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Microscopic Understanding of ultrarel. HIC – How dissipative is the RHIC matter ?
C. Greiner,
30th Course of Intl. School of Nuclear Physics , Erice-Sicily, september 2008
Johann Wolfgang Goethe-Universität Frankfurt
Institut für Theoretische Physik
in collaboration with: I.Bouras, L. Chen, A. El, O. Fochler, J. Uphoff, Zhe Xu
- fast thermalization within a pQCD cascade- viscosity and its extraction from elliptic flow- jet quenching … same phenomena?- new: dissipative shocks
list of contents
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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)
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),(),(),( 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,radiative „corrections“
(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)
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)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(
223
3
qfgppd
sDD fnftxmm
screening mass:
LPM suppression: the formation time g1 cosh
ykg: mean free path
radiative part
elastic part
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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 ...
collision probability:
23321
3232
32323
32222
)(823
32
22
x
t
EEE
IPfor
x
tvPfor
x
tvPfor
rel
rel
)()2(2)2(2)2(2
1'2'1321
)4(42
'2'1123'2
3'2
3
'13
'13
32 pppppME
pdE
pdI
cell configuration in space
3x
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Initial production of partons
dt
dpxfxpxfxK
dydydp
d cdab
tbtadcbat
jet
),(),( 2
222
11,;,21
2
minijets
string matter
color glass condensate
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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
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gg gg: small-angle scatterings
gg ggg: large-angle bremsstrahlung
distribution of collision angles
at RHIC energies
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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 !
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Transport Rates
trggggg
trggggg
trgggg
trdrift RRRR
1
Z. Xu and CG, PRC 76, 024911 (2007)
ggggggggggggggi
vn
Cpd
vCvpd
R
z
iziztri
,,
,)
31
(
)2()2( with
2
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.
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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 2-3 !
ggggggggg
mb 0.57
mb 0.82
MeV 400T,3.0 for s
ggggg
gggg
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Shear Viscosity
)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 Z. Xu and CG,
Phys.Rev.Lett.100:172301,2008.
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)(7
1)( gggg
sggggg
s
Ratio of shear viscosity to entropy density in 2<->3
AdS/CFTRHIC
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Dissipative HydrodynamicsShear, bulk viscosity and heat conductivity of dense QCD matter could be prime
candidates for the next Particle Data Group, if they can be extracted from data.
Need a causal hydrodynamical theory.What are the criteria of applicability?
Causal stable hydrodynamics can be derrived from the Boltzmann Equation:
-Renormalization Group Method by Kunihiro/Tsumura-->stable 1st Order linearized BE with f=f
0+εf
1+ε²f
2 yields (2nd Order – work in progress)
can be solved by introducing projector P on Ker{A}, where A-linearized collision operator
-Grad‘s 14-momentum method-->2nd Order causal hydrodynamics.
Calculate momenta of the BE. Transport coefficients and relaxation times for dissipative quantities can be calculated as functions of collision terms in BE.
Compare dissipative relaxation times to the mean free pass from cascade simulation.
Andrej E
l
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Semiclassical kinetic theory:
Validity of kinetic transport - relation to shear viscosity
Quantum mechanis: quasiparticle limit:
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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
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Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS Z. Xu, CG, H. Stöcker, PRL 101:082302,2008
viscous hydro.Romatschke, PRL 99, 172301,2007
322323
31
31
1)(
5
1
2
2
2
2
RRR
En
tr
E
p
E
p
z
z
/s at RHIC > 0.08
Z. Xu
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Rapidity Dependence of v2: Importance of 2-3! BAMPS
evolution of transverse energy
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more details on elliptic flow at RHIC …
moderate dependence on critical energy density
/s at RHIC: 0.08-0.2
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… looking on transverse momentum distributions
gluons are not simply pions …
need hadronization (and models) to understand the particle spectra
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RAA ~ 0.06
cf. S. Wicks et al.Nucl.Phys.A784, 426
nuclear modification factorcentral (b=0 fm) Au-Au at 200 AGeV
O. Fochler et al
Quenching of jetsfirst realistic 3d results with BAMPS
arXiv:0806.1169
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LPM-effect transport model: incoherent treatment of ggggg processes parent gluon must not scatter during formation time of emitted gluon
discard all possible interference effects (Bethe-Heitler regime)
kt
CM frame
p1 p2
lab frame
kt
= 1 / kt
total boost
O. Fochler
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inclusion of light quarks is
mandatory !
… lower color factor
comparison to other
approaches
… LPM bremsstrahlung
jet fragmentation scheme
… possible improvements of microscopic treatment
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Barbara Betz, Dirk Rischke, Horst Stöcker, Giorgio Torrieri
Mach Cones in Ideal Hydrodynamics
Box Simulation
Bjorken Expansion
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Parton cascade meets ideal shocks: Riemann problem
λ = 0.1 fm
λ = 0.01 fm
λ = 0.001 fm
Tleft = 400 MeVTright = 200 MeVt = 1.0 fm/c
I. Bouras
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Time evolution of viscous shocksTleft = 400 MeVTright = 320 MeV
η/s = 1/(4 π)
t=0.5 fm/c t=1.5 fm/c
t=3 fm/c t=5 fm/c
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Viscous shocks
η/s ~ 0.01 - 1.0
Tleft = 400 MeV - Tright = 320 MeV ,t = 3.0 fm/c
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Comparison to Israel-Stewart
Comparison to full pQCD transport
η/s = 0.02 η/s = 0.1
η/s ~ 0.1 - 0.13
Tleft = 400 MeVTright = 320 MeV
t = 3 fm/c
t = 1.6 fm/c
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Inelastic/radiative pQCD interactions (23 + 32) explain:
fast thermalization
large collective flow
small shear viscosity of QCD matter at RHIC
realistic jet-quenching of gluons
Summary
Future/ongoing analysis and developments:
light and heavy quarks
jet-quenching (Mach Cones, ridge)
hadronisation and afterburning (UrQMD) needed to determine
how imperfect the QGP at RHIC and LHC can be
… and dependence on initial conditions
dissipative hydrodynamics
Thanks to the organizers for the invitation !