joint cathie/techqm workshop, bnl, dec 14-18, 2009

Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009

Huichao Song

The Ohio State University

Supported by DOE

12/14/2009

Lawrence Berkeley National Lab

QGP viscosity from RHIC data -- a hydrodynamic perspective

Thanks for collaborations and discussions from U. Heinz; Thanks for figures and discussions from K. Dusling, A. El, S. Pratt, Z. Xu, and many others

What is viscosity Shear viscosity – measures the resistance to flow gradients

Bulk viscosity – measures the resistance to expansion

Heat conductivity – measures the ability of heat transfer

Assume: (RHIC&LHC)0,0 n

act against the buildup of flow anisotropy

act against the buildup of radial flow

Ideal hydrodynamics

0)( xT

S.Bass

Conservation laws: pguupeT )(

ideal hydro: local equilibrium

)( p Input: “EOS” epcs /2

- 4 equations

- 5 unknowns ,e )3(u,p

-EOS is one of the important factors that influence the expansion of system harder EOS (with larger )2

sc faster expansion e

e

c

cu

s

s

2

2

1

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

viscous hydro: near equilibrium

shear pressure tensorbulk pressure:

ideal hydro: local equilibrium

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S

viscous hydro: near-equilibrium system

pre-equilibrium dynamics + viscous hydro + hadron cascade

Initial conditions final conditions

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S

)( p Input: “EOS” initial and final conditions

Bjorken appro. : reduces (3+1)-d hydro to (2+1)-d hydro / tzvz

Qualitative effects of & on spectra

-shear viscosity: flatter spectra

-bulk viscosity: steeper spectra

spectra

The same initial & final conditions:ideal hydro viscous hydro-shear only viscous hydro-bulk only

0,4/1 c1,0 c

0,0 css //

Song & Heinz, 0909

-shear viscosity: flatter spectra; increases radial flow

-bulk viscosity: steeper spectra; decreases radial flow

radial flow spectra

The same initial & final conditions:ideal hydro viscous hydro-shear only viscous hydro-bulk only

0,4/1 c1,0 c

0,0 css //

Song & Heinz, 0909

Qualitative effects of & on spectra

Elliptic flow v2

-both shear & bulk viscosity suppress V2 at low PT

Song & Heinz, 0909

Qualitative effects of & on V2

Shear viscosity & elliptic flow V2

20-25% v2 suppression

4

1

s

Elliptic flow v2

-V2 can be used to extract the QGP shear viscosity

-For an acurrate extraction of QGP viscosity, one needs very precise V2 (experimental data & theoretical results)

-V2 can be used to extract the QGP shear viscosity

20-25% v2 suppression

4

1

s

Elliptic flow v2

Shear viscosity & elliptic flow V2

-For an acurrate extraction of QGP viscosity, one needs very precise V2 (experimental data & theoretical results)

-V2 can be used to extract the QGP shear viscosity

20-25% v2 suppression

-10% uncertainties in V2 translate into 50% uncertainties for the extracted value of

s/

4

1

s

Elliptic flow v2

Example: If v2 is increased by 10%, one need to increase by in order to describe the same exp. data

s/ )4/(5.0

Shear viscosity & elliptic flow V2

-For an acurrate extraction of QGP viscosity, one needs very precise V2 (experimental data & theoretical results)

)4/1(O~/for s

Extracting from V2 data

Input / parameters for viscous hydro

-initial conditions:

-EoS: EOS Q, EOS L, EOS L + chemical non-equil. HRG EOS

-treatment of hadronic stage and freeze-out procedure:

-viscosities & relaxation times:

s/

-initial eccentricity (Glauber/CGC ; optical/fluctuations)

),,(/),,(, 000 byxsbyxe

-initialization for

,,,

,mn

Effects of initial eccentricity on Luzum & Romatschke, PRC 2008 Glauber CGC

-event by event fluctuations: talk by A. Dumitru

-Glauber vs.CGC: ~20-30% effect on ~100% uncertainties on s/2v

2v

Luzum & Romatschke, PRC 2008 Glauber CGC

?16.0/ s-Effects from highly viscous & non-chemical equilibrium hadronic stage, bulk viscosity …

Effects of initial eccentricity on 2v

NOT so fast !

Extracting from V2 data

Input / parameters for viscous hydro

-initial conditions:

-EoS:

-treatment of hadronic stage and freeze-out procedure:

-viscosities & relaxation times:

s/

-initial eccentricity

-chemical composition of HRG -effects of highly viscous HRG

-initialization for shear and bulk pressure

Effects of chemical composition of HRG on

(GeV)Tp0 1

30%

PCE vs.CE (HRG)

Ideal hydro

P. Huovinen 07

-PCE EoS vs. CE EoS (ideal hydro): change v2 by ~30%

2vPartial Chemical Equilibrium (PCE)

vs. Chemical Equilibrium (CE)

(GeV)Tp0 1

30%

PCE vs.CE (HRG)

-Constraining requires: a proper description of partial chemical equilibrium in HRG s/

Glauber

CGC

30%

P. Huovinen 07Luzum &Romatschke 08

Effects of chemical composition of HRG on 2v

-PCE EoS vs. CE EoS (ideal hydro): change V2 ~30% influence ~100%

s/

Ideal hydro

Effects of highly viscous hadronic stage on

-highly viscous hadronic stage: change V2 ~30-50% influence ~100-150%

-need viscous hydro + hadron cascade hybrid approach

30-50%

T. Hirano

2v

Ideal hydro

s/

Extracting from V2 data

Input / parameters for viscous hydro

-initial conditions:

-EoS: (EOSQ vs EOSL)

-treatment of hadronic stage and freeze-out procedures:

-viscosities & relaxation times:

s/

-initial eccentricity

-chemical composition of HRG -viscosity of HRG

-initialization for shear and bulk pressure

talk by P. Houvinen

Effects from softness of EOS

40%

30%

Song & Heinz PRC 08

-- EOS L: Katz 05 lattice data for QGP

SM-EOS Q vs. EOS L

--more realistic EOS for hydro

-- softness of EOS: ~5-10% effects ons/V2 ~25% uncertainties on

+ CE EOS for HRG

0903 lattice data for QGP+ PCE EOS for HRG

Extracting from V2 data

Input / parameters for viscous hydro

-initial conditions:

-EoS: (EOSQ vs EOSL)

-treatment of hadronic stage and freeze-out procedures:

-viscosities & relaxation times:

s/

-initial eccentricity

-chemical composition of HRG -viscosity of HRG

-initialization for shear and bulk pressure

,,,

shear pressure: relaxation times & initialization

- is insensitive to initializations of and relaxation time !

mn2v

Song, Ph.D thesis

-when extracting : one can neglect the uncertainties from & initialization of s/ mn

(since is short)

Extracting from V2 data

Input / parameters for viscous hydro

-initial conditions:

-EoS: (EOSQ vs EOSL)

-treatment of hadronic stage and freeze-out procedures:

s/

-initial eccentricity

-chemical composition of HRG -viscosity of HRG

-effects from bulk viscosity

- shear pressure: relaxation times and initialization

QGPHRG

bulk viscosity and relaxation time Bulk viscosity:

Relaxation times: also peaks near Tc, ~

this plays an important role for bulk viscous dynamics

QGPHRG

bulk viscosity and relaxation time Bulk viscosity:

Relaxation times: also peaks near Tc, ~

this plays an important role for bulk viscous dynamics

Zero initialization:

large near Tc prevents from growing to large values

00

suppresses bulk viscous effects

QGPHRG

bulk viscosity and relaxation time Bulk viscosity:

Relaxation times: also peaks near Tc, ~

N-S initialization: )(0 u

s/viscous hydro breaks down ( ) for larger 0p

viscous hydro is only valid with small small bulk viscous effects on V2

large near Tc keeps large negative value of in phase transition region

this plays an important role for bulk viscous dynamics

s/

Uncertainties from bulk viscosity

fm/c120)/( s

1C3.1C

1C100C

N-S initialization Zero initialization

-with a critical slowing down , effects from bulk viscosity effects are much smaller than from shear viscosity

bulk viscosity influences V2 ~5% (N-S initial.) <4% (zero initial.)

Song & Heinz, 0909

s/uncertainties to ~20% (N-S initial.) <15% (zero initial.)

fm/c120)/( s

s/ s/

Extracting from RHIC data --the current status of viscous hydrodynamics

s/

-initial conditions: CGC vs. Glauber ~20-30%

-EoS: EOS Q, vs. EOS L ~5-10%-chemical composition of HRG : (PEC vs. CE) ~30%-viscosity of HRG (or equil. HRG vs. non-equil. HRG) : ~30-50%-bulk viscosity: ~5%

(uncertainties in V2 )

Extracting from RHIC data --the current status of viscous hydrodynamics

s/

Glauber CGC

Luzum & Romatschke, PRC 2008 

-initial conditions: CGC vs. Glauber ~100%

-EoS: EOS Q, vs. EOS L ~25%

-chemical composition of HRG : (PEC vs. CE) ~100%-viscosity of HRG (or equil. HRG vs. non-equil. HRG) : ~100-150%-bulk viscosity: ~20%

(uncertainties in )s/

conservative upper limit:

)41(5/ s

Extracting from RHIC data --the current status of viscous hydrodynamics

s/

Glauber CGC

Luzum & Romatschke, PRC 2008 

-initial conditions: CGC vs. Glauber ~100%

-EoS: EOS Q, vs. EOS L ~25%

-chemical composition of HRG : (PEC vs. CE) ~100%-viscosity of HRG (or equil. HRG vs. non-equil. HRG) : ~100-150%-bulk viscosity: ~20%

(uncertainties in )s/

conservative upper limit:

)41(5/ s

Can we further increase the accuracy of extracted ? YES !s/

recent progress: Heinz et al. 0907

Extracting from RHIC data --the current status of viscous hydrodynamics

s/

Glauber CGC

Luzum & Romatschke, PRC 2008 

-initial conditions: CGC vs. Glauber ~100%

-EoS: EOS Q, vs. EOS L ~25%

-chemical composition of HRG : (PEC vs. CE) ~100%-viscosity of HRG (or equil. HRG vs. non-equil. HRG) : ~100-150%-bulk viscosity: ~20%

(uncertainties in )s/

conservative upper limit:

)41(5/ s

recent progress: Heinz et al. 0907

-To further decrease the uncertainties from bulk viscosity, (or to extract both shear & bulk viscosity from exp. data), one need more sensitive exp. observables

other observables that are sensitive to s/

- v2/ε: dependence on system size & shear viscosity

-photon spectra

-HBT radii

… …

Song & Heinz PRC 08

-larger shear viscous suppression of elliptic flow in smaller systems

System size dependence of shear viscous effects/v2

Song & Heinz PRC 08

System size dependence of shear viscous effects/v2

-the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity

-larger shear viscous suppression of elliptic flow in smaller systems

Song & Heinz PRC 08

System size dependence of shear viscous effects/v2

-larger shear viscous suppression of elliptic flow in smaller systems

-the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity

Song & Heinz PRC 08

System size dependence of shear viscous effects/v2

-larger shear viscous suppression of elliptic flow in smaller systems

-the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity

Multiplicity scaling of v2/ε Song & Heinz PRC 08

-to reproduce the experimental data (slope), a constant is not enough!

-the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity

s/

Multiplicity scaling of v2/ε Song & Heinz PRC 08

-to reproduce the experimental data (slope), a constant is not enough!

-the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity

-data indicate: smaller viscous effects in QGP; larger viscous effects in HRG

s/

-need viscous hydro + hadron cascade hybrid approach or inputting )(/ Ts

other observables that are sensitive to s/

-photon spectra

-HBT radii

… …

- v2/ε: dependence on system size & shear viscosity

EM probes: Photons Pion spectra

-Viscous hardening of PT-spectra is stronger for photons than hadrons

K. Dusling, 0903

20 ~/T

pp

peff

Photon spectra

1

~sTpe

-Photon spectra MAY HELP to constrain the 2-d range of QGP viscosity & thermalization time, together with other observables (V2 …)

-However, earlier thermalization also leads to harder photon spectra (Dusling 0903)

other observables that are sensitive to s/

-photon spectra

-HBT radii

… …

- v2/ε: dependence on system size & shear viscosity

HBT radii

sideout RR /- is sensitive to the QGP viscosity

- HBT HELPS to constrain the QGP viscosity, together with other observables (V2 …)

S. Pratt QM09

with viscosity

without viscosity

- However, viscosity is only one of the many ingredients that affect HBT radii (Pratt QM09)

Recent theroetical developments in viscous hydrodynamics

(MSU, Frankfurt, Krakow, etc)

- 3+1-d viscous hydro: Several groups are working on it

- in multi-component systems

- 3rd order viscous hydrodynamics

f

Talk by A. El

Talk by G. Denicol

Talk by D.Teaney and D. Molnar

- PT-dependent of viscous modification of thefparticle distributions

A short summary

BUT: to extract QGP viscosity, one must consider (at least) all the following aspects:

- a realistic EOS: EOS L vs. SM-EOS Q, PCE vs. CE

- initial conditions: CGC vs. Glauber initialization, optical vs. fluctuations

- bulk viscosity: uncertainties from bulk viscosity

… … … …

- hadronic stage : viscous hydro+ hadron cascade

- is sensitive to

A first attempt to constrain from RHIC data indicates

)41(5/ ss/

s/2v

Thank You

EOS

EOS

Elliptical flow v2

-v2 is sensitive to viscosity, especially shear viscosity

Qualitative effects of & on V2

Change the flow profile during hydro evolution

Flow + spectra correc.

ppf ~

Spectra correc.:

viscous hydro (shear only)

ideal hydro

viscous hydro (bulk only)

(with only flow correction here) A. Monnai talk : spectra correc. for bulk viscosity

Song & Heinz, 0909

EM probes: Photons

-Photon spectra are more sensitive to QGP shear viscosity than hadrons

Photon spectra

2T

Photon spectra

-Photon spectra may HELP to constrain QGP shear viscosity and hydro starting time

-Photon spectra are also sensitive to hydro starting time

-More sophisticated theoretical modeling in the future: including photon emitted from hadronic stage with modified photon emission rate, etc ; better experimental data

K. Dusling, 0903

-To describe the experimental data, one need to consider the contribution from all kinds of aspects besides shear viscosity

S. Pratt QM09

-Heinz, Moreland and Song

the effects from different initializations

-Heinz, Moreland and Song

the effects from different initializations

Glauber

CGC

Glauber

CGC