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


0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S


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


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)



4

1

s

Elliptic flow v2





-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



)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 !




-EoS:

-treatment of hadronic stage and freeze-out procedure:


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/




-EoS: (EOSQ vs EOSL)

-treatment of hadronic stage and freeze-out procedures:


s/


-chemical composition of HRG -viscosity of HRG


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







s/




,,,

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)






s/



-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




Zero initialization:

large near Tc prevents from growing to large values

00

suppresses bulk viscous effects

QGPHRG



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


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 )


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


s/

Glauber CGC







)41(5/ s

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

recent progress: Heinz et al. 0907


s/

Glauber CGC







)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


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


Song & Heinz PRC 08




Multiplicity scaling of v2/ε Song & Heinz PRC 08

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


s/

Multiplicity scaling of v2/ε Song & Heinz PRC 08

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


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

s/

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


-photon spectra

-HBT radii

… …


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)


-photon spectra

-HBT radii

… …


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

Glauber

CGC

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

Documents

viscosity shear viscosity

shear bulk viscosity

qgp shear viscosity

spectrashear viscosity

radial flowbulk viscosity

spectraelliptic flow

gradients bulk viscosity

v2 data initial conditions