Search for the Quark-Gluon Plasma
in Heavy Ion Collision
V. Greco
Outline II
Probes of QGP in HIC
What we have find till now!
strangeness enhancement
jet quenching
coalescence
J/Y suppression
What we have learned
?
Probes of QGP
 Strangeness enhancement
 J/Ψ suppression
 Jet quenching
 Thermal QGP radiation
 Dilepton enhancement
 Quark recombination
 Enhancement of fluctuations
…
Strangeness Enhancement
Basic Idea:
 Production threshold is lowered by the chiral restoration
In the QGP:
qq ss
 QQGP  2ms  250  300 MeV
g  g  s  s
Hadronic channels:
  K  K (Q  2mK  2m  710 MeV )
NN  NK
(Q  m  mK  mN  670 MeV )
N  K
(Q  m  mK  mN  m  530 MeV )
Equilibration timescale ? How much time do you have?
QGP Scenario
Hadronic Scenario
Decreasing threshold in
a Resonance Gas
N  NK (Q  380 MeV )
  K (Q  240 MeV )
  NK (Q  90 MeV )
   (Q  80 MeV )
To be weighted with
the abundances
npQCD calculation with quasi particle picture
and hard-thermal loop Still give t~5-10 fm/c
How one calculates the Equilibration Time
d3p
Tm2  1  nm 
eq  g 
K2 


3 f ( p) 
2

n
T
(2 )
n 1


d S
 g12  v
dt
12  v
12 SS
72 qq
g12  N N N f  
256 gg
2
c
2
s

SS 12
2
S

Similarly in hadronic case
but more channels
Reaction dominate by gg
6 fm/c
(pQCD) Equilibration time in QGP
teq ~10 fm/c > tQGP
 Hadronic matter teq ~ 20-30 fm/c
Experimental results
Strangeness enh. 1
Strangeness enhancement 2
S 
SPS
2 ss
uu  dd
e+e- collisions
Ej

Y /N

Y / N


j
wound AA
j
wound ref
Schwinger mechanism
Present Knoweldge
 AGS (6GeV) explained by hadronic models
 Enhancement at SPS and RHIC (8.8 GeV-200 GeV)
- not explained by hadronic models
- unless chiral symmetry effects are modelled
 Enh. Agrees with statistical models in grand-canonical ensemble
- no canonical suppression
Present Unknoweldge
 What means the absence of canonical suppression?
- multiparticle dynamics in QGP
- higher cross section respect to pQCD
 Enh. is more a signal of chiral
restoration already in dense hadronic matter?
 Why Enh. Larger at SPS than at RHIC?
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 ?
High pT Particle Production
High pT (>
~ 2.0 GeV/c) hadron production in pp collisions
Jet: A localized collection of hadrons which
come from a fragmenting parton
hadrons
Parton Distribution Functions
Hard-scattering cross-section
c
a
b
d
hadrons
Fragmentation Function
leading
particle
phad= z pc , z <1 energy needed
to create quarks from vacuum
h
d pp
0
D
d

2
2
h/c

K
dx
dx
f
(
x
,
Q
)
f
(
x
,
Q
)
(
ab

cd
)

a
b a
a
b
b

dyd 2 pT
dtˆ
z c
abcd
“Collinear factorization”
Jet Fragmentation-factorization
, K, p ...
c
b
a
A
B
dN h
dN c

dz
Dch ( z c )

c
2
2

d ph
d pc
c
d
ph= z pc , z <1 energy needed
to create quarks from vacuum
AB= pp (e+e)
a,b,c,d= g,u,d,s….
dN c distribution after pp2collision 2
Parton
   dxa dxb f ( xa , Q ) f ( xb , Q )
2
d pc
c
sˆ dσ
( ab  cd ) δ( sˆ  tˆ  uˆ )
π dtˆ
a
A
b
B
(+ phenomenological kT smearing
due to vacuum radiation)
Dc p ( z )
Dc ( z )
 0.2
p/ < 0.2
B.A. Kniehl et al., NPB 582 (00) 514
High pT Particle Production in A+A
h
AB
dN
2
2

ABK
dx
dx
d
k
d
kb

a
b
a

2
abcd
dyd pT
 f a / A ( xa , Q 2 ) f b / B ( xb , Q 2 )
 g (k a ) g (k b )
0
h/c
*
c
2
c
zc*  zc /(1   )
Parton Distribution Functions
Intrinsic kT , Cronin Effect
 S A ( xa , Qa2 ) S B ( xb , Qb2 )
d

(ab  cd )
dtˆ
1
zc*
 0 dP( )
zc
pc*  pc (1   )
Shadowing, EMC Effect
Hard-scattering cross-section
c
Partonic Energy Loss
D (z ,Q )
Fragmentation Function

zc
a
b
d
hadrons
leading particle
suppressed
Energy Loss
~ Brehmstralung radiation in QED
Color makes a difference
k
pi
pi
pf
×
×
pi
pf
a
Static scattering centers assumed
Gauge invariance O(1/E2)
×
pf
c
k
Gluon multiple scattering
thickness

dE
dx
  s N c qˆ L  E  qˆL2
Non-Abelian gauge
Transport coefficient
qˆ 
q
2


2
 Debye

x 1 
t form  
 lcoh
v k k
N
scatt
coh
 lcoh /   1
Medium Induced Radiation
c
M 2,1,1
Clearly similar Recursion Method is needed
to go toward a large number of scatterings!
Ivan Vitev, LANL
Jet Quenching
L/ opacity
Large radiative energy loss
in a QGP medium
E/E ~ 0.5
Jet distribution
Non – abelian energy loss
E ( 0 ) 3α μL  2 E 

log  2 
E
4 g
μ L
E  E  weak pT dependence
of quenching
Quenching
Energy Loss and expanding QGP
qL 
2
eff
 2E 

  d   ( , ) ln 
2 

(

)




 ( )  0  / 0 
 out
0
Probe the density
 ( )  gT ( )  g  ( ) / 2
In the transverse plane
Quenching is angle dependent

dN
dN 

1  2  v n cos(n )

dpT d dpT 
n
px2  p y2
v2  cos2 
px2  p y2
1/ 3
How to measure the quenching
Self-Analyzing (High pT) Probes of the Matter at RHIC
Nuclear
Modification
Factor:
d 2 N AA / dpT d
RAA ( pT ) 
Ncoll d 2 N NN / dpT d
nucleon-nucleon
cross section
<Ncoll>
AA
If R = 1 here, nothing new
going on
Centrality Dependence
Au + Au Experiment
d + Au Control
• Dramatically different and opposite centrality evolution of
AuAu experiment from dAu control.
• Jet suppression is clearly a final state effect.
Is the plasma a QCD-QGP?
 Consistent with L2 non-abelian plasma behavior
 Consistent with  ~ 10 GeV (similar to hydro)
Baryon-Meson Puzzle
pions
protons
PHENIX,nucl-ex/0212014
PHENIX, nucl-ex/0304022
0 suppression: evidence of jet
quenching before fragmentation
 Fragmentation p/ ~ 0.10.2
 Jet quenching should affect both
Fragmentation is not the dominant
mechanism of hadronization at
pT ~ 1-5 GeV !?
Coalescence vs. Fragmentation
Parton spectrum
Fragmentation:
 Leading parton pT
ph= z pT
according to a probability Dh(z)
 z < 1, energy needed to create quarks
from vacuum
Coalescence:
BM
 partons are already there
$ to be close in phase space $
 ph= n pT ,, n = 2 , 3
baryons from lower momenta

Even if eventually
Fragm. takes over …
p  p 
C ( pT )   T   T 
 2   2 
p 
F ( pT )   T 
 z 


C  4
 
F   z  pT




Coalescence
dNm
2
3
3
 VF  d p1d p2 f q ( p1 ) f q ( p2 ) Μ( qq  m)
3
d P
Our implementation
M qq  m
2
npQCD
1 dNq
f q ( p) 
VF d 3 p
  
2
  
3
W  
(3)
  p1 , p2 | P, m  g m  d r f m (r , q ) δ ( P  p1  p2 )
9π
f  2x  ( x1  x2 )2  2p  ( p1  p2 )2  (m1  m2 ) 2 
2
 x  1/  p coal. parameter
|Mqq->m|2 depends only on the
g m spin  color probabilit y
phase space weighted by wave
function (npQCD also encoded
 Energy not conserved
in the quark masses , mq=0.3
 No confinement constraint
GeV, ms=0.475 GeV)
W
m
Coalescence Formula
n


d 3 pi
dN H

    pi dσ i
f ( xi , pi )  f H ( x1 ... xn , p1... pn )δ( pT  piT )
2
3 q
d pT
( 2π )
i 1 

fq invariant parton distribution function
thermal (mq=0.3 GeV, ms=0.47 GeV)
with radial flow b0.5)
+
quenched minijets (L/3.5
fH hadron Wigner function
fM 

 
9π
2
2
2
2
2



(
x

x
)



(
p

p
)

(
m

m
)
x
1
2
p
1
2
1
2
2( x  p )3
x = 1/p coalescence radius


 2
( p1  p2 ) In the rest frame
Distribution Function
T=170 MeV
| y |  0.5
soft
ET ~ 700 GeV
b(r) ~ 0.5 r/R
T ~ 170 MeV
hard
L/3.5
P. Levai et al., NPA698(02)631
V ~ 900 fm-3
 ~ 0.8 GeV fm-3)
Hadron from coalescence may
follow jet structure (away suppr.)
REALITY: one spectrum with correlation kept also at pT < 2 GeV
Pion & Proton spectra
Au+Au @200AGeV (central)
ρ  ππ
V. Greco et al., PRL90 (03)202302
PRC68(03) 034904
R. Fries et al., PRL90(03)202303
PRC68(03)44902
R. C. Hwa et al., PRC66(02)025205
 Proton suppression hidden
by coalescence!
Baryon/Meson ratio
Be careful , there are mass effects !
 Resonance decays    
 Shrinking of baryon phase
space
p
Fragmentation not included for 
Elliptic Flow from Coalescence
Enhancement
partonic v2
Coalescenceofscaling
v 2,M (p1T ) 2v
pT2,q (p T /2)
V2  
v 2,B (pnT ) 3vn2,q (p T /3)
Wave function effects
 scaling breaking 10% q/m
5% b/m
wave function effect
Effect of Resonances on Elliptic Flow
Pions from resonances
w.f. + resonance decay
K&p
*
K, , moved
p … v2 not
affected
 coal.
towards
 data
by resonances!
nucl-th/0402020
Back-to-Back Correlation
trigger
Assoc.
quenched
Trigger is a particle at
4 GeV < pTrig < 6 GeV
Associated is a particle at
2 GeV < pT < pTrig
Away Side: quenching
has di-jet structure
Same Side: Indep. Fragm.
equal (?!) to pp
Coalescence with s-h with away side suppressed,
but same side is reduced if no futher correlation …
What was not emphasized
 dN 


d
(

φ
)
φ
 d (φ)  AuAu
I AA (φ) 
 dN 


d
(

φ
)
φ
 d (φ)  pp
IAA ~ 1 peak like in pp
IAA > 1 against the …
• how explain p/ ratio,
v2B/v2M ?
• at lower pT correlation
increase !?
J/Y suppression
cc bound state, MY = 3.1 GeV
   6%
e e 6%
Charm Thermalize in the plasma
J/Y suppression
In a QGP enviroment:
• Color charge is subject to screening of the medium
 qq interaction is weakened
• Linear string term vanish in the confined phase
(T)  0 deconfinement
q
V / TC
q
q,q,g distribution modified
T ~ 4 Tc
T ~ Tc
Coulomb  Yukawa
V 
 eff
r

 eff
r

e
r
D
rTC
 =0 doesn’t mean no bound !
cu , cd  D cs  Ds
c u, c d  D
J/Y
Initial production
Dissociation
In the plasma
c s  Ds
Suppression
respect
Recombine
with to
extrapolation
from pp
light quarks
Associated suppression of charmonium resonances Y’, cc , …
as a “thermometer”, like spectral
lines for stellar interiors
B quark in similar condition at RHIC as Charmonium at SPS
NUCLEAR ABSORBTION
pre-equilibrium cc formation time and
absorption by co-moving hadrons
HADRONIC ABSORBTION
re-scattering after QGP formation
J / Y  h ( ,  ,,...)  D  D
DYNAMICAL SUPPRESSION
(time scale, g+J/Y  cc,…)
pA ( & models)
abs ~ 6 mb
W. Liu
Fireball dynamical evolution
Dynamical dissociation
J/y + g
c+c+X
regeneration
gluon-dissociation,
inefficient for
my≈ 2 mc*
“quasifree” dissoc.
[Grandchamp ’01]
Life-time
• RHIC central: Ncc≈10-20,
• QCD lattice: J/y’s to ~2Tc
If c-quarks
thermalize:
dNy
d
Regeneration in QGP / at Tc
J/y + g
c+c+X
→
←
  y ( Ny  Nyeq )
SPS
RHIC
[Grandchamp
+Rapp ’03]
Charmonia in URHIC’s
RHIC
• dominated by regeneration
• sensitive to:
mc* , open-charm degeneracy
SPS
Does Charm quark thermalize?
 pT Spectra and Yield of D and/or J/Y
 v2 of D meson (single e)
From hard pp collision
D meson spectra
V. Greco , PLB595 (04) 202
S. Batsouli,PLB557 (03) 26
D mesons
D mesons
B mesons
No B mes.
Single electron does not
resolve the two scenarios
Elliptic flow better probe of interaction
Charmed Elliptic Flow
Flow mass effect
V2q from , p, , 
Coalescence can predict
v2D for v2c = 0
&
v2c = v2q
V2 of electrons
S. Kelly,QM04
Quenching
VGCMKRR, PLB595 (04) 202
AMPT, L.W. Chen, C.M. Ko, nucl-th 0409058
Similar to the cross section needed in the light sector !
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 describe well the bulk of the matter
Transport codes needs a quite large npQCD cross section
Charm quark strongly interact with the plasma
Recent lattice QCD find bound states of cc and qq at T>Tc
Rethinking the QGP at Tc < T < 2Tc
“Strong” QGP
Result for V channel (J/y)
A()  2 ()
J/y (p  0) disappears
between 1.62Tc and 1.70Tc
Result for PS channel (c)
A()  2 ()
c (p  0) also disappears
between 1.62Tc and 1.70Tc
Sketch of “Strong” QGP
The elementary excitation are not free gluons and quarks,
but hadronic excitations with strongly modified “in-medium”
properties and with chirally restored phase
Loosely bound states crucial for particle
scattering
 large cross section (Breit-Wigner )
One has also to reproduce lattice EOS
In Conclusion
Matter with energy density too high for simple hadronic
phase ( e > ec from lattice)
Matter is with good approximation thermalized (T >T c )
Jet quenching consistent with the hot and dense medium
described by the hydro approach
Hadrons seem to have typical features of recombination
Strangeness consistent with grand canonical ensemble
J/y ...
Needed : - Thermal spectrum
- Dilepton enhancement
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!
Screening Effect
• Abelian
• Non Abelian
(gauge boson self-interaction)
 eff (T )
1
H

e
2 r 2
r
Bound state
dE ( r )
dr
TBound 
0.84
2 eff
One loop pQCD
r
D ( T )
solution
0


  2
c  c g (T )
V
4
4 r
D 
 210 MeV
9
150 MeV
 Nc N f 
D   

6 
 3
1.2
 eff 
 1.2 rBohr

1
2
 gT 
1
 2 / 3  gT 
1
  0.3T
latt
D
TBound is not Tc !
In HIC at √s ~ SPS J/Y should be supressed !
1