Shear Viscosity and Collective Flow in Heavy Ion Collisions within Parton Cascade Calculations
Zhe Xu, Carsten Greiner
Trento, Sept. 17, 2009
Institut für Theoretische PhysikGoethe-Universität Frankfurt, Germany
Zhe Xu, Trento 2009 2/23
Y
X
Motivation: how small is the QGP viscosity at RHIC?
P.Huovinen et al., PLB 503, 58 (2001)
Viscous HydrodynamicsMurongaLuzum / RomatschkeSong / HeinzTeaney / DuslingMolnar / Niemi / Rischke
Kinetic Transport Model(Z)MPC: Zhang / Molnar / GyulassyAMPT: Lin / Chen / Ma / Ko UrQMD: Petersen, Bleicher et al.BAMPS: Xu, Greiner et al.
Zhe Xu, Trento 2009 3/23
Outline
• Parton Cascade BAMPS
• Elliptic Flow at RHIC
• Extracting /s
• v2(pT)
• Summary
Zhe Xu, Trento 2009 4/23
),(),(),( pxCpxCpxfp 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, Trento 2009 5/23
Stochastic algorithm
3xcollision probability -- stochastic
Space is dividedinto small cells !
ZX and C. Greiner, PRC 71, 064901 (2005)
23232
32132
323
23
322
22
)(8
123for
32for
22for
x
t
N
I
EEEP
x
t
NvP
x
t
NvP
test
testrel
testrel
)''()2('2)2(
'
'2)2(
'
2
121321
)4(42
'2'11232
32
3
13
13
32 pppppME
pd
E
pdI
x
y
Zhe Xu, Trento 2009 6/23
)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)
screened pQCD based partonic interactions
treatment for incoherent interactions:
the formation time g1 cosh
yk g: mean free path
LPM suppression:
),(1)2(
23
3
pxfNdm gppd
scGD
Zhe Xu, Trento 2009 7/23
Results: Transverse Energy in Au+Au at RHIC
Initial conditions: gluon minijets production in independent binary NN collisions
3GeV/fm 6.0 ,0.1 6.0 ,3.0 cs e
Zhe Xu, Trento 2009 8/23
Elliptic Flow at RHICusing BAMPS
ZX, Greiner, Stöcker, PRL 101, 2008
gg<->ggg processes generatelarge elliptic flow !
3GeV/fm 0.1ce
Zhe Xu, Trento 2009 9/23
Zhe Xu, Trento 2009 10/23
)3(2
2
uu
TTT
zz
zzyyxx
Navier-Stokes approximation
][fCfp Boltzmann-Eq.
Shear Viscosity PguuPeT )(
)( 32
uuu
]ln3ln[ln
])([ 31
21
i
teeq
iji
jj
iji
eqeq
PTEeEffp
uuuppffpfp
AMY, JHEP 11 (2000) ),()1( ,][ 1 pxffffffCfp eqeqeqeq
solve f1(x,p) using the variational method, which determinesthe coefficients of the functions of p in f1(x,p)
Zhe Xu, Trento 2009 11/23
][][
1)(
5
13
31
31
2
2
2
2
fCdwfR
En
ntr
E
p
E
p
NSz
z
][)41()3(15
2
][
2
2
2
2
2
2
fCdwE
puun
fCE
pdwfp
E
pdw
zzz
zeq
z
ZX and C.Greiner, PRL 100, 172301, (2008)
2
2
2
2
2
2
2
sin~
)31
(
][][
d
ddnn
Ep
n
fCdwEp
fCEp
dw
R tr
z
zz
tr
E
pddw
3
3
)2(
transport rate
ZX and C. Greiner, PRC 76, 024911 (2007)
Zhe Xu, Trento 2009 12/23
5.
22
.32
.23 tr
trtr
R
RR
.
.32
.23
.22
trdrift
tr
tr
tr
R
R
R
R
Transport Rates
Zhe Xu, Trento 2009 13/23
gg gg: small-angle scatterings
gg ggg: large-angle bremsstrahlung
distribution of collision angles
at RHIC energies
central plateau
Zhe Xu, Trento 2009 14/23
Elliptic Flow and Shear Viscosity at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 2008
viscous hydro.Romatschke, PRL 99, 2007
/s > 0.08
/s at the collision center
Zhe Xu, Trento 2009 15/23
A. El, A. Muronga, ZX and C. Greiner, PRC 79, 044914 (2009)
ppxpxf )(),(1 6
00 ~ , CC
Shear Viscosity
),(1 pxffff eqeq
PTC
TJs
fCppdwPPCs
ffpdws
Grad0
1
2
)2(ln withcomparing
][ withln
)1(ln
Grad´s method
Zhe Xu, Trento 2009 16/23
Zhe Xu, Trento 2009 17/23
comparison
][)31
(4][31
][5
1
][33
1][
3
9
4
2
22
22
fCdwEp
fCdwfCEp
dw
n
fCTE
dwfCTp
dw
n
zz
zzNS
z
zzGrad
= 0in chemical equilibration
For minijets initial conditions:
0][
3
12
2
fCdw
E
pz No kinetic equilibrium
No chemical equilibrium
Zhe Xu, Trento 2009 18/23
Uncertainty: dependence of v2 on freeze-out condition3GeV/fm 6.0 ,0.1 6.0 ,3.0 cs e
3
3
GeV/fm 0.1 and 6.0
GeV/fm 6.0 and 3.0
cs
cs
e
e
generate the same elliptic flow.
Therefore, /sbetween 0.08 and 0.16.
Zhe Xu, Trento 2009 19/23
V2(pT)
lower than data
ZX and C. Greiner, PRC 79, 014904 (2009)
Zhe Xu, Trento 2009 20/23
)(22 TT
T pvdp
dNdpv
4/34/13d
4 ~~n ,~ eNTNTNe dccd
e does not depend on Nd.If changing Nd from 16 to 40 (gluons+quarks with 2 flavors),<pT> ~ e/n decreases by a factor of 1.26.
)()(
)()(
pionNgluonN
pionEgluonE TT
Zhe Xu, Trento 2009 21/23
Including `quarks´ in BAMPS
3GeV/fm 0.1
6.0
c
s
e
Assume: Quark dynamics is as same as the gluon one.Changing the degrees of freedom of gluons 16to 40 (gluons+quarks with 2 flavors)
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Including `quarks´
15% effect instead of 26% due to imcomplete chemical equilibration
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Summary
Inelastic pQCD based interactions (23 + 32) explain:
• Large Collective Flow
• Small shear Viscosity of QCD matter at RHIC
/s: 0.08 ~ 0.2
Uncertainties of /s: freezeout conditions, initial conditions,
quark dynamics, hadronization, hadron cascade
v2(pt) and v2 do not match data simultanously:
need better understanding of quark dynamics and hadronization
Zhe Xu, Trento 2009 24/23
Variational method: AMY, JHEP 11 (2000)
1000
0
)1(
)],,([),( BE linearized
)],([),( BE
fffff
pxfCpxfp
pxfCpxfp
f1 to be solved.
|)(|)3
1ˆˆ(2
3)(
)3
2(
6
1)(
with
)()(21
pppp
uuuxX
pxXf
ijji
ijijji
Zhe Xu, Trento 2009 25/23
p
ijji
ijji
phpghg
ppffpTpS
pppp
)()(),(
)3
1ˆˆ(2
3)1(||)(
|)(|)3
1ˆˆ(2
3)(
3
00
The maximun value of S) –(,C)/2 occurs when satisfied the linearized BE.
||)()1(
1)(
1
)(
|||)(| |,||)(|
or ,|)|1(
|)|(|)(|
sets with
|)(||)(|
pcm
N
mm
N
m
mm
mepppp
p
pp
pap
Zhe Xu, Trento 2009 26/23
Transport Rates
trggggg
trggggg
trgggg
trdrift
z
z
eq
RRRRtEp
Epdtd
)(/3/1
/122
22
ZX and C. Greiner, PRC 76, 024911 (2007)
ggggggggggggggi
Ep
n
fCdwEp
fCEp
dw
Rz
iz
iz
tri
,,
,
)31
(
][][
with
2
2
2
2
2
2
• Transport rate is the correct quantity describing kinetic equilibration.
• Transport collision rates have an indirect relationship to the collision-angle distribution.
Zhe Xu, Trento 2009 27/23
Zhe Xu, Trento 2009 28/23
De Broglie length over mean free path
Changing the mean free path by the inverse of the transport rate will lower the ratios.
