inside nuclei strong interaction manifest in an extremely non-perturbative regime (QCD~ 1 fm-1) and quarks are not the relevant degrees of freedom

1) ASYMPTOTIC FREEDOM At large T there are interaction q2 ~ (3T)2 and the coupling is weak

2) OVERLAP (percolation) Hadrons Overlap does not allow to identify the hadrons itself: T0 ~ 150 MeV

3) BAG PRESSURE MODELING Pressure of pion gas smaller than the quark gas one: T0 ~ 150 MeV

4) HAGERDON LIMITING TEMPERATURE Hadron gas partition function has a singularity at T0 ~ 160 MeV

Hagerdon’s limiting temperatureHagerdon’s limiting temperature

From the Hadronic side increasing temperature leads to the productionof higher mass hadronic states, but the density of states grows exponentially with the mass

Cabibbo-Parisi, PLB59(1975): Divergency of the partition function has to be associated with a phase transition of hadronic matter to quark-gluon matter

Hagerdon, Nuovo Cimento (1965): T0 is a limiting temperature for hadronic systems

Partition functon for a gas o particle with density of states (m)

m>>T

Quark-antiQuark free energy in lQCD

Kaczmarek et al., PPS 129,560(2004)

lQCD

String breaking

Charm Quarks

We cannot observe quarks, but at large Twe can envisage a weakly interacting gas of quarks and gluons

Asymptotic value

vacuum

Order Parameters of the Phase TransitionOrder Parameters of the Phase Transition

int0 0 ),( HdtxAig eTreTrL

0)250( 3 MeVqq

Polyakov Loop Chiral Condensate

What is the order of the phase transition? [Ratti]

T~170 MeV T~170 MeVlQCD

The basic relations of reference

Ideally our reference is a gas of non-interacting massless quarks and gluons

Multiplied by degrees of freedomdq+q=2*2*3*Nf =24-30 , dg=8*2

x d.o.f

x d.o.f

From lattice QCDFrom lattice QCD

Enhancement of the degrees Enhancement of the degrees of freedom towards the QGPof freedom towards the QGP

MeVT

fmGeV

c

c

15175

/7.0 3

RHIC

Stefan-Boltzmann limit Stefan-Boltzmann limit not reached by 20 % for not reached by 20 % for : :

QGP as a weak interacting gas?!QGP as a weak interacting gas?!

In Ads/CFT this can be a very strongIn Ads/CFT this can be a very strong

interacting systeminteracting system

B=0

gqq

SB ddT 8

7

30

2

4

RHIC

LHC

Interaction measure

No interaction means also =3p(for a massless gas)

[Cotrone]

QGP in the Early Universe Evolution

• Hadronization (Hadronization (T~ 0.2 GeV, t~ 10T~ 0.2 GeV, t~ 10-5-5ss) )

• Quark and gluonsQuark 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 “

BangBang

g(T

)g

(T)

...215.3116...33442)( cbudsgeTg

Quark-Gluon Plasma

HICHIC

10-5s4

)(T

Tg

Degrees of freedom in the Universe

D.J.Schwartz, Ann. Phys. 2004

How to produce a matter How to produce a matter

with with >>1 GeV/fm >>1 GeV/fm33

lasting for lasting for > 1 fm/c > 1 fm/c

in a volume much larger than an hadron?in a volume much larger than an hadron?

Let’s bash again at higher energy…

High Energy Heavy Ion Collision FacilitiesHigh Energy Heavy Ion Collision FacilitiesAccelerator Lab. Ebeam

[AGeV]

Contraction

AGS

(’80s)

BNL 10 (*) 4.5 2

SPS

(94-…)

CERN 160(*) 17.3 9

RHIC

(00-…)

BNL 100 +100 200 100

LHC

(09-…)

CERN 2750+2750 5500 2750

beamNN Es 2

beamNN Ems 2Fixed target

Collider

AGeVs

m

s

m

ECMγ

22)( CMSBANN Epps

Max energy density complete stopping

33max 4

3

4

3

mR

sN

R

Ns

V

E partpart

A

CM

RHIC -> max~ 102 GeV/fm3

LHC -> emax~ 3 103 GeV/fm3

Exploring the phase diagram

Time – 5-15 fm/c = 15-45ys~10-22s

RHIC

LHCLHC

new medium created from the energy deposited B=0 (quark=antiquarks)

Hotter-denser-longer increasing EHotter-denser-longer increasing Ebeambeam

nuclei

RHIC

SPS

Increasing beam energy -> transparencyEnergy distributed in a larger volume

How to make simple estimates?

AGS (BNL)

SPS(CERN)

RHIC (BNL)

Hagerdon limitingtemperature

Yield Mass Quantum Numbers

Temperature Chemical Potential

F. Becattini

Statistical Model analysis

T

Energy Density and Temperature Estimate I

dyydz

yt

zzz

cosh

tanhv

Energy density a la Bjorken:

dy

dE

Rz

NE

V

E T

02

02T

T0

1

y

N

τπR

m

Aε

dET/dy ~ 720 GeV

385~ GeV/fmRHIC

5.0|| y

Particle streaming from origin

experimentstheory estimate

RHIC~0.6-1 fm/c

We can estimate the initial Is this correct?

Energy Density and Temperature Estimate II

TTsssVS 03

000cost

But this means that the previous estimate cannot be correct because it supposes that but to conserve entropy

3

3/1

002

151021

ε

fmGeV

dy

dE

R BjorkenfT

Estimate of QGP lifetimeEstimate of QGP lifetime (~0.6 fm/c at RHIC)

RHIC - T=2TcQGP=0.6*23 =5 fm/c

LHC - T=3.5 TcQGP=0.4*3.53 =15 fm/c

So with uRHIC 0>>c

QGP>fm/c

V> 103 fm3

1D expansion

3

00

cQGP T

T

3

00

T

T3/4

00

Entropy Conservation

MeVfmfmg

T 3357.110

12830 114/14/1

020

Different stages of the Little Bang

2 Freeze-out

Hadron Gas

Phase Transition

Plasma-phase

Pre-Equilibrium <0.2 fm/c

~0.6 fm/c

~20 fm/c

System expands and cools down

cost2/122 zt

~5 fm/c

Soft and Hard probes

SOFT (pT ~QCD,T) driven by non perturbative QCD

HARD (pT >> QCD)Early production, pQCD applicable, comparable with pp, pA

95% of particles

jet quenching, heavy quarks, quarkonia, hard photons

Hadron yields, collective modes of the bulk, strangeness enhancement, fluctuations, thermal radiation, dilepton enhancement

BULK (pT~T)

MINIJETS MINIJETS (p(pTT>>T,>>T,QCDQCD))

CGC (x<<1)Gluon saturation

Heavy Quarks Heavy Quarks (m(mqq>>T,>>T,QCDQCD))

Microscopic Microscopic MechanismMechanism

Matters!Matters!

Initial Conditions Quark-Gluon Plasma Hadronization

Initial ConditionInitial Condition – “exotic” non equilibrium CGC Bulk Bulk –– Hydrodynamics BUTBUT finite viscosities () MinijetsMinijets – perturbative QCD BUTBUT strong Jet-Bulk “talk” Heavy QuarksHeavy Quarks – Brownian motion (?) BUT strongly dragged by the Bulk Quarkonia – Are suppressed (only resonances?) or regenerated HadronizationHadronization – Microscopic mechanism can modify QGP observables

The Several ProbesThe Several Probes

[Albacete] [Bruna] [Arnaldi]

[Romatschke], [Snellings],[Beraudo]

[Becattini][Blume]

LHCRHIC

Dominance of QGP phase (Dominance of QGP phase (QGPQGP> > 10 10

fm/cfm/c)) Vanishing hadronic contamination?

Very large yield of heavy quark (Very large yield of heavy quark (mmqq>>T>>T) and jets ) and jets ((ppTT>>T>>T))

Increasing relevance of non-equilibrated “objects”!

A new QGP phase: perturbative plasma? A new QGP phase: perturbative plasma? Larger /s we get close to the pQCD estimates?

Existence of a primordial non-equilibrium phaseExistence of a primordial non-equilibrium phase Color Glass Condensate (CGC) as high-energy limit of QCD?

Hopefully with several other surprises…Enjoy the School!

Collective Expansion of the BulkCollective Expansion of the Bulk

x

yz

px

py

22

22

2yx

yx

pp

ppv

22

22

xy

xyx

cc22ss=dP/=dP/

ddEoSEoS

ssviscosityviscosity

v2/ measures efficiencyin converting the eccentricity

from CoordinateCoordinate to Momentum Momentum spacespace

SPSRHIC

Vis

cosi

ty s

Transverse Density [fm-2]

For the first time closeFor the first time close to ideal Hydrodynamicsto ideal Hydrodynamics

The fluid with lowest The fluid with lowest ever observed ever observed /s/s

QGP

Color Glass Condensate initial conditions?Color Glass Condensate initial conditions?

pT

dN

/d2p

T

Qsat(s)

3/12

222 ),()()( A

R

QxxgQsQ ssat

At RHIC Q2 ~ 2 GeV2

At LHC Q2 ~ ?

Ideal Sketch

yT es

px

At small x (pT) dense gluon matter

Gluons of small x (pT) -> larger size >1/Qs

overlapand the gluon dostribution stops growing

Parton distr. funct

What is the impactWhat is the impactof a different intial condition?of a different intial condition?

Jet QuenchingJet Quenching

Suppression of minijetsSuppression of minijets

Suppression should increase with density and temperature.Allows a further measure of energy density.

It is due to gluon radiation?Jet energy loss produce mach cones?

Jet triggered angular Jet triggered angular correl.correl.

y

x

away

near

Medium

Heavy Quarks dragged by the medium?Heavy Quarks dragged by the medium?

Strong suppression Large elliptic Flow

Indirect measurement from semileptonic decay (D->Ke) came as a surprise:

- m- mc,bc,b >> >> QCDQCD produced by pQCD processes (out of

equil.)- 00 << << QGPQGP they go through all the QGP lifetime

-mmc,bc,b >> T >> T00 no thermal production no thermal production

A better test of pQCD scattering and energy loss:- mQ>>mq small drag from the bulk

r

eV

rm

eff

D

Quarkonia Suppression?Quarkonia Suppression?

QQ Quarkonium dissoved by charge screening: Thermometer

gTmr

DQQ

11

More binding smaller radiushigher temperature

cJbY, …

Suppression at SPS! More suppression at RHIC

because of high the higher temperature?!and even more at LHC?

Hadronization ModifiedHadronization ModifiedBaryon/MesonsBaryon/Mesons

Au+Au

p+p

PHENIX, PRL89(2003)

Use medium and not vacuumUse medium and not vacuum-> Quark coalescence-> Quark coalescenceMore easy to produce baryons!More easy to produce baryons!

Quark number scalingQuark number scaling

Hadronization is modifiedHadronization is modifiedDynamical quarks are visibleDynamical quarks are visible

Fries-Greco-Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)

ababMbbbaaba

aM qrprfprfPd

dN,),(),(

,3

/3)(p3v)(pv

/2)(p2v)(pv

Tq2,TB2,

Tq2,TM2,

n

p

nT

2V1

Baryon

Meson

Hadronization ModifiedHadronization Modified

Baryon/MesonsBaryon/Mesons

Au+Au

p+p

PHENIX, PRL89(2003)

Quark number scalingQuark number scaling

n

TT

qT

T

H nppd

dNp

pd

dN

)()(

22

n

p

nT

2V1

Dynamical quarks are visibleDynamical quarks are visibleCollective flowsCollective flows

)2cos(v21φ 2

TT

q

TT

q

dpp

dN

ddpp

dN

/3)(p3v)(pv

/2)(p2v)(pv

Tq2,TB2,

Tq2,TM2,

Enhancement of vEnhancement of v22

v2q fitted from v2

GKL

Coalescence scalingCoalescence scaling