Kaon and pion femtoscopy in the hydrokinetic model of ultrarelativistic heavy-ion collisions
Collective Flow Effects and Energy Loss in ultrarelativistic Heavy Ion Collisions Zhe Xu USTC,...
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Transcript of Collective Flow Effects and Energy Loss in ultrarelativistic Heavy Ion Collisions Zhe Xu USTC,...
Collective Flow Effects and Energy Loss in ultrarelativistic
Heavy Ion Collisions
Zhe Xu
USTC, Hefei, July 11, 2008
with A. El, O. Fochler, C. Greiner and H. Stöcker
Zhe Xu
• Fast Thermalization from
pQCD: 2-3 important
Equilibr. time: 1 fm/c
• Elliptic flow v2: high in 2-3
Viscosity: small ~ 0.08
• Hard probe: RAA ~ 0.1
collisional 2-2 vs. radiational 2-3
energy loss
Motivation and Summary
P.Huovinen et al., PLB 503, 58 (2001)
Zhe Xu
Outline
• Transport model
• Results from simulations
• Analytical calculations
Zhe Xu
),(),(),( pxCpxCpxfv ggggggggg
BAMPS: Boltzmann Approach of MultiParton Scatterings
A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions
new development ggg gg(Z)MPC, VNI/BMS, AMPT, PACIAE
Elastic scatterings are ineffective in thermalization !
Inelastic interactions are needed !
Transport Model
Zhe Xu
Old collision algorithm
BUT, difficult to 3 2 !
/ particles incoming two of distance closest The
collision criterion:
(ZPC, MPC, VNI/BMS, AMPT, PACIAE)
Zhe Xu
Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991)A.Lang et al., J. Comp. Phys. 106, 391(1993)
3x
)''()2(||'2)2(
'
'2)2(
'
!2
1
2)2(2
1
)''()2(||'''2)2(
'
'2)2(
'
!2
1
2)2(2
1 ),(
2121)4(42
'2'112212
32
3
13
13
23
23
1
2121)4(42
12'2'1212
32
3
13
13
23
23
1122
ppppMffE
pd
E
pd
E
pd
E
ppppMffE
pd
E
pd
E
pd
EpxC
collision rate per unit phase space for incomingparticles p1 and p2 with 3p1 and 3p2:
22212
32
3
1133
)2(1
22
22)2(2
1
3
sffE
p
Epxt
Ncoll
j
jj px
Nf
33
)2(1
3
x
tv
NN
Nrel
coll322
21
22
collision probability (Monte Carlo)
Space has to be dividedinto small cells !
Zhe Xu
ZX and C. Greiner, PRC 71, 064901 (2005)
Interaction Probability
23321
3232
32323
32222
)(823for
32for
22for
x
t
EEE
IP
x
tvP
x
tvP
rel
rel
)''()2('2)2(
'
'2)2(
'
2
121321
)4(42
'2'11232
32
3
13
13
32 pppppME
pd
E
pdI
Zhe Xu
)cosh()(
12
)(2
9
,)(2
9
222
22
222
242
222
242
ykmqkk
qg
mq
sgM
mq
sgM
gLPM
DDggggg
Dgggg
J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982)T.S.Biro at el., PRC 48, 1275 (1993)S.M.Wong, NPA 607, 442 (1996)
screened partonic interactions in leading order pQCD
),3(16 1)2(
23
3
qfgppd
sD fnfm
screening mass:
LPM suppression: the formation time g1 cosh
ykg: mean free path
Gluons freeze out at local energy density = 1 GeV/fm3.
Zhe Xu
Results from the parton cascade BAMPS
thermalization
transverse energyelliptic flow
shear viscosityjet quenching
Zhe Xu
3-2 + 2-3: thermalization! Hydrodynamic behavior! 2-2: NO thermalization
simulation pQCD 2-2 + 2-3 + 3-2simulation pQCD, only 2-2
at collision center: xT<1.5 fm, z < 0.4 t fm of a central Au+Au at s1/2=200 GeVInitial conditions: minijets pT>1.4 GeV; coupling s=0.3
pT spectra
Zhe Xu
time scale of thermalization
0
2
2
02
2
2
2
2
2
exp)()(tt
E
pt
E
p
E
pt
E
peq
ZZeq
ZZ
= time scale of kinetic equilibration.
fm/c 1Theoretical Result !
ZX and C. Greiner, PRC 76, 024911 (2007)
Zhe Xu
total transverse energy per rapidity at midrapidity y=0
Zhe Xu
Rapidity dependence of total transverse energy
ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]
Zhe Xu
Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]
viscous hydro.Romatschke, PRL 99, 172301,2007
ln4
1)(
5
1
322323
31
31
2
2
2
2
nns
RRR
En
tr
E
p
E
p
z
z
/s at RHIC > 0.08
Zhe Xu
Rapidity Dependence of v2: Importance of 2-3! BAMPS ZX,G,S
Zhe Xu
first realistic 3d results on jet-quenching with BAMPS
3.0s
dE/dx, static medium (T = 400 MeV)
RAA ~ 0.1
cf. S. Wicks et al.Nucl.Phys.A784, 426
central (b=0 fm) Au-Au at 200 AGeV
O. Fochler
2-32-2
Zhe Xu
Inelastic pQCD interactions (23+32) explain:
• Fast Thermalization
• Large Collective Flow
• Small shear Viscosity of QCD matter at RHIC
• Part of energy loss (for very high energy parton
collisional energy loss due to 2-2 dominates.)
Zhe Xu
Analytical Calculations for a Gluon Gas
Zhe Xu
)cosh()(
12
)(2
9
,)(2
9
222
22
222
242
222
242
ykmqkk
qg
mq
sgM
mq
sgM
gLPM
DDggggg
Dgggg
J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982)T.S.Biro at el., PRC 48, 1275 (1993)S.M.Wong, NPA 607, 442 (1996)
screened partonic interactions in leading order pQCD
),3(16 1)2(
23
3
qfgppd
sD fnfm
screening mass:
LPM suppression: the formation time g1 cosh
ykg: mean free path
Zhe Xu
mb 0.57
mb 0.82
MeV 400T,3.0 for s
ggggg
gggg
Cross section does not determine !
relvnR
11
ggggggggg
Collision Rate
Zhe Xu
gg gg: small-angle scatterings
gg ggg: large-angle bremsstrahlung
distribution of collision angles
at RHIC energies
Zhe Xu
2tr sin section cross transportd
dd
trgggg
trggggg
BUT, this is not the full story !
Zhe Xu
Transport Rates
trggggg
trggggg
trgggg
trdrift RRRR
1
ZX and C. Greiner, PRC 76, 024911 (2007)
ggggggggggggggi
Ep
n
fCpd
Ep
fCEppd
Rz
iz
iz
tri
,,
,
)31
(
][)2(
][)2(
with
2
2
3
3
2
2
2
2
3
3
• Transport rate is the correct quantity describing kinetic equilibration.
• Transport collision rates have an indirect relationship to the collision-angle distribution.
0 ,2
12
E
pedf zE
Gassume
Zhe Xu
trggggg
trggggg
trgggg
trggggg
RR
R
R
3
2
53
Transport Rates
2222 )(ln~: sstrRgggg
01.0for)(ln~: 2223 ssstrRggggg
01.0for)(ln~ 2323 ssstrR
Large Effect of gg->ggg !
Zhe Xu
)3(2
2
uu
TTT
zz
zzyyxx
From Navier-Stokes approximation
Cfv From Boltzmann-Eq.
Cpd
vuun
Cvpd
fvvpd
zzz
zz
3
32
23
32
3
3
)2()41()3(
15
2
)2()2(
322323
31
31
1)(
5
1
2
2
2
2
RRR
En
tr
E
p
E
p
z
z
relation between and Rtr
Shear Viscosity
Zhe Xu
)(7
1)( gggg
sggggg
s
Ratio of shear viscosity to entropy density in 2-3
AdS/CFTRHIC
ZX and C.Greiner, PRL 100, 172301, 2008; arXiv: 0710.5719 [nucl-th].
0.13/s
3.0 for s
Zhe Xu
Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]
viscous hydro.Romatschke, PRL 99, 172301,2007
ln4
1)(
5
1
322323
31
31
2
2
2
2
nns
RRR
En
tr
E
p
E
p
z
z
/s at RHIC > 0.08
Zhe Xu
Inelastic pQCD interactions (23 + 32) explain:
• Fast Thermalization
• Large Collective Flow
• Small shear Viscosity of QCD matter at RHIC
• Part of energy loss (for very high energy parton
collisional energy loss due to 2-2 dominates.)
Initial conditions, hadronization and afterburning
determine
how imperfect the QGP at RHIC & LHC can be.
Conclusion
Zhe Xu
Initial conditions in heavy ion collisions
dcba
cdab
TbTaT
jet
td
dpxfxpxfxK
dydydp
d
,;,
222
211
212 ˆ
),(),(
ppjetAA
AAjet bTN )0(2
Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision
700/ dydNgfor a central Au+Au collision at RHICat 200 AGeV using p0=1.4 GeV
minijets production with pt > p0
Zhe Xu
Zhe Xu
5.
22
.32
.23 tr
trtr
R
RR
The drift term is large.
.
.32
.23
.22
trdrift
tr
tr
tr
R
R
R
R
ggggg interactions are essential for kinetic equilibration!
Zhe Xu
A,El, ZX and C.Greiner, arXiv: 0712.3734 [hep-ph], published in NPA
ggg gg !This 3-2 is missing in the Bottom-Up scenario(Baier et al.).
Initial conditions: Color Glass Condensate Qs=3 GeV; coupling s=0.3
pT spectra
Zhe Xu
trireli
tri vnAR
due to the fact that a 2->3 process brings one more particletoward isotropy than a gg->gg process.
ggggggggg AA