Download Space-time evolution of QCD matter

Johann Wolfgang Goethe-Universität Frankfurt
Institut für Theoretische Physik
Space time evolution of QCD matter
I. Bouras, A. El, O. Fochler, F. Reining, Z. Xu, CG
Focus week, HIC at the LHC, CERN , may 2007
• Parton cascade with stochastic algorithm
• Transport rates and momentum isotropization
• Thermalization of gluons due to
• Results: bottom-up scenario, jet-quenching,
elliptic flow, viscosity,… viscous hydro, …
Relativistic Quantum Transport for URHIC
RHIC, LHC
• microscopic transport calculations of partonic degrees of freedom
p    f ( x, p)  Cgg gg ( x, p)  Cgg ggg ( x, p)
new development
Boltzmann Approach of MultiParton Scatterings (BAMPS)
2
 9g 4

s2
12 g 2 q2



M gg  ggg  
 2
2
2 2  2
2
 2 ( q   mD )   k  ( k   q  )  mD

Dt
D3 x
Dt
for 2  3 P23  vrel 23 3
Dx
I 32
Dt
for 3  2 P32 
8 E1 E2 E3 (D3 x) 2


  LPM


Z. Xu and C. Greiner,
PRC 71, 064901 (2005)
for 2  2 P22  vrel 22
D3x
particle in cell method
collision probability
parton scatterings in leading order pQCD
M gg  gg
M gg  ggg
s2
9g 4
,

2 2
2
2 ( q  mD )
2
2

 9g 4
12 g 2 q2
s2

  2
 
2 2  2
2
2
)
m

q
(
2
m

)
q

k
(
k
D

  

D




  LPM


J.F.Gunion, G.F.Bertsch, Phys. Rev. D 25, 746(1982)
 s  (332n
screening mass:
12
f ) ln(s /  QCD )
m  16s  ( 2 )3 1p (3 f g  n f f q ),
2
D
d3p
LPM suppression: the formation time D 
1
k
cosh y   g
(k  g  cosh y )
Example
 s ~ 0.3  g ~ 0.5 fm T ~ 400MeV
fugacity ~ 0.5
Important scales for kinetic transport & simulations
Simulations solve Boltzmann equation:
→ test particles and other schemes
Semiclassical kinetic theory:
(Quantum mechanics:
)
Initial production of partons
minijets
d jet
abcd
d

2
2

K
x
f
(
x
,
p
)
x
f
(
x
,
p

1 a 1
t
2 b 2
t )
2
dt
a ,b;c ,d
dpt dy1dy2
CGC
string matter
fast isotropization and thermalisation
elliptic flow in noncentral
Au+Au collisions at RHIC:
Z. Xu and C. Greiner,
hep-ph/0703233

Z. Xu and C. Greiner,
NPA 774, 787 (2006)
 pZ2

 t  t0 
pZ2
pZ2
pZ2


 


(
t
)






(
t
)



exp
eq
0
eq
2
2
2
2
 E

E
E
E

(
t
)




central
hydrodynamical evolution of momentum spectrum,
… micr. determination of transport parameter …
3+1dim. full cascade: comparison with RHIC data
tr .
R22
tr .
R23
Z. Xu and C. Greiner,
arXiv:hep-ph/0703233
tr .
R32
tr .
 Rdrift
The drift term is large.
tr .
tr .
R23
 R32
5
tr .
R22
1
 n
5
3
2
1
d
p
E
(

v
z)f
3

3
2
1
d
p
(

v
z)f
3

1
tr
R
ggggg interactions are essential for kinetic equilibration!
transverse energy at y=0 in Au+Au central collision
Initial condition with Color Glass Condensate
: [-0.05:0.05] and xt < 1.5 fm
bottom-up scenario of thermalization
R.Baier, A.H.Mueller, D.Schiff and D.T.Son, PLB502(2001)51
• Qs-1 << t << -3/2 Qs-1 Hard gluons with momenta about Qs are freed
and phase space occupation becomes of order 1.
• -3/2 Qs-1 << t << -5/2 Qs-1 (h+h  h+h+s)
Hard gluons still outnumber soft ones, but soft gluons give most of the
Debye screening.
• -5/2 Qs-1 << t << -13/5 Qs-1 (h+h  h+h+s; s+s  s+s; h+s  sh+sh+s)
Soft gluons strongly outnumber hard gluons.
Hard gluons loose their entire energy to the thermal bath.
• After -13/5 Qs-1 the system is thermalized: T ~ t-1/3, T0 ~ 2/5 Qs
Not the full Bottom-Up story...
evolution of particle number in bottom-up scenario in 1+1 dim. geometry
LHC …
RHIC
→ Particle number decreases in the very first moment
→ No net soft gluon production at early times!
Evolution of temperature and spectrum …
Andrej El
extracting the viscosity
preliminary
Bjorken geometry:
Jet-Quenching in a central Au Au collision at RHIC
Oliver Fochler
preliminary
new:
RAA higher?
old:
RAA ~ 0.04–0.05
quarks not yet
included …
Summary
• A new parton cascade including inelastic multiparton scatterings gg↔ggg
• Explains thermalization and hydrodynamical expansion at RHIC
• PQCD inspired gg↔ggg are important for the thermalization.
• PQCD gg↔ggg generate the elliptic flow in noncentral collisions.
• Not full bottom-up thermalization scenario with CGC
• 3~4 too much jet-quenching
Outlook
• viscosity
• including quarks, heavy quark production
• Test for initial conditions (boundaries)
possible Chromo/Weibel instabilities
B.Schenke, A. Dumitru,
Y. Nara, M. Strickland
Initial conditions: minijets production with pt > p0
abcd
d jet
d

2
2

K
x
f
(
x
,
p
)
x
f
(
x
,
p
)

1
a
1
T
2
b
2
T
2
dpT dy1dy2
dtˆ
a ,b ;c ,d
binary approximation 
N g  830
AA
pp
N jet
 2 TAA (b  0)  jet
for a central Au+Au collision at RHIC
at 200 AGeV using p0=2 GeV
Results
rapidity distribution
the central region:
: [-0.5:0.5] and xt < 1.5 fm
including ggggg
thermalization and
hydrodynamical behavior
without ggggg
NO thermalization and
free streaming
Why fast thermalization?
… transport rates !
gg  gg
transport cross section:
 t   d sin 2 cm
gg  ggg
gg  ggg
2
gg  gg
BUT! This is not the whole story...
Q  PZ2 / E 2 ,

Q

d3p
( 2 ) 3
d3p
( 2 ) 3
1 d3p

Q (t )   ( 2 )3
n
 pZ2

pZ2
pZ2
pZ2
 t  t0 
 2  (t )   2 eq    2  (t0 )   2 eq  exp  

E
E
E
E





f
t
f ( p , x, t ) Q
f ( p , x, t )
1
d3p
Q  Q (t )  ( 2 )3
n
f
t

 f
P
  f  I 22  I 23  I 32
t
E
 Q (t )  Cdrift  C22  C23  C32
(t) gives the timescale of kinetic equilibration.
1
Q (t )
tr .
tr.
tr .
tr .
 Rdrift
 R22
 R23
 R32
,


Qeq  Q (t )
f ( x, p)   ( pZ  E)   ( pZ  E)
special case
3
tr .
R  n  vrel  22 ,
2
tr .
22
33
tr .
R 
n  vrel  23 
22
tr .
23
 t   d sin 2 cm
for isotropic distribution of collision angle
R  R22 ,
tr .
22
3
R  R23 ,
2
tr .
23
2
R  R32
3
tr .
32
momentum isotropization and kinetic equilibration
Initial condition: Minijets p0=1.4 GeV
Important scales for kinetic transport & simulations
Simulations solve Boltzmann equation:
→ test particles and other schemes
Semiclassical kinetic theory:
(Quantum mechanics:
)
E
mfp  d
... kinetic transport still valid
Thermalization times: comparison with bottom-up prediction
• 1/Qs behavior seems to be correct.
• instead -13/5 behavior but -x with x < 13/5
Jet-Quenching
Box calculation: T=400MeV
dominant
process is 2->3
Oliver Fochler
Bremsstrahlung processes
M gg  ggg
2
 9g 4

s2
12 g 2 q2

  2
 
2
2 2  2
2
2
(
q

m
)
k
(
k

q
)

m

D

  

D

LPM suppression: the formation time D 
 LPM (k   g  cosh y )
varying the cut-off for kT:
1
k


  LPM


cosh y   g
Bethe-Heitler regime
 LPM (k   g  A cosh y )