qcd plasma equilibration and collective flow effects
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QCD Plasma Equilibration and Collective Flow Effects
Zhe Xu
with C. Greiner and H. Stöcker
Quark Matter 2008, Jaipur, India, Feb. 6
Zhe Xu, Jaipur, Quark Matter 2008
Y
X• Fast Thermalization from
QCD: 3-2 important!
• Equilibr. time short in 2-3!
• Elliptic flow v2 high in 2-3!
• Viscosity small ~ 0.08!
Three body effects in parton cascades!
P.Huovinen et al., PLB 503, 58 (2001)
from R. Bellwied
Zhe Xu, Jaipur, Quark Matter 2008
Thermalization driven by plasma instabilitiesRefs.:
Mrowczynski;
Arnold, Lenaghan, Moore, Yaffe;
Rebhan, Romatschke, Strickland,
Bödeker, Rummukainen;
Dumitru, Nara;
Berges, Scheffler, Sexty
Dumitru, Nara, Strickland, PRD 75, 025016 (2007)
Dumitru, Nara, Schenke, Strickland, arXiv:0710.1223
talk by B. Schenkeparallel session VIII
Zhe Xu, Jaipur, Quark Matter 2008
QCD thermalization usingparton cascade
VNI/BMS: K.Geiger and B.Müller, NPB 369, 600 (1992)
S.A.Bass, B.Müller and D.K.Srivastava, PLB 551, 277(2003)
ZPC: B. Zhang, Comput. Phys.Commun. 109, 193 (1998)
MPC: D.Molnar and M.Gyulassy, PRC 62, 054907 (2000)
AMPT: B. Zhang, C.M. Ko, B.A. Li, and Z.W. Lin, PRC 61, 067901 (2000)
BAMPS: Z. Xu and C. Greiner, PRC 71, 064901 (2005); 76, 024911 (2007)
Zhe Xu, Jaipur, Quark Matter 2008
),(),(),( 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
Elastic scatterings are ineffective in thermalization !
Inelastic interactions are needed !
Xiong, Shuryak, PRC 49, 2203 (1994)Dumitru, Gyulassy, PLB 494, 215 (2000)Serreau, Schiff, JHEP 0111, 039 (2001)Baier, Mueller, Schiff, Son, PLB 502, 51 (2001)
Zhe Xu, Jaipur, Quark Matter 2008
)cosh()(
12)(2
9
,)(2
9
222
22
222
242
222
242
ykmqkk
qgmqsgM
mqsgM
gLPMDD
ggggg
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, Jaipur, Quark Matter 2008
gg gg: small-angle scatterings
gg ggg: large-angle bremsstrahlung
distribution of collision angles
at RHIC energies
Zhe Xu, Jaipur, Quark Matter 2008
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, Jaipur, Quark Matter 2008
A,El, ZX and C.Greiner, arXiv: 0712.3734 [hep-ph]
talk by A. Elparallel session VI
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, Jaipur, Quark Matter 2008
time scale of thermalization
0
2
2
02
2
2
2
2
2
exp)()( ttEpt
Ep
Ept
Ep
eqZZ
eqZZ
= time scale of kinetic equilibration.
fm/c 1Theoretical Result !
Zhe Xu, Jaipur, Quark Matter 2008
mb 0.57
mb 0.82
MeV 400T,3.0 for s
ggggg
gggg
Cross section does not determine !
relvnR11~
ZX and C.Greiner, arXiv: 0710.5719 [nucl-th]
ggggggggg
What determinesthe equilibration time scale ?
Zhe Xu, Jaipur, Quark Matter 2008
2tr sin section cross transportddd
trgggg
trggggg BUT, this is not the full story !
Zhe Xu, Jaipur, Quark Matter 2008
Transport Rates
trggggg
trggggg
trgggg
trdrift RRRR
1
ZX and C. Greiner, PRC 76, 024911 (2007)
ggggggggggggggi
vn
CpdvCvpd
Rz
iziztri
,,
,)
31(
)2()2( with2
3
322
3
3
• Transport rate is the correct quantity describing kinetic equilibration.• Transport collision rates have an indirect relationship to the collision-angle distribution.
Zhe Xu, Jaipur, Quark Matter 2008
trggggg
trggggg
trgggg
trggggg
RR
RR
32
53
Transport Rates
2222 )(ln~: sstrRgggg
01.0for)(ln~: 2223 ssstrRggggg
01.0for)(ln~ 2323 ssstrR
Large Effect of 2-3 !
Zhe Xu, Jaipur, Quark Matter 2008
Shear Viscosity
D.Teaney, PRC 68, 034913 (2003)
P.Arnold, G.D.Moore, L.G.Yaffe, JHEP 0011, 001 (2001); 0305, 051 (2003)
T.Hirano, M.Gyulassy, NPA 769, 71 (2006)
M.Asakawa, S.A.Bass, B.Müller, Prog.Theor.Phys. 116, 725 (2007)
A.Muronga, PRC 76, 014910 (2007)
ZX, C.Greiner, arXiv: 0710.5719 [nucl-th]
Zhe Xu, Jaipur, Quark Matter 2008
)3(22uuTTT
zz
zzyyxx
From Navier-Stokes approximation
Cfv From Boltzmann-Eq.
Cpdvuun
Cvpdfvvpd
zzz
zz
3
32
23
32
3
3
)2()41()3(
152
)2()2(
322323
31
31
1)(
51
2
2
2
2
RRR
En tr
Ep
Ep
z
z
relation between and Rtr
Zhe Xu, Jaipur, Quark Matter 2008
)(71)( ggggs
gggggs
Ratio of shear viscosity to entropy density in 2-3
AdS/CFTRHIC
Zhe Xu, Jaipur, Quark Matter 2008
transverse flow velocity of local cell in thetransverse plane of central rapidity bin
Au+Au b=8.6 fmusing BAMPS =c
22yx vv
Collective Effects
Zhe Xu, Jaipur, Quark Matter 2008
Zhe Xu, Jaipur, Quark Matter 2008
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
322323
31
31
1)(
51
2
2
2
2
RRR
En tr
Ep
Ep
z
z
/s at RHIC > 0.08
Zhe Xu, Jaipur, Quark Matter 2008
Rapidity Dependence of v2: Importance of 2-3! BAMPS ZX,G,S
see also:
L.W.Chen, et al., PLB 605, 95 (2005)
C.Nonaka, et al., JPG 31, 429 (2005)
T.Hirano, et al., PLB 636, 299 (2006)
J.Bleibel, et al., PRC 76, 024912 (2007); PLB 659, 520 (2008)
Hama, et al., arXiv: 0711.4544 [hep-ph]
A.K.Chaudhuri, arXiv: 0801.3180
Session XVI, Collectivity-theoryHirano, Molnar, Bhalerao, Song,Muronga, Csorgo
Zhe Xu, Jaipur, Quark Matter 2008
Inelastic pQCD interactions (23 + 32) explain:
• Fast Thermalization• Large Collective Flow• Small shear Viscosity of QCD matter at RHIC
Initial conditions, hadronization and afterburning determine
how imperfect the QGP at RHIC & LHC can be.
further investigations in progress:H. Petersen, G. Burau, J. Steinheimer, M. Bleicher (University of Frankfurt)see Poster P68
Summary
Zhe Xu, Jaipur, Quark Matter 2008
Zhe Xu, Jaipur, Quark Matter 2008
Zhe Xu, Jaipur, Quark Matter 2008
total transverse energy per rapidity at midrapidity
Zhe Xu, Jaipur, Quark Matter 2008
Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991)A.Lang et al., J. Comp. Phys. 106, 391(1993)
for particles in 3x with momentum p1,p2,p3 ...
interaction probability:
23321
3232
32323
32222
)(823
32
22
xt
EEEIPfor
xtvPfor
xtvPfor
rel
rel
)()2(2)2(2)2(2
1'2'1321
)4(42'2'1123
'23
'23
'13
'13
32 pppppME
pdE
pdI
cell configuration in space
3x
)())((),( )3()3(i
ii pptxxpxf
Zhe Xu, Jaipur, Quark Matter 2008
Initial conditions
dcba
cdab
TbTa
T
jet
tddpxfxpxfxK
dydydpd
,;,
2
22
2
11
21
2 ˆ),(),(
ppjetAA
AAjet bTN )0(2
Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision
700/ dydN gfor a central Au+Au collision at RHICat 200 AGeV using p0=1.4 GeV
minijets production with pt > p0
Zhe Xu, Jaipur, Quark Matter 2008
5.22
.32
.23 tr
trtr
RRR
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, Jaipur, Quark Matter 2008
trireli
tri vnAR
due to the fact that a 2->3 process brings one more particletoward isotropy than a gg->gg process.
ggggggggg AA
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