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

€

≈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

11

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

7

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 , Pb-Pb@2.76 TeV, LHC

Glauber CGC

/s value increases with centrality Larger /s for CGC

Roy et al, arXiv 1210.1700

9

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

12

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

15

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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