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