shear viscosity and collective flow in heavy ion collisions within parton cascade calculations
DESCRIPTION
Shear Viscosity and Collective Flow in Heavy Ion Collisions within Parton Cascade Calculations. Zhe Xu, Carsten Greiner. Institut für Theoretische Physik Goethe-Universität Frankfurt, Germany. Trento, Sept. 17, 2009. Y. X. Motivation: how small is the QGP viscosity at RHIC?. - PowerPoint PPT PresentationTRANSCRIPT
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)
Zhe Xu, Trento 2009 22/23
Including `quarks´
15% effect instead of 26% due to imcomplete chemical equilibration
Zhe Xu, Trento 2009 23/23
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.