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Introduction to the physics of the
Quark-Gluon Plasma
and the relativistic heavy-ion collisions
Villa Gualino-Torino, 7-3-2011
Matter under extreme conditions…
Fermi Notes on Thermodynamics
QGP
Eleven Science Questions for the New Century
NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES…
No. 7 - What Are the New States of Matter at Exceedingly
High Density and Temperature? QGP is at T>1012K and r > 1040 cm-3
Let’s start from 100 years ago …
1911 - Rutherford discovered the Nucleus
In ’30 started the study of a new force:
Nuclear Force between nucleons
Bashing nucleons
with increasing energy …
p
p
p,n,L,S,D,..
It became clear that nucleons
and more generally hadrons are made of
quarks exchanging gluons
p,r,w,f,K, ..
In 1974 the theory of the strong interaction
was written down and called
Quantum Chromodynamics
Quantum Chromodynamics
 
1
 a 
ψi  mi ψi ψi   Fa Fa
  ψi γ   i  gAa
2 
4 a
i 1

nf
LQCD
Fa    Aa   Aa  i f abc Ab Ac
electric charge
Similar to QED but 3 charges + gauge invariance
imply that the gauge field (gluons) self-interact:
- Asymptotic freedom
- Confinement
colour charge
Two regimes:
- Q>>LQCD one can use perturbative QCD (pQCD)
- Q ~LQCD , Q >LQCD non perturbative methods :
lattice QCD (lQCD) and effective lagrangian approach
Quark-Gluon Plasma
Inside nuclei strong interaction manifest in an
extremely non-perturbative regime (LQCD~ 1 fm-1)
and quarks are not the relevant degrees of freedom
Several arguments already in the ’70-’80 lead
to think that at some temperature and/or
density quarks “can roam freely in a medium”-> QGP
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 temperature
From the Hadronic side increasing temperature leads to the production
of higher mass hadronic states, but the density of states grows
exponentially with the mass
Partition functon for a gas o particle with density of states r(m)
m>>T
Hagerdon, Nuovo Cimento (1965): T0 is a limiting
temperature for hadronic systems
Cabibbo-Parisi, PLB59(1975): Divergency
of the partition function has to be associated
with a phase transition of hadronic matter to
quark-gluon matter
Quark-antiQuark free energy in lQCD
We cannot observe quarks, but at large T
we can envisage a weakly interacting
gas of quarks and gluons
Asymptotic value
Charm Quarks
String breaking
vacuum
lQCD
Kaczmarek et al., PPS 129,560(2004)
Order Parameters of the Phase Transition
Polyakov Loop
lQCD

L Tr e
Chiral Condensate
T~170 MeV
T~170 MeV


ig 0 A0 ( x ,t ) d
 Tre
 H int

qq  (250 MeV )3  0
What is the order of the phase transition? [Ratti]
The basic relations of reference
Ideally our reference is a gas of non-interacting massless quarks and gluons
x d.o.f
x d.o.f
Multiplied by degrees of freedom
dq+q=2*2*3*Nf =24-30 , dg=8*2
From lattice QCD
 SB
T
4

p 2 7

d

d
qq
g
30  8
RHIC 
Enhancement of the degrees
of freedom towards the QGP
 c  0.7 GeV / fm3
Tc  175  15 MeV
Stefan-Boltzmann limit
not reached by 20 % for  :
QGP as a weak interacting gas?!
B=0
In Ads/CFT this can be a very strong
Interaction measure
interacting system
[Cotrone]
LHC
No interaction means also =3p
(for a massless gas)
QGP in the Early Universe Evolution
• e. m. decouple (T~ 1eV , t ~ 3.105 ys)
“thermal freeze-out “
• but matter opaque to e.m. radiation
• Atomic nuclei (T~100 KeV, t ~200s)
“chemical freeze-out”
• Hadronization (T~ 0.2 GeV, t~ 10-5s)
• Quark and gluons
Bang
Degrees of freedom in the Universe

T4
g(T)
g (T ) 
g (T )  2  4e  4  3  3p  ...  16 g  31.5uds  21cb  ...
D.J.Schwartz, Ann. Phys. 2004
Quark-Gluon Plasma
How to produce a matter
with  >>1 GeV/fm3
lasting for  > 1 fm/c
in a volume much larger than an hadron?
Let’s bash again at higher energy…
High Energy Heavy Ion Collision Facilities
Accelerator Lab.
Ebeam
[AGeV]
s AGeV  Contrac
tion
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
Fixed
target
sNN  2 mEbeam
Collider
sNN  2 Ebeam
2
s NN  ( p A  pB ) 2  ECMS
γ CM 
E
s

m m
2750
Max energy density complete stopping
3 s N part 3sN part
E
 max  CM 

3
VA
4p R
4p mR3
RHIC -> max~ 102 GeV/fm3
LHC -> emax~ 3 103 GeV/fm3
LHC
Exploring the phase diagram
RHIC
RHIC
SPS
nuclei
new medium created from the energy
deposited B=0 (quark=antiquarks)
Hotter-denser-longer increasing Ebeam
Increasing beam energy -> transparency
Energy distributed in a larger volume
How to make simple estimates?
Time – 5-15 fm/c = 15-45ys~10-22s
Statistical Model analysis
Temperature
Chemical
Potential
T
Yield
Mass
Quantum Numbers
F. Becattini
Hagerdon limiting
temperature
AGS (BNL)
SPS(CERN)
RHIC (BNL)
Energy Density and Temperature Estimate I
| Dy |  0.5
Particle streaming from origin
z
 v z  tanh yz
t
 dz   cosh y dy
Energy density a la Bjorken:
DE
E  DN
m T DN
1 dET
ε0 



2
DV
A T  Dz πR τ 0 Dy pR 2 0 dy
theory estimate
experiments
RHIC ~0.6-1 fm/c
dET/dy ~ 720 GeV
We can estimate the initial 0
 RHIC ~ 5  8 GeV/fm3 Is this correct?
Energy Density and Temperature Estimate II
Entropy Conservation
S  sV  cost  s0 0  s  T03 0  T
1D expansion
 T0 

T 
3
 0 
0 

 
4/3
  0
But this means that the previous estimate cannot be correct
because it supposes that  ~ 1, but to conserve entropy  ~ 4/3
1 dET   f

ε
2
pR  0 dy   0
1/ 4
 30  
T0   2 0 
p g 
1/ 3



  Bjorken  2  10  15 GeV  fm3
 8 12 


 10 
1/ 4
fm1  1.7 fm1  335MeV
Estimate of QGP lifetime (0~0.6 fm/c at RHIC)
 T0  RHIC - T=2Tc > QGP=0.6*23 =5 fm/c
  0  
 Tc  LHC - T=3.5 Tc > QGP=0.4*3.53 =15 fm/c
3
 QGP
So with uRHIC
0>>c
QGP>1fm/c
V> 103 fm3
Different stages of the Little Bang
System expands and cools down
2 Freeze-out
 ~20 fm/c
Hadron Gas
  t 2  z 2 1/ 2  cost
Phase Transition
 ~5 fm/c
Plasma-phase
 ~0.6 fm/c
Pre-Equilibrium
 <0.2 fm/c
Soft and Hard probes
SOFT (pT ~LQCD,T)
driven by non perturbative QCD
Hadron yields, collective modes of the bulk,
strangeness enhancement, fluctuations,
thermal radiation, dilepton enhancement
HARD (pT >> LQCD)
Early production, pQCD applicable,
comparable with pp, pA
jet quenching, heavy quarks, quarkonia,
hard photons
95% of particles
The Several Probes
[Romatschke], [Snellings],[Beraudo]
Initial Conditions
Quark-Gluon Plasma
Hadronization
BULK
(pT~T)
CGC (x<<1)
Gluon saturation
[Albacete]
MINIJETS
(pT>>T,LQCD)
[Bruna]
Heavy Quarks
(mq>>T,LQCD)
[Arnaldi]
Microscopic
Mechanism
Matters!
[Becattini]
[Blume]
 Initial Condition – “exotic” non equilibrium CGC
 Bulk – Hydrodynamics BUT finite viscosities (h,z)
 Minijets – perturbative QCD BUT strong Jet-Bulk “talk”
 Heavy Quarks – Brownian motion (?) BUT strongly dragged by the Bulk
 Quarkonia – Are suppressed (only resonances?) or regenerated
 Hadronization – Microscopic mechanism can modify QGP observables
RHIC
LHC
 Dominance of QGP phase (QGP> 10 fm/c)
 Vanishing hadronic contamination?
 A new QGP phase: perturbative plasma?
 Larger h/s we get close to the pQCD estimates?
Hopefully with several other surprises…
 Very large yield of heavy
quarkthe
(m >>T
) and jets (p >>T)
Enjoy
School!
 Increasing relevance of non-equilibrated “objects”!
q
T
 Existence of a primordial non-equilibrium phase
 Color Glass Condensate (CGC) as high-energy limit of QCD?
Collective Expansion of the Bulk
v2/ measures efficiency
in converting the eccentricity
from Coordinate to Momentum space
z
y
x
 x
y2  x2
y x
2
2
c2
s=dP/d
 EoS
v2 
p x2  p y2
p x2  p y2
The fluid with lowest ever
observed h/s
Viscosity h/s
For the first time close
to ideal Hydrodynamics
h/s viscosity
QGP
Transverse Density [fm-2]
Color Glass Condensate initial conditions?
dN/d2pT
Parton distr. funct
Ideal Sketch
Qsat(s)
At small x (pT) dense gluon matter
Gluons of small x (pT) -> larger size >1/Qs overlap
and the gluon dostribution stops growing
pT y
x
e
s
pT
At RHIC Q2 ~ 2 GeV2
At LHC Q2 ~ ?
2
What is the impact
xg
(
x
,
Q
)
2
2
1/ 3
Qsat ( s)   s (Q )
A
2
of a different intial condition?
pR
Jet Quenching
y
x
Suppression of minijets

Jet triggered angular correl.
near
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?
Medium
away
Heavy Quarks dragged by the medium?
- mc,b >> LQCD produced by pQCD processes (out of equil.)
- 0 << QGP they go through all the QGP lifetime
-mc,b >> T0 no thermal production
A better test of pQCD scattering and energy loss:
- mQ>>mq small drag from the bulk
Indirect measurement from semileptonic decay (D->Ke) came as a surprise:
Strong suppression
Large elliptic Flow
Quarkonia Suppression?
QQ Quarkonium dissoved by charge screening: Thermometer
V    eff
e  mD r
r
rQQ 
1
1

mD gT
cc, J/Y, cb, Y, …
More binding smaller radius
higher temperature
Suppression at SPS!
More suppression at RHIC
because of high the higher temperature?!
and even more at LHC?
Hadronization Modified
Baryon/Mesons
Quark number scaling
Meson
p+p
PHENIX, PRL89(2003)
Use medium and not vacuum
-> Quark coalescence
More easy to produce baryons!
v 2,M (p1T )  2v
pT 2,q (p T /2)
V2  
v 2,B (pnT )  3v
n 2,q (p T /3)
dN M
  f a (ra , pa )  f b (rb , pb )   M rab , qab 
d 3 P a ,b
Hadronization is modified
Dynamical quarks are visible
Fries-Greco-Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)
Hadronization Modified
Baryon/Mesons
Quark number scaling
p+p
v2q fitted from v2p
GKL
PHENIX, PRL89(2003)
dN q
pT dpT dφ

dN q
pT dpT
1  2v 2 cos(2 )
 dN q

dN H
( pT )   2 ( pT n)
2
d pT
 d pT

n
Coalescence
scaling
Enhancement
of v2
v 2,M (p T1)  2v
 p2,Tq (p T /2)
V2  
v 2,B (p Tn)  3v
 n2,q (p T /3)
Dynamical quarks are visible
Collective flows