Recent progresses in viscous hydrodynamics and the shear viscosity of QGP
Victor RoyNational Institute of Science Education and Research
Bhubaneswar
•Motivation
•Relativistic hydrodynamics
•Results from viscous hydrodynamics
•Conclusion & Outlook
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Evaluate transport coefficient of QGP
From first principle lattice QCD From phenomenological study
Uncertain Viscous hydrodynamics &
Transport model
topic of this talk
Motivation of this talk
2Nakamura et al. PRL 94,072305
0.0
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≈0.2 −1.0 fm /c
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≈15 fm /c
Hydrodynamic regime
Evolution of Heavy ion collision
Assumption: Near local thermal equilibrium
3
Relativistic hydrodynamics
EoS, Initial condition
D 1
2
u
u u Du
)(2
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T
uTuD
• Relaxation equation for shear and bulk stress
Roy et al. PRC 85,024909
4
Parameters RHIC LHC
Thermalization time :
0.6 fm/c
same
Initial central energy density:
~30 GeV/fm3 ~100 GeV/fm3
Initial transverse velocity :
0
same
Freeze-out temperature
130 MeV
same
Relaxation time 2η/3p
same
Initial shear stress same
Initial bulk stress same
uyx ),(
3
2 yyxx
0xy
Input Parameters to viscous hydrodynamics
EoS: Lattice+Hadron Resonance Gas
Tc=175 MeV
Borsanyi et al JHEP 11(2010)077
and are input in viscous hydrodynamics 5
Initial energy density & freeze-out
€
ε b,x,y( ) = ε 0 1 − x( )N part (b,x,y)
2+ xNcoll (b,x,y)
⎡
⎣ ⎢
⎤
⎦ ⎥
Optical Glauber model
Pb-Pb for 0-5% centrality at 2.76 TeV
V Roy et al
Phys. Lett. B. 703, 313-317 (2011).
Glauber Model:
Color Glass Condensate Model:
€
ε b,x,y( ) =C ×dNgdxdydY
b,x,y( ) ⎡
⎣ ⎢
⎤
⎦ ⎥
4
3
Cooper-Frey freeze-out:
€
EdN
d3P=
g
(2π )3 dΣμ pμ f (pμuμ ,T)∫
Luzum et al. PRC 78, 034915
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2+1D viscous hydrodynamics “AZHYDRO-KOLKATA”
LQCD
EoS &
HRG
Initial condition:
Glauber: Smooth CGC : Smooth (fKLN) QGP phase: Evolution: 2+1 D viscous hydrodynamics /s: constant
Hadronic Phase:
Evolution: 2+1D viscous hydrodynamics /s: constant
Freeze-out: Hyper-surface: Smooth Viscous correction: Grad 14-moment
Roy et al., PRC 86, 014902
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Charged hadrons V2 , Au-Au@200 GeV, RHIC
/s value increases with centrality Larger /s for CGC
Glauber CGC
Roy et al. PRC 86,014902 (2012)8
Charged hadrons V2 , [email protected] TeV, LHC
Glauber CGC
/s value increases with centrality Larger /s for CGC
Roy et al, arXiv 1210.1700
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2+1D viscous hydrodynamics + URQMD “VISHNU”
Initial condition:
Glauber: fluctuating CGC : fluctuating (MC-KLN) QGP phase: Evolution: 2+1 D viscous hydrodynamics /s: constant
Hadronic Phase:
Evolution: Transport model URQMD /s: temperature dependent
Freeze-out: Hyper-surface: Non-smooth Viscous correction: Grad 14 moment
Song et al., PRL106,192301(2011)
LQCD
EoS &
HRG
10
Inclusion of viscosity in hadronic phase
H song et al., PRL106,192301(2011)
•High shear viscosity in late hadronic phase
Value of extracted /s depends on initial condition
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2+1D viscous hydrodynamics with /s (T)
Initial condition:
Glauber: smooth QGP phase: Evolution: 2+1 D viscous hydrodynamics /s: temperature dependent
Hadronic Phase:
Evolution: 2+1D viscous hydrodynamics, chemical freeze-out /s: temperature dependent
Freeze-out: Hyper-surface: Smooth Viscous correction: Grad 14-moment
Niemi et al., PRL106,212302 (2011) PRC 86,014909 (2012)
s95 p-PCE-v1, Houvinen et al.,NPA, 837,26(2010)
LQCD
EoS &
HRG
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Niemi et al. PRL106,212302
Temperature Dependent /s
RHIC @ 200 GeV
LHC @2.76 TeV
Au-Au @200GeV Pb-Pb @2.76TeV
Temperature dependence of /s in QGP phase has little effect on v2(pT)
Temperature dependence of /s in hadronic phase has little effect on v2(pT)
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3+1D event by event viscous hydrodynamics “MUSIC”
Initial condition:
Glauber: fluctuating (MC-Glauber) QGP phase: Evolution: 3+1 D viscous hydrodynamics /s: constant
Hadronic Phase:
Evolution:3+1 D viscous hydrodynamics /s: constant
Freeze-out: Hyper-surface: Non-smooth Viscous correction: Relaxation time approximation f dependence on momentum ‘p’
Schenke et al., PRC 85,024901 (2012)
S95 p-v1, Houvinen et al.,NPA, 837,26(2010)
LQCD
EoS &
HRG
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Results from 3+1D hydro
3+1D No assumption on s symmetry Allows to explain s dependence of experimental data
Higher /s needed for larger rapidity
Schenke et al. PRL 106,042301 (2011)
/s=0.08
/s=0.16
s
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Schenke et al., arXiv:1209.6330 PRC 85,024901
Result from 3+1D hydrodynamics with fluctuating initial condition
Higher harmonicsmore sensitive to /s
0 0.5 1 1.5 2
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Comprehensive Heavy Ion Model Evaluation and Reporting Algorithm (CHIMERA)
Initial condition:
Glauber: Average of fluctuating condition Pre-equilibrium flow
QGP phase: Evolution: 2+1 D viscous hydrodynamics /s: constant
Hadronic Phase:
Evolution: Transport (URQMD) /s: Temperature dependent
Freeze-out: Hyper-surface: Smooth Viscous correction: Pratt, Torrieri formalism
S Pratt et al., arXiv: 1208.0897
Laine et al., PRD 73 (2006)
Pratt et al., PRC 82 (2010)
LQCD
EoS &
HRG
17
Combined 2 analysis
Spectra + v2 + HBT radii in 0-20% centrality Au-Au collision at 200 GeV
S Pratt et al., arXiv: 1208.0897
Experimental data: PHENIX (PRC 69, 034909) and STAR (PRL 92, 112301)
0 < /s < 6 x 1/4
Initial energy density scales with Npart
Initial energy density scales with Ncoll
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Pre equil flow No pre equil flow Pre equil flow No pre equil flow
Au-Au @ 200 GeV
1/4 < /s < 6(1/4)
Pb-Pb @ 2.76 TeV
1/4 < /s < 4(1/4)
•Bulk Viscosity & Grad 14-moment correction to freeze-out distribution function
•Large initial angular momentum of the reaction zone in non-central collisions
Conclusion & Outlook
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Thank You
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