Download Slide 1

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
• 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~ 10-2s)
• Quark and gluons
We’ll never see what happened t < 3 .105 ys
(hidden behind the curtain of the cosmic
microwave background)
Bang
HIC can do it!
Little Bang
From high rB regime
to high T regime
AGS
SPS
RHIC
2
sNN  ( pA  pB )2  ECMS
We do not observe hadronic systems
with T> 170 MeV (Hagerdon prediction)
Different stages of the Little Bang
N  D  N “Elastic”
finite Dt
Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Pre-Equilibrium
Euristic QGP phase transition
Free massless gas
E
g  3
 4 gtot  g g  78 ( g q  g q )

d p p f ( p)  gtot T
3 0
V (2 )
30 g g  16 , g q  gq  Nc N s N f
Bag Model (cosm. cost.)
EH
C
PH  
 B 
V
4R 4
P  0  RH
Pressure exceeds the Bag
pressure -> quark liberation
37  2 904  1/ 4 B1/4 ~ 210 MeV
Tc  T 2 B B > Tc~ 145 MeV
90  37 
1/ 4
Extension to
finite mB , mI
Phase Transition
Def.
Phase transition of order n-th means the n-th derivative
of the free energy F is discontinous

F  T FT
I order
Mixed phase
V
F
CV  2
T
2
II order
Critical behavior
Cross over
Not a mixed phase, but a continous modification
of the matter between the two phases
Quantum ChromoDynamics
1
 m
m a 
   ψi γ m  i  gAa ψi  mi ψi ψi   Fam Fam
2
4 a
i 1

nf
Fa   Aa   Aa  i f abc Ab Ac
m
m


m
m
m
Similar to QED, but much richer structure:
 SU(3) gauge symmetry in color space
Confinement

Approximate Chiral Symmetry in the light sector
broken in the vacuum.
 Chiral Symmetry Restoration
 UA(1) ciral
 Scale Invariance broken by quantum effects
Chiral Symmetry
SU C (3)  SU A (3)  SU V (3)  UV (1)  U A (1)
L,R  (1   5 )
L , R  e
 i Lj ,R  j
L , R
QCD is nearly invariant under rotation among u,d,s
associate Axial and Vector currents are conserved
qq  (250 MeV )3
 Eight goldstone Bosons
(,K,h)
 Absence of parity doublets
Mass (MeV)
Constituent quark masses >
explicit breaking of chiral simmetry
a1 (1260) f1 (1285)
s (4001200) r (770)
 (140)
w (782)
P-S V-A splitting
In the physical vacuum
Lattice QCD
QCD can be solved in a discretized space !

Z   D Ama ( x)D ( x) D ( x) e
i  d  d 3 x L  A , , 
0
i  d 4 x L  A, , 
to 
evaluate
ZLattice
  D Am ( xthe)Dalgorithm
 ( x) D
( x) eZ in the
QCDais
Space-time -> static at finite temperature
 iHt
ie
1
/ TeH 
Dynamics -> Statistics
time dim. regulate
the temperature
ψ(n) U (n, n  mˆ )  exp (ig t a Ama (n))
Gluon field
Continuum limit
1
1
1 4


2 2
m
a 0
S   2  Tr  U m (n)   2  Tr expia g Fm (n) 

d
x
F
F
m

p
p

closed

2g
2g
4
p
It is less trivial than it seems, Ex.: fermion action, determinant
Lattice QCD
Prospectives
Quark –gluon plasma properties (vs density and temperature)
 Hadron properties (mass, spin, )
 vacuum QCD structure (istantons ..)
 CKM matrix elements (f,fk,fc,fB)
CPU time is very large
 quark loops is very time consuming
(mq=∞ > no quark loops = “quenched approximation”)
 lattice spacing a > 0
 baryon chemical potential
Limitations
 No real time processes
 Scattering
 Non equilibrium
 Physical understanding
Effective models
are always necessary !!!
(
Polyakov Loop


ig 0 A0 ( x ,t ) d
L Tr e
) Tr(e
a



3
a
a
a 
H int   d y J m ( y) Am ( y)  ig A0 ( x )
2
J m ( y)  ig
a
a
2
 H int
)
-static quark
-only gluon dynamics
 
 ( y  x )(1,0,0,0)
L  0  H int  
 confinement
If quark mass is not infinite and quark loops are present
L is not really an order parameter !
Lattice QCD
Polyakov Loop
Chiral Condensate
• Coincident transitions:
deconfinement and chiral symmetry restoration
it is seen to hold also vs quark mass
Phase Transition to Quark-Gluon Plasma
Enhancement of the degrees
of freedom towards the QGP
  0.7 GeV / fm
3
Tc  173 15 MeV
Quantum-massless non interacting
   qq
 2 7
 4
  g   6n f  16 T
30  4

Gap in the energy density
(I0 order or cross over ?)
Definitions and concepts
in HIC
Kinematics
Observables
Language of experimentalist
The RHIC Experiments
Au+Au
STAR
Soft and Hard
SOFT (npQCD) string fragmentation in e+e , pp … or
(pT<2 GeV)
string melting in AA (AMPT, HIJING, NEXUS…)
QGP
HARD minijets from first NN collisions
Indipendent Fragmentation : pQCD + phenomenology
• Small momentum transfer
• Bulk particle production
– How ? How many ? How are
distributed?
• Only phenomenological
descriptions available (pQCD
doesn’t work)
99% of particles
Collision Geometry - “Centrality”
Spectators
Participants
S. Modiuswescki
15 fm
0
b
N_part
For a given b,
Glauber model
0 fm predicts N
part
394 and Nbinary
Kinematical observables
1 E  pz Additive like Galilean velocity
y z  ln
2 E  pz y j / CM  y j / LAB  yLAB / CM
Transverse mass
 1/ 2
mT  (m 2  pT2 )
E  mT cosh y , pz  mT sinh y z
Angle respect z beam axis

1  | p |  pz 
h   ln tan( / 2)  ln  

2  | p |  pz 
Rapidity -pseudorapidity
dN
m2
dN
  1 2

2
dhdpT
mT cosh y dydpT
Energy Density
| Dy |  0.5
Energy density a la Bjorken:
dET
1 dET
ε

A T dz πR 2 τ dy
Particle streaming from origin
z
 v z  tanh yz
t
 dz   cosh y dy
R  1.18 A  7 fm
τSPS  1 fm/c
Estimate  for RHIC:
dET/dy ~ 720 GeV
Time estimate from hydro:
  0.6 fm/c   ~ 8 GeV/fm
3
1/3
τ RHIC  0.4  1 fm/c
 Tinitial ~ 300-350 MeV
Collective Flow I: Radial
Observable in the spectra, that have a slope
due to temperature folded with Radial flow
expansion <T> due to the pressure.
Absence
1
Non  Relativist ic p T  m , Tsl  Tf  m v T
2
1  vT
Ultra  Relativist ic p T >> m, Tsl  Tf
1  vT
Slope for hadrons with different masses
allow to separate thermal from collective
flow
Tf ~ (120 ± 10) MeV
<T> ~ (0.5 ± 0.05)
2
Collective flow II: Elliptic Flow
Perform a Fourier decomposition of the
momentum space particle distributions
in the x-y plane
dN
dN 

1  2  v n cos(n )

dpT d dpT 
n
z
y
x
Anisotropic Flow
Measure of the Pressure gradient
Good probe of
early pressure
v2 is the 2nd harmonic Fourier coeff.
of the distribution of particles.
px2  p y2
v2  cos2  2
px  p y2
Statistical Model
Temperature
Yield
Maximum entropy principle
Mass
Chemical Potential
Quantum Numbers
There is a dynamical evolution that
Leads to such values of
Temp. & abundances?
Hydro add radial flow,
freeze-out hypersurface
for describing the
differential spectrum
Yes, but what is Hydro?
Maximum Entropy Principle
d 3 pd 3 x
 f ln f  (1  f ) ln(1  f )
S    
3
k DV
(2 )
 E >  dw  Ei fi
i
 B >  dw  Bi fi
All processes costrained
by the conservation laws
i
 S >  dw  si fi
i
Maximizing S with this constraints
the solution is the statistical thermal
equilibrium
The apparent “equilibrium” is not achieved
kinetically but statistically !
HYDRODYNAMICS
Local conservation Laws 5 partial diff. eq. for 6 fields (p,e,n,u)
+ Equation of State p(e,nB)
m
 mT ( x)  0 T m ( x)  e( x)  p( x)u m ( x)u ( x)  p( x) g m
 m
 m jB ( x)  0 jBm ( x)  nB ( x)u m ( x)
No details about collision
dynamics (mean free path >0)
Another level of Knoweledge
Follow 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
Transport Theory
 
f q , g (r , p, t ) Follow distribution function time evolution
From the initial non-equilibrium gluon phase
 


f p
   r f   rU   p f  I coll
Non-relativistically
t m
drifting
mean field
collision
2 2 m
2
2 f f )W
23  4 (1p
 2 p  p Relativistically
Ipcoll

(
f
f

1 2I
1234
 f  I3 4 
 I 1 2... 3  p4 )
m
1 2 3
coll
coll
coll
gg>ggg
g>gg
To be treated:
- Multiparticle collision (elastic and inelastic)
- Quantum transport theory (off-shell effect, … )
- Mean field or condensate dynamics
at High density
Transport
Spectra still appear thermal
Hydro
Elliptic Flow
rapidity
rapidity
• Chemical equilibrium with a limiting Tc ~170MeV
• Thermal equilibrium with collective behavior
- Tth ~120 MeV and <T>~ 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 HIC
What we have find till now!
strangeness enhancement
jet quenching
coalescence
J/ suppression
What we have learned
?
Glauber model
N
Binary Collisions
Participants
b (fm)