(b) (a)

Initial shape and final flow fluctuations in
event-by-event hydrodynamics for RHIC and LHC ∗
Ulrich Heinz, The Ohio State University
Exploring QCD Frontiers: From RHIC and LHC to EIC
Stellenbosch, Jan. 30 - Feb. 3, 2012
with Zhi Qiu, Chun Shen & Huichao Song
∗ Work supported by the U.S. Department of Energy

Probing thelandscapeof QCD matter: The future is now
Probes:
• Collective flow
• Jet modification
and quenching
• Thermal electromagnetic
radiation
• Critical fluctuations
• . . .
Ulrich Heinz CPTEIC, 31 Jan. 2012 1(43)

PbPb@LHC: Bjorken boost-invariance finally observed!
CMS (J. Velkovska) Quark Matter 2011
Small narrow bump near η=0 due to Jacobian dN
dη = ∫
(dip in dN/dη corresponds to bump in v 2 (η))
d 2 p T
p T coshη dN
√
m 2 + p 2 T cosh2 η
dyd 2 p T
Ulrich Heinz CPTEIC, 31 Jan. 2012 2(43)

Panta rhei: “soft ridge”=“Mach cone”=flow!
ATLAS (J. Jia), Quark Matter 2011
ALICE (J. Grosse-Oetringhaus), QM11
• anisotropic flow coefficients v n and flow angles ψ n correlated over large rapidity range!
M.Luzum, PLB 696 (2011) 499: All long-range rapidity correlations seen at RHIC are consistent with being entirely
generated by hydrodynamic flow.
• in the 1% most central collisions v 3 >v 2
=⇒ prominent “Mach cone”-like structure!
=⇒ event-by-event eccentricity fluctuations dominate!
Ulrich Heinz CPTEIC, 31 Jan. 2012 3(43)

Event-by-event shape and flow fluctuations rule!
(Alver and Roland, PRC81 (2010) 054905)
• Each event has a different initial shape and density distribution, characterized by different set of
harmonic eccentricity coefficients ε n
• Each event develops its individual hydrodynamic flow, characterized by a set of harmonic flow
coefficients v n and flow angles ψ n
• At small impact parameters fluctuations (“hot spots”) dominate over geometric overlap effects
(Alver & Roland, PRC81 (2010) 054905; Qin, Petersen, Bass, Müller, PRC82 (2010) 064903)
Ulrich Heinz CPTEIC, 31 Jan. 2012 4(43)

Event-by-event shape and flow fluctuations rule!
ALICE (A. Bilandzic) Quark Matter 2011
• in the 1% most central collisions v 3 >v 2 =⇒ prominent “Mach cone”-like structure!
• triangular flow angle uncorrelated with reaction plane and elliptic flow angles
=⇒ due to event-by-event eccentricity fluctuations which dominate the anisotropic flows in the
most central collisions
Ulrich Heinz CPTEIC, 31 Jan. 2012 5(43)

Fluctuation-driven anisotropic flow is indeed collective!
ALICE (J. Grosse-Oetringhaus) Quark Matter 2011
n = 2 0-10%
fit
v a n )
0.015
t
n
〈cos(n∆φ)〉, (v
0.01
0.005
0
Pb-Pb 2.76 TeV
Stat. error only
〈cos(n∆φ)〉
fit
v a n )
t
n
(v
1.6
1.4
1.2
0.8 1
0.6
0.4
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54
1 1 1 2 1 2 1 2 3 1 2 34 1 2 346 1 2 3468
1 1.5 2 2.5 3 4 6 8 15
assoc. p
T
[GeV/c]
trigger p
T
• Two-particle Fourier coefficients factorize (v n∆ (p T1 ,p T2 ) = v n (p T1 )v n (p T2 )) as required
• Factorization shown to work for n=2,3,4,5 as long as both p T1 ,p T2

Initial-state shape fluctuations
Ulrich Heinz CPTEIC, 31 Jan. 2012 7(43)

Smearing effects from nucleon growth at high energies
6
4
2
x (fm) 0
-2
-4
-6
6
4
2
x (fm) 0
-2
-4
-6
6
4
2
x (fm) 0
-2
-4
-6
200 GeV Disk
-6 -4 -2 0 2 4 6
y (fm)
200 GeV Gauss
-6 -4 -2 0 2 4 6
y (fm)
2.76 TeV Gauss
-6 -4 -2 0 2 4 6
y (fm)
UH & Scott Moreland, PRC84 (2011) 054905
60
50
40
30
20
10
0
50
45
40
35
30
25
20
15
10
5
0
100
90
80
70
60
50
40
30
20
10
0
y (fm)
y (fm)
8
6
4
2
0
-2
-4
-6
-8
23.5 GeV
2.76 TeV
8
6
4
2
0
-2
-4
-6
-8
-8 -6 -4 -2 0 2 4 6 8
x (fm)
16
14
12
10
8
6
4
2
0
100
90
80
70
60
50
40
30
20
10
0
200 GeV
7 TeV
-8 -6 -4 -2 0 2 4 6 8
x (fm)
50
45
40
35
30
25
20
15
10
5
0
120
100
Between √ s = 23.5 and 7,000GeV, nucleon area grows
by factor O(2) =⇒ significant smoothing of event-by-event
density fluctuations from RHIC to LHC
Ulrich Heinz CPTEIC, 31 Jan. 2012 8(43)
80
60
40
20
0

Eccentricity definitions:
Define event average {...}, ensemble average 〈...〉
Two choices for weight function in event average: (i) Energy density e(x ⊥ ;b)
(ii) Entropy density s(x ⊥ ;b)
Define σ 2 x = {x 2 }−{x} 2 , σ xy = {xy}−{x}{y}, etc.,
where x,y are reaction-plane coordinates (e x ‖ b)
1. Standard eccentricity: ε s ≡ ¯ε RP = 〈σ2 y −σ2 x 〉
2. Average reaction-plane eccentricity: 〈ε RP 〉 =
〈σ 2 y +σ2 x 〉 (calculated from RP-averaged 〈e〉 or 〈s〉)
〈
σ 2 y −σ2 x
σ 2 y +σ2 x
3. Eccentricity of the participant-plane averaged source: ¯ε part = 〈√ (σy 2−σ2 x )2 +4σxy〉
2
〈σy 2+σ2 x
〈√ 〉
〉
(σ 2
4. Average participant-plane eccentricity: 〈ε part 〉 = y −σx 2)2 +4σxy
2
σy 2+σ2 x
√
5. r.m.s. part.-plane eccentricity: ε part {2} ≡ 〈ε 2 part〉 (= √ 〈ε part 〉 2 +σε 2 /2 for Gauss. fl.)
6. 4thcumulanteccentricity: ε part {4} ≡ [ 〈ε 2 part〉 2 −(〈ε 4 part〉−〈ε 2 part〉 2 ) ] 1/4
〉
(= √ 〈ε part 〉 2 −σε 2 /2 for Gauss. fl.)
Ulrich Heinz CPTEIC, 31 Jan. 2012 9(43)

MC-Glauber eccentricities (e-weighted):
0.6
0.5
0.4
〈ǫ part 〉
ǫ part {2}
ǫ part {4}
〈ǫ RP 〉
¯ǫ part
¯ǫ RP
ǫ
0.3
0.2
0.1
0
0 5 10
Impact parameter b (fm)
Ulrich Heinz CPTEIC, 31 Jan. 2012 10(43)

MC-KLN eccentricities (e-weighted):
0.6
0.5
0.4
〈ǫ part 〉
ǫ part {2}
ǫ part {4}
〈ǫ RP 〉
¯ǫ part
¯ǫ RP
ǫ
0.3
0.2
0.1
0
0 5 10
Impact parameter b (fm)
Ulrich Heinz CPTEIC, 31 Jan. 2012 11(43)

Initial eccentricities ε n (n=2−5) vs. impact parameter
Zhi Qiu, UH, PRC84 (2011) 024911
ε3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
〈ε 3 (e)〉 (MC-KLN)
〈ε 3 (s)〉 (MC-KLN)
〈ε 3 (e)〉 (MC-Glb)
〈ε 3 (s)〉 (MC-Glb)
(b)
0
0 5 10 15
b (fm)
0.8
0.7
0.6
〈ε 4 (e)〉 (MC-KLN)
〈ε 4 (s)〉 (MC-KLN)
〈ε 4 (e)〉 (MC-Glb)
〈ε 4 (s)〉 (MC-Glb)
(c)
0.8
0.7
0.6
〈ε 5 (e)〉 (MC-KLN)
〈ε 5 (s)〉 (MC-KLN)
〈ε 5 (e)〉 (MC-Glb)
〈ε 5 (s)〉 (MC-Glb)
(d)
0.5
0.5
ε4
0.4
ε5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
• Contours: e(r,φ) = e 0 exp
0
0 5 10 15
[ b (fm)
(
− r2
2ρ 2
1+ε n cos(n(φ−ψ n ))) ] where ε n e inψn = −
0
0 5 10 15
b (fm)
∫ rdrdφr
2 e
inφ e(r,φ)
∫
rdrdφr 2 e(r,φ)
• MC-KLN has larger ε 2 and ε 4 , but similar ε 5 and almost identical ε 3 as MC-Glauber (ε 3,5 are purely fluctuation-driven!)
Ulrich Heinz CPTEIC, 31 Jan. 2012 12(43)

Flow fluctuations in
event-by-event hydro
Ulrich Heinz CPTEIC, 31 Jan. 2012 13(43)

Flow angle distributions (0–60% centrality):
d(Number of events)/dΨ
10000
8000
6000
4000
2000
Ψ P P
2
Ψ P P
3
Ψ P P
4
Ψ P P
5
d(Number of events)/dΨ
10000
8000
6000
4000
2000
Ψ EP
2
Ψ EP
3
Ψ EP
4
Ψ EP
5
0
−1 0 1
Ψ P P − Ψ RP
0
−1 0 1
Ψ EP − Ψ RP
ε n e inψPP n = −∫
rdrdφr
2 e
inφ e(r,φ)
∫
rdrdφr 2 e(r,φ)
v n e inψEP n =
∫
dφp e inφp (dN/dφ p )
∫
dφp (dN/dφ p )
• Angles of ε 3,5 and v 3,5 uncorrelated with reaction plane (Qin et al., PRC 82 (2010) 064903)
• v 4 -angle ψ EP
4 lies (on average) in the reaction plane even though ε 4 -angle ψ PP
4 points
at ± π 4 = ±45◦ =⇒ v 4 driven mostly by elliptic deformation ε 2 , not ε 4 .
Ulrich Heinz CPTEIC, 31 Jan. 2012 14(43)

Correlation between flow and eccentricity angles:
ψ2 EP −ψ2 PP mod π 2
2 x 104 Ψ EP
d(Number of events)/d(Ψ)
1.5
1
0.5
2 )
σ(Ψ EP
2 − Ψ P P
0.25
0.2
0.15
0.1
0.05
0
0 10 20 30 40 50 60
Centrality (%)
50−60%
30−40%
20−30%
15−20%
0−5%
b=0
0
0 0.2 0.4 0.6 0.8 1
2 − Ψ P 2
P
Strong angular correlation between elliptic flow and eccentricity, except near b=0.
Ulrich Heinz CPTEIC, 31 Jan. 2012 15(43)

Correlation between flow and eccentricity angles:
ψ3 EP −ψ3 PP mod π 3
d(Number of events)/d(Ψ)
8000
7000
6000
5000
4000
3000
2000
1000
σ(Ψ EP
3 − Ψ P 3 P )
0.35
0.3
0.25
0.2
0 10 20 30 40 50 60
Centrality (%)
50−60%
30−40%
20−30%
15−20%
0−5%
b=0
0
0 0.2 0.4 0.6 0.8 1
Ψ EP
3 − Ψ P 3
P
Four times weaker angular correlation between triangular flow and triangularity
than for 2nd harmonic.
Ulrich Heinz CPTEIC, 31 Jan. 2012 16(43)

Correlation between flow and eccentricity angles:
ψ4 EP −ψ4 PP mod π 4
d(Number of events)/d(Ψ)
5000
4000
3000
2000
1000
σ(Ψ EP
4 − Ψ P 4 P )
0.7
0.6
0.5
0.4
0.3
0.2
0 20 40 60
Centrality (%)
50−60%
30−40%
20−30%
15−20%
0−5%
b=0
0
0 0.2 0.4 0.6 0.8
Ψ EP
4 − Ψ P 4
P
• Near-central collisions: ψ EP
4
(weakly) correlated with ψ PP
4
⇐⇒ v 4 driven by ε 4
• Peripheral collisions: ψ EP
4
(weakly) anti-correlated with ψ PP
4
⇐⇒ v 4 driven by ε 2
• Mid-central to mid-peripheral: no correlation between ψ EP
4
and ψ PP
4
Ulrich Heinz CPTEIC, 31 Jan. 2012 17(43)

Correlation between flow and eccentricity angles:
ψ5 EP −ψ5 PP mod π 5
d(Number of events)/d(Ψ)
5000
4000
3000
2000
1000
σ(Ψ EP
5 − Ψ P 5 P )
0.5
0.4
0.3
0.2
0 20 40 60
Centrality (%)
50−60%
30−40%
20−30%
15−20%
0−5%
b=0
0
0 0.2 0.4 0.6 0.8
Ψ EP
5 − Ψ P 5
P
• Near-central collisions: ψ EP
5
(weakly) correlated with ψ PP
5
⇐⇒ v 5 driven by ε 5
• Peripheral collisions: ψ EP
5
(weakly) anti-correlated with ψ PP
5
⇐⇒ v 5 strongly influenced by ε n≠5
• Mid-central to mid-peripheral: no correlation between ψ EP
5
and ψ PP
5
Ulrich Heinz CPTEIC, 31 Jan. 2012 18(43)

Higher harmonic flows and associated eccentricities:
v 2 vs. ε 2 (MC-KLN, e-weighted)
0.25
v2
0.2
0.15
0.1
50−60%
30−40%
20−30%
15−20%
0−5%
b=0
0.05
0
0 0.2 0.4 0.6 0.8 1
• Slightly non-linear dependence of v 2 on ε 2 , especially in central and very peripheral collisions
• In the most peripheral centrality classes, slope of v 2 (ε 2 ) decreases
ǫ 2
Ulrich Heinz CPTEIC, 31 Jan. 2012 19(43)

Higher harmonic flows and associated eccentricities:
v 3 vs. ε 3 (MC-KLN, e-weighted)
0.12
0.1
0.08
v3
0.06
50−60%
0.04
30−40%
20−30%
0.02
15−20%
0−5%
b=0
0
0 0.2 0.4 0.6 0.8
• Slope of v 3 (ε 3 ) and value of v 3 /ε 3 depend on centrality class
• Non-zero triangular flow v 3 ∼ 1−2% even for zero triangularity ε 3
=⇒ other (odd) harmonic eccentricity coefficients feed into v 3
Ulrich Heinz CPTEIC, 31 Jan. 2012 20(43)
ǫ 3

Higher harmonic flows and associated eccentricities:
v 4 vs. ε 4 (MC-KLN, e-weighted)
v4
0.045
0.04
0.035
0.03
0.025
0.02
50−60%
30−40%
0.015
20−30%
15−20%
0.01
0−5%
b=0
0.005
0 0.2 0.4 0.6 0.8
• Correlation between v 4 and ε 4 strongly centrality dependent
• In mid-central and peripheral collisions, v 4 is mostly generated by ε n≠4 , in particular ε 2
• Even in central collisions, other ε n≠4 feed into v 4 , generating non-zero v 4 for zero ε 4
ǫ 4
Ulrich Heinz CPTEIC, 31 Jan. 2012 21(43)

Higher harmonic flows and associated eccentricities:
v 5 vs. ε 5 (MC-KLN, e-weighted)
v5
0.035
0.03
0.025
0.02
0.015
50−60%
30−40%
0.01
20−30%
15−20%
0.005
0−5%
b=0
0
0 0.2 0.4 0.6 0.8
• Correlation between v 5 and ε 5 strongly centrality dependent
• In mid-central and peripheral collisions, v 5 is mostly generated by ε n≠5
• Even in central collisions, other ε n≠5 feed into v 5 , generating non-zero v 5 for zero ε 5
ǫ 5
Ulrich Heinz CPTEIC, 31 Jan. 2012 22(43)

Event-by-event vs.
single-shot hydro
Ulrich Heinz CPTEIC, 31 Jan. 2012 23(43)

Eccentricity-scaled v 2,3 flow from e-by-e and single-shot hydro
v2/ε2 (π)
v3/ε3 (π)
0.25
0.2
MC-KLN
ideal hydro
0.15 ¯v 2 /¯ε part (e)
〈v 2 〉/〈ε 2 (e)〉
v 2 {2}/ε 2 {2}(e)
0.1
0
v 2 {4}/ε 2 {4}(e)
5
b (fm)
10
0.25
0.2
0.15 MC-KLN
ideal hydro
0.1
¯v 3 /¯ε part (e)
0.05
〈v 3 〉/〈ε 3 (e)〉
v 3 {2}/ε 3 {2}(e)
0
0
v 3 {4}/ε 3 {4}(e)
5
b (fm)
10
Zhi Qiu, UH, in preparation
(a)
(c)
v2/ε2 (π)
v3/ε3 (π)
0.15
0.1
0.05
0.1
0.08
0.06
MC-KLN
η/s = 0.2
¯v 2 /¯ε part (e)
〈v 2 〉/〈ε 2 (e)〉
v 2 {2}/ε 2 {2}(e)
v 2 {4}/ε 2 {4}(e)
0 5 10
b (fm)
MC-KLN
η/s = 0.2
0.04 ¯v 3 /¯ε part (e)
〈v 3 〉/〈ε 3 (e)〉
0.02 v 3 {2}/ε 3 {2}(e)
0
0
v 3 {4}/ε 3 {4}(e)
5
b (fm)
10
• For most centralities, eccentricity-scaled v 2,3 from e-by-e and single-shot hydro agree within 5-10%
• Agreement between 〈v 2,3 〉/〈ε 2,3 〉 and v 2,3 {2}/ε 2,3 {2} is excellent at all centralities
• Agreement between v 2 {2}/ε 2 {2} and v 2 {4}/ε 2 {4} is good over most of the centrality range, but the analog relation
for triangular flow does not work (note, however, limited statistics)
• =⇒ Can use single-shot hydro to compute 〈v 2,3 〉/〈ε 2,3 〉 = v 2,3 {2}/ε 2,3 {2}
(b)
(d)
Ulrich Heinz CPTEIC, 31 Jan. 2012 24(43)

(η/s) QGP
Ulrich Heinz CPTEIC, 31 Jan. 2012 25(43)

How to use elliptic flow for measuring (η/s) QGP
Hydrodynamics converts
spatial deformation of initial state =⇒
momentum anisotropy of final state,
through anisotropic pressure gradients
0.16
0.14
0.12
0.10
Au+Au RHIC
20~30%
Shear viscosity degrades conversion efficiency
ε x = 〈〈y2 −x 2 〉〉
〈〈y 2 +x 2 〉〉 =⇒ ε p= 〈Txx −T yy 〉
〈T xx +T yy 〉
of the fluid; the suppression of ε p is monotonically
related to η/s. 0 1 2 3 4 5 6
0.00
7
p
0.08
0.06
0.04
0.02
(fm/c)
ideal
/s = 0.08
/s = 0.16
/s = 0.24
The observable that is most directly related to the total hydrodynamic momentum
anisotropy ε p is the total (p T -integrated) charged hadron elliptic flow v ch
2 :
∑
ε p = 〈Txx −T yy 〉
〈T xx +T yy 〉 ⇐⇒
i∫ pT dp ∫ T dφp p2 T cos(2φp)
∑ ∫
i∫
pT dp T dφp p 2 T
dN i
dyp T dp T dφ p
dN i
dyp T dp T dφ p
⇐⇒ v ch
2
Ulrich Heinz CPTEIC, 31 Jan. 2012 26(43)

How to use elliptic flow for measuring (η/s) QGP (contd.)
• If ε p saturates before hadronization (e.g. in PbPb@LHC (?))
⇒ v ch
2 ≈ not affected by details of hadronic rescattering below T c
but: v (i)
2 (p dN
T), i
change during hadronic phase (addl. radial flow!), and these
dyd 2 p T
changes depend on details of the hadronic dynamics (chemical composition etc.)
⇒ v 2 (p T ) of a single particle species not a good starting point for extracting η/s
• If ε p does not saturate before hadronization (e.g. AuAu@RHIC), dissipative hadronic
dynamics affects not only the distribution of ε p over hadronic species and in p T , but
even the final value of ε p itself (from which we want to get η/s)
⇒ need hybrid code that couples viscous hydrodynamic evolution of QGP to realistic
microscopic dynamics of late-stage hadron gas phase
⇒ VISHNU (“Viscous Israel-Steward Hydrodynamics ’n’ UrQMD”)
(Song, Bass, UH, PRC83 (2011) 024912) Note: this paper shows that UrQMD ≠ viscous hydro!
Ulrich Heinz CPTEIC, 31 Jan. 2012 27(43)

Extraction of (η/s) QGP from AuAu@RHIC
v 2
/ε
0.25
0.2
0.15
0.1
0.05
0
hydro (η/s)+UrQMD
0 10 20 30 40
(1/S) dN ch
/dy (fm -2 )
H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRL106 (2011) 192301
η/s
0.0
0.08
0.16
0.24
(fm/c) max.
η/s τ 0
dN/dy
Glauber / KLN
0.0 . 0.4 810
0.08 . 0.6 810
0.16 0.9 . 810
0.24 . 1.2 0.9 810
v 2
/ε
0.25
0.2
0.15
0.1
0.05
0
MC-KLN
(a)
hydro (η/s) + UrQMD
v 2
{2} / 〈ε 2 part 〉1/2 KLN
〈v 2
〉 / 〈ε part
〉 KLN
0 10 20 30
(1/S) dN ch
/dy (fm -2 )
η/s
0.0
0.08
0.16
0.24
MC-Glauber
(b)
hydro (η/s) + UrQMD
v 2
{2} / 〈ε 2 part 〉1/2 Gl
〈v 2
〉 / 〈ε part
〉 Gl
η/s
0.0
0.08
0.16
0.24
0 10 20 30 40
(1/S) dN ch
/dy (fm -2 )
1 < 4π(η/s) QGP < 2.5
• All shown theoretical curves correspond to parameter sets that correctly
describe centrality dependence of charged hadron production as well as
p T -spectra of charged hadrons, pions and protons at all centralities
• v2 ch /ε x vs. (1/S)(dN ch /dy) is “universal”, i.e. depends only on
η/s but (in good approximation) not on initial-state model (Glauber
vs. KLN, optical vs. MC, RP vs. PP average, etc.)
• dominant source of uncertainty: ε Gl
x vs. εKLN x −→
• smaller effects: early flow → increases v 2 ε
by ∼few% → larger η/s
bulk viscosity → affects v ch
2 (p T), but ≈ not v ch
2
Zhi Qiu, UH, PRC84 (2011) 024911
Ulrich Heinz CPTEIC, 31 Jan. 2012 28(43)

dN/(2 dy p T
dp T
) (GeV -2 )
Global description of AuAu@RHIC spectra and v 2
VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (2011) 054910)
+
10 3 MC-Glauber initialization
2
0%~10%*10 p
200 A GeV Au+Au charged hadrons
2
10 2
1.8 s = 0.08
s = 0.16
s = 0.16
s = 0.24
10 1 10%~20%*10
1.6
10 0 20%~40%
1.4
1.2
10 -1
40%~60%/10
1
10 -2
0.8
10 -3 60%~80%/10 2
0.6
10 -4
/s = 0.0
0.4
(ideal hydro)
10 -5 /s = 0.08
0.2
/s = 0.16
/s = 0.24 (b)
(a)
0.0 0.5 1.0 1.5 2.0
10 5
5%~10%*10 2
10%~15%*10
10 3
15%~20%*1
20%~30%/10
10 1
30%~40%/10 2
10 -1 40%~50%/10 3
50%~60%/10 4
10 -3
60%~70%/10 5
10 -5 70%~80%/10 6
10 -7
10 -9
PHENIX
STAR
MC-KLN
MC-Glauber
0%~5%*10 3
0.0 0.5 1.0 1.5 2.0
10 -6
10 7
10 -11
p T
(GeV)
dN/(2 dy p T
dp T
) (GeV -2 )
p T
(GeV)
v 2
/
0
0.0 0.4 0.8 1.2 1.6
p T
(GeV)
MC-KLN initialization
0.0 0.4 0.8 1.2 1.6 2.0
p T
(GeV)
VISHNU PHENIX v 2
{EP}
(0-5%)+1.2
(5-10%)+1.0
(10-20%)+0.8
(20-30%)+0.6
(30-40%)+0.4
(40-50%)+0.2
(50-60%)
• (η/s) QGP = 0.08 for MC-Glauber and (η/s) QGP = 0.16 for MC-KLN work well
for charged hadron, pion and proton spectra and v 2 (p T ) at all collision centralities
• Note: T chem =165MeV reproduces the proton spectra from STAR, but not from
PHENIX! =⇒ Slightly incorrect chemical composition in hadronic phase? Not enough
p¯p annihilation in UrQMD?
Ulrich Heinz CPTEIC, 31 Jan. 2012 29(43)

dN/(2 dy p T
dp T
) (GeV -2 )
Global description of AuAu@RHIC spectra and v 2
VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (2011) 054910)
10 3 1.2
+
s = 0.08
0%~10%*10 p
2
1.0 /s = 0.16
VISHNU STAR v 2 {2} p
10 2
(5-10%)+0.6
(20-30%)+0.4
0.8
(30-40%)+0.2
10 1 10%~20%*10
(40-50%)
0.6
0.4
10 0 20%~40%
0.2
10 -1
0.0
MC-Glauber initialization
40%~60%/10
MC-Glauber initialization
10 -2
s = 0.16
1.0
Au + Au 200 A GeV p
/s = 0.24
0.8
10 -3 60%~80%/10 2
0.6
10 -4
/s = 0.0
0.4
(ideal hydro)
10 -5 /s = 0.08
0.2
/s = 0.16
/s = 0.24 (b)
0.0 MC-KLN initialization
MC-KLN initialization
10 -6
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
(a)
0.0 0.5 1.0 1.5 2.0
10 5
5%~10%*10 2
10%~15%*10
10 3
15%~20%*1
20%~30%/10
10 1
30%~40%/10 2
10 -1 40%~50%/10 3
50%~60%/10 4
10 -3
60%~70%/10 5
10 -5 70%~80%/10 6
10 -7
10 -9
PHENIX
STAR
MC-KLN
MC-Glauber
0%~5%*10 3
0.0 0.5 1.0 1.5 2.0
10 7
10 -11
p T
(GeV)
dN/(2 dy p T
dp T
) (GeV -2 )
p T
(GeV)
v 2
/
v 2
/
p T
(GeV)
p T
(GeV)
• (η/s) QGP = 0.08 for MC-Glauber and (η/s) QGP = 0.16 for MC-KLN work well for charged hadron, pion and proton
spectra and v 2 (p T ) at all collision centralities
• A purely hydrodynamic model (without UrQMD afterburner) with the same values of η/s does almost as well (except for
centrality dependence of proton v 2 (p T )) (C. Shen et al., PRC84 (2011) 044903)
Main difference: VISHNU develops more radial flow in the hadronic phase (larger shear viscosity), pure viscous hydro must
start earlier than VISHNU (τ 0 = 0.6 instead of 1.05fm/c), otherwise proton spectra are too steep
• These η/s values agree with Luzum & Romatschke, PRC78 (2008), even though they used EOS with incorrect hadronic
chemical composition =⇒ shows robustness of extracting η/s from total charged hadron v 2
Ulrich Heinz CPTEIC, 31 Jan. 2012 30(43)

(dN ch /dη)/(N part /2)
8
6
4
2
Pb+Pb 2.76 A TeV: ALICE
Au+Au 200 A GeV: STAR
Au+Au 200 A GeV: PHOBOS
MC-KLN
reaction plane
0
0 100 200 300 400
N part
Pre- and postdictions for PbPb@LHC
LHC: η/s=0.16
LHC: η/s=0.20
LHC:η/s=0.24
RHIC: η/s=0.16
VISHNU with MC-KLN (Song, Bass, UH, PRC83 (2011) 054912)
(b)
STAR
10-20% 0.1
v +0.3
0.4 ALICE 2
{4}
v 2
0.3
0.2
0.1
0
MC-KLN
reaction plane
VISHNU
RHIC: η/s=0.16
LHC: η/s=0.16
LHC: η/s=0.20
LHC: η/s=0.24
0 0.5 1 1.5 2
p T
(GeV)
20-30%
+0.2
30-40%
+0.1
40-50%
v 2
0.08
0.06
0.04
0.02
STAR
ALICE v 2 {4}
MC-KLN
Reaction Plane
RHIC: η/s=0.16
LHC: η/s=0.16
LHC: η/s=0.20
LHC: η/s=0.24
0
0 20 40 60 80
centrality
• After normalization in 0-5% centrality collisions, MC-KLN + VISHNU (w/o running coupling, but
including viscous entropy production!) reproduces centrality dependence of dN ch /dη well in both
AuAu@RHIC and PbPb@LHC
• (η/s) QGP = 0.16 for MC-KLN works well for charged hadron v 2 (p T ) and integrated v 2 in
AuAu@RHIC, but overpredicts both by about 10-15% in PbPb@LHC
• Similar results from predictions based on pure viscous hydro (C. Shen et al., PRC84 (2011) 044903)
• but: At LHC significant sensitivity of v 2 to initialization of viscous pressure tensor π µν (Navier-Stokes
or zero) =⇒ need pre-equilibrium model.
=⇒ QGP at LHC not much more viscous than at RHIC!
Ulrich Heinz CPTEIC, 31 Jan. 2012 31(43)

Why is v ch
2 (p T ) the same at RHIC and LHC?
Answer: Pure accident! (Kestin & Heinz EPJC61 (2009) 545)
v 2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
C. Shen, UH, P. Huovinen, H. Song, PRC84 (2011) 044903
AuAu@ PbPb@ MC-KLN, /s = 0.20
RHIC LHC
+
p
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
p T
(GeV)
20~30%
v π 2 (p T) increases a bit from RHIC to LHC, for heavier hadrons v 2 (p T ) at fixed p T decreases
(radial flow pushes momentum anisotropy of heavy hadrons to larger p T )
This is a hard prediction of hydrodynamics! (See also Nagle, Bearden, Zajc, NJP13 (2011) 075004)
Ulrich Heinz CPTEIC, 31 Jan. 2012 32(43)

Confirmation of increased mass splitting at LHC
Data: ALICE @ LHC, Quark Matter 2011 (symbols), PHENIX @ RHIC (shaded)
Lines: Shen et al., PRC84 (2011) 044903 (VISH2+1 + MC-KLN, η/s=0.2)
• Qualitative features of data agree with VISH2+1 predictions
• VISH2+1 does not push proton v 2 strongly enough to higher p T , both at RHIC and LHC
• At RHIC we know that this is fixed when using VISHNU – is the same true at LHC?
Ulrich Heinz CPTEIC, 31 Jan. 2012 33(43)

Successful prediction of v 2 (p T ) for identified hadrons in
PbPb@LHC
Data: ALICE, Quark Matter 2011
Prediction: Shen et al., PRC84 (2011) 044903 (VISH2+1)
Perfect fit in semi-peripheral collisions!
The problem with insufficient proton radial flow exists only in more central collisions
Adding the hadronic cascade (VISHNU) helps:
Ulrich Heinz CPTEIC, 31 Jan. 2012 34(43)

v 2 (p T ) in PbPb@LHC: ALICE vs. VISHNU
v2
Data: ALICE, preliminary (Snellings, Krzewicki, Quark Matter 2011)
Dashed lines: Shen et al., PRC84 (2011) 044903 (VISH2+1, MC-KLN, (η/s) QGP =0.2)
Solid lines: Song, Shen, UH 2011 (VISHNU, MC-KLN, (η/s) QGP =0.16)
0.3
0.2
0.1
π +
K +
p
ALICE Preliminary
VISHNU
(η/s) QGP = 0.16
VISH2+1
η/s = 0.20
0
5−10%
10−20%
20−30%
0.2
v2
0.1
30−40%
40−50%
50−60%
0
0 1.0 2.0 0 1.0 2.0 0 1.0 2.0 3.0
p T (GeV) p T (GeV) p T (GeV)
VISHNU yields correct magnitude and centrality dependence of v 2 (p T ) for pions, kaons and protons!
Same (η/s) QGP =0.16 (for MC-KLN) at RHIC and LHC!
Ulrich Heinz CPTEIC, 31 Jan. 2012 35(43)

PbPb@LHC p T -spectra: ALICE vs. VISH2+1 and VISHNU:
dN/(dydpT)
dN/(dydpT)
10 3 0~5%
10 2
10 1
10 0
10 −1
10 2
10 1
10 0
10 −1
ALICE Preliminary
π +
K +
p
10 3 30~40%
5~10%
(η/s) QGP = 0.16
VISHNU
40~50%
10~20%
η/s = 0.20
VISH2+1
50~60%
20~30%
60~70%
0 1.0 2.0 0 1.0 2.0 0 1.0 2.0 0 1.0 2.0 3.0
p T (GeV) p T (GeV) p T (GeV) p T (GeV)
• Good description also of identified hadron spectra for centralities

The new “proton anomaly”: disagreement with the thermal model
Data: ALICE, preliminary (A. Kalweit, Strange Quark Matter 2011)
Model: A. Andronic et al., PLB673 (2009) 142; similar: S. Wheaton et al. (THERMUS), Comp. Phys. Comm. 180 (2009) 84
• “Standard” T chem =164MeV reproduces strange hadrons but overpredicts (anti-)protons by 50%!
• p¯p annihilation in UrQMD not strong enough to repair this
• Similar problem already seen at RHIC but not taken seriously (STAR/PHENIX disagreement)
???
Ulrich Heinz CPTEIC, 31 Jan. 2012 37(43)

Back to the
“elephant in the room”:
How to eliminate the large
model uncertainty
in the initial eccentricity?
Ulrich Heinz CPTEIC, 31 Jan. 2012 38(43)

Two observations:
I. Shear viscosity suppresses higher flow harmonics more strongly
v n /ε n
Alver et al., PRC82 (2010) 034913
(averaged initial conditions)
0.3
0.25
0.2
0.15
0.1
0.05
v 2 /ε 2
v 3 /ε 3
v 4 /ε 4
v 5 /ε 5
v n (viscous)/v n (ideal)
1.4
1.2
1
0.8
0.6
0.4
0.2
Schenke et al., arXiv:1109.6289
(event-by-event hydro)
v n (η/s=0.08)/v n (ideal)
v n (η/s=0.16)/v n (ideal)
20-30%
0
0 0.08 0.16
η/s
0
1 2 3 4 5 6
n
=⇒ Idea: Use simultaneous analysis of elliptic and triangular flow to constrain initial state models
(see also Bhalerao, Luzum Ollitrault, PRC 84 (2011) 034910)
II. ε 3 is ≈ model independent
While v 4 and v 5 have mode-coupling contributions from ε 2 , v 3 is almost pure response to ε 3 and
v 3 /ε 3 ≈const. over a wide range of centralities
=⇒ Idea: Use total charged hadron v ch
3 to determine (η/s) QGP,
then check v ch
2
to distinguish between MC-KLN and MC-Glauber!
Ulrich Heinz CPTEIC, 31 Jan. 2012 39(43)

Glauber in, KLN out!
Zhi Qiu, C. Shen, UH, arXiv:1110.3033 (VISH2+1)
v2/ε2
v3/ε3
0.4
0.3
0.2
0.1
0
0.3
0.2
ALICE v 2 {2}/ε 2 {2}
ALICE v 2 {4}/ε 2 {4}
MC-KLN v 2 /¯ε 2
(a)
ALICE v 3 {2}/ε 3 {2}
0
0.3
MC-KLN v 3 /¯ε 3
0.1
MC-KLN η/s = 0.20
(b)
0
0 10 20 30 40
Centrality (%)
50 60 70
v3/ε3
v2/ε20.4
0.2
0.2
ALICE v 2 {2}/ε 2 {2}
ALICE v 2 {4}/ε 2 {4}
MC-Glb. v 2 /¯ε 2
(c)
ALICE v 3 {2}/ε 3 {2}
MC-Glb. v 3 /¯ε 3
0.1
MC-Glb. η/s = 0.08
(d)
0
0 10 20 30 40
Centrality (%)
50 60 70
• Both MC-KLN with η/s=0.2 and MC-Glauber with η/s=0.08 give very good
description of v 2 /ε 2 at all centralities.
• Only MC-Glauber initial conditions with η/s=0.08 describe v 3 /ε 3
PHENIX, comparing to calculations by Alver et al. (PRC82 (2010) 034913), come to similar conclusions at RHIC energies
(Adare et al., arXiv:1105.3928, and Lacey et al., arXiv:1108.0457)
• Large v 3 measured at RHIC and LHC requires small (η/s) QGP ≃1/(4π) unless
the fluctuations predicted by both models are completely wrong and ε 3 is really 50%
larger than we presently believe!
Ulrich Heinz CPTEIC, 31 Jan. 2012 40(43)

Conclusions
• We have come a long way over the last couple of years:
I believe that the issue of the QGP shear viscosity at RHIC and LHC energies is now settled:
(η/s) QGP (T c

Outlook: A beautiful analogy with the Big Bang:
The fluctuation “power spectrum” of the Little Bang
Mishra, Mohapatra, Saumia, Srivastava, PRC77 (2008) 064902 and C81 (2010) 034903
Mocsy & Sorensen, NPA855 (2011) 241, PLB705 (2011) 71
Ulrich Heinz CPTEIC, 31 Jan. 2012 42(43)

The fluctuation “power spectrum” of the Little Bang
Staig & Shuryak, arXiv:1106.3243
• Relating the measured “anisotropic flow power spectrum” (i.e. v n vs. n) to the “initial fluctuation
power spectrum” (i.e. ε n vs. n) provides access to the QGP transport coefficients (likely not only η/s,
but also ζ/s, τ π , τ Π ...)
• Power spectrum of initial fluctuations (in particular its √ s dependence) can (probably) be calculated
from first principles via CGC effective theory (Dusling, Gelis, Venugopalan, arXiv:1106.3927)
• Collisions between different species, at different collision centralities, and at different √ s create
Little Bangs with characteristically different power spectra
−→ The Concordance Model of Little Bang Cosmology!
Ulrich Heinz CPTEIC, 31 Jan. 2012 43(43)

Supplements
Ulrich Heinz CPTEIC, 31 Jan. 2012 44(43)

dN/(2 dy p T
dp T
) (GeV -2 )
Global description of AuAu@RHIC spectra and v 2
VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC, arXiv:1101.4638)
10 3 2.4
MC-Glauber initialization MC-KLN initialization
200 A GeV Au+Au charged hadrons
+
0%~10%*10 p
2
10 2
2.2 s = 0.08
VISHNU STAR v
s = 0.16
2
{EP}
s = 0.16
s = 0.24
(0-5%)+1.6
10 1 10%~20%*10
2.0
1.8
(5-10%)+1.4
10 0 20%~40%
1.6
(10-20%)+1.2
1.4
(20-30%)+1.0
10 -1
40%~60%/10
1.2
(30-40%)+0.8
10 -2
1.0
(40-50%)+0.6
10 -3 60%~80%/10 2
0.8
0.6
(50-60%)+0.4
/s = 0.0
(60-70%)+0.2
PHENIX
(ideal hydro)
STAR
10 -5 /s = 0.08
(70-80%)
MC-KLN
0.2
/s = 0.16
MC-Glauber
/s = 0.24 (b)
0.0
10 -6
0.0 0.4 0.8 1.2 1.6 0.0 0.4 0.8 1.2 1.6 2.0
10 -4
0.4
0%~5%*10 3 0.0 0.5 1.0 1.5 2.0
10 5
5%~10%*10 2
10%~15%*10
10 3
15%~20%*1
20%~30%/10
10 1
30%~40%/10 2
10 -1 40%~50%/10 3
50%~60%/10 4
10 -3
60%~70%/10 5
10 -5 70%~80%/10 6
10 -7
10 -9
(a)
0.0 0.5 1.0 1.5 2.0
10 7
10 -11
p T
(GeV)
dN/(2 dy p T
dp T
) (GeV -2 )
p T
(GeV)
v 2
/
p T
(GeV)
p T
(GeV)
• (η/s) QGP = 0.08 for MC-Glauber and (η/s) QGP = 0.16 for MC-KLN works well for
charged hadron, pion and proton spectra and v 2 (p T ) at all collision centralities
Ulrich Heinz CPTEIC, 31 Jan. 2012 45(43)

Comparison of ALICE PbPb@LHC v 2 data with
VISH2+1
v 2
v 2
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.30
0.25
Data: ALICE, preliminary (Snellings, Krzewicki, Quark Matter 2011)
Prediction: C. Shen et al., PRC84 (2011) 044903 (VISH2+1, MC-KLN, η/s=0.2)
Pb+Pb @ 2.76 A TeV
5%~10%
30%~40%
0.20
0.15
0.10
0.05
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
p T
(GeV)
data: ALICE Preliminary
10%~20%
40%~50%
20%~30%
pion
kaon
anti-proton
VISH2+1
( /s = 0.20)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
p T
(GeV)
50%~60%
p T
(GeV)
Ulrich Heinz CPTEIC, 31 Jan. 2012 46(43)

PbPb@LHC p T -spectra: Glauber vs. KLN
dN/(dydpT)
dN/(dydpT)
10 3 0~5%
10 2
10 1
10 0
10 −1
10 2
10 1
10 0
10 −1
PbPb@2.76A TeV
ALICE Preliminary
π +
K +
p
10 3 30~40%
5~10%
MC−KLN
η/s = 0.20
40~50%
10~20%
MC−Glb
η/s = 0.08
50~60%
20~30%
60~70%
0 1.0 2.0 0 1.0 2.0 0 1.0 2.0 0 1.0 2.0 3.0
p T (GeV) p T (GeV) p T (GeV) p T (GeV)
• In central collisions no difference between the models.
• In peripheral collisions p T -spectra from MC-Glauber IC too steep!
This is an artifact of single-shot hydro with averaged initial profile; for small η/s=0.08 (but not
for η/s=0.2!), e-by-e hydro gives flatter p T -spectra in peripheral collisions, due to hot spots
Ulrich Heinz CPTEIC, 31 Jan. 2012 47(43)

s95p-PCE: A realistic, lattice-QCD-based EOS
Huovinen, Petreczky, NPA 837 (2010) 26
Shen, Heinz, Huovinen, Song, PRC 82 (2010) 054904
1.6
p (GeV/fm 3 )
c 2 S
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.35
0.30
0.25
0.20
0.15
0.10
s95p-PCE
SM-EOS Q
EOS L
High T: Lattice QCD (latest
hotQCD results)
Low T: Chemically frozen HRG
(T chem = 165MeV)
No softest point!
0.05
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
e (GeV/fm 3 )
Ulrich Heinz CPTEIC, 31 Jan. 2012 48(43)

s95p-PCE: A realistic, lattice-QCD-based EOS
1/2 *dN/(dyp T
dp T
)
v 2
1000
100
10
1
0.1
0.01
1E-3
1E-4
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
p/10
Huovinen, Petreczky, NPA 837 (2010) 26
Shen, Heinz, Huovinen, Song, PRC 82 (2010) 054904
PHENIX data
s95p-PCE
SM-EOS Q
EOS L
central Au+Au
(b = 2.33 fm)
Au+Au 20~30% (b = 7.5 fm)
charged hadrons
/s = 0.16
T dec
= 140 MeV
0
= 0.4 fm/c
CGC initialization
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
p T
(GeV)
v 2
v 2
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0.00
0.28
0.24
0.20
0.16
0.12
0.08
0.04
p
Au+Au 20~30% (b = 7.5 fm)
Au+Au 20~30% (b = 7.5 fm)
s95p-PCE without f
SM-EOS Q without f
EOS L without f
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
p T
(GeV)
Generates less radial
flow than SM-EOS Q
and EOS L but larger
momentum anisotropy
Smooth transition leads to
smaller δf at freeze-out
=⇒ larger v 2
Ulrich Heinz CPTEIC, 31 Jan. 2012 49(43)

H 2 O: Hydro-to-OSCAR converter
Monte-Carlo interface that samples hydrodynamic Cooper-Frye spectra (including viscous
correction δf) on conversion surface to generate particles at positions x µ i with momenta
p µ i for subsequent propagation in UrQMD (or any other OSCAR-compatible hadron cascade
afterburner)
Song, Bass, Heinz, PRC 83 (2011) 024912
200 AGeV Au+Au, b = 0
200 AGeV Au+Au, b = 7fm
15
T dec
= 130 MeV
η/s = 0.08
0.2
VISH2+1: hydrodynamic results
H 2
O: statistical results for 500000 events
80
VISH2+1: hydro results
H 2
O: statistical results
0.15
τ (fm/c)
10
dN/dτ
60
40
v 2
0.1
η/s = 0.08
5
0
20
0
0 5 10 15
τ (fm/c)
0 2 4 6 8 10
r (fm)
0.05
π K p
Au+Au, b = 7 fm; SM-EOSQ
T dec
= 130 MeV
0
0 0.5 1 1.5 2
p T
(GeV)
(b)
Ulrich Heinz CPTEIC, 31 Jan. 2012 50(43)

VISHNU: hydro (VISH2+1) + cascade (UrQMD) hybrid
Sensitivity to H 2 O switching temperature:
With chemically frozen EOS (s95p-PCE),
p T -spectra show very little sensitivity to T sw (Teaney, 2000):
Song, Bass, Heinz, PRC 83 (2011) 024912
200 AGeV Au+Au, b = 7fm
dN/dyp T
dp T
(GeV -2 )
100
1
0.01
π
p X0.2
(a)
hydro + UrQMD; T sw
η/s = 0.08 165 MeV
140 MeV
120 MeV
100 MeV
s95p-PCE
0 0.5 1 1.5 2
p T
(GeV)
Ulrich Heinz CPTEIC, 31 Jan. 2012 51(43)

VISHNU: hydro (VISH2+1) + cascade (UrQMD) hybrid
Sensitivity to H 2 O switching temperature:
With chemically frozen EOS (s95p-PCE),
p T -spectra show very little sensitivity to T sw
Song, Bass, Heinz, PRC 83 (2011) 024912
but v 2 does:
200 AGeV Au+Au, b = 7fm
200 AGeV Au+Au, b = 7fm
dN/dyp T
dp T
(GeV -2 )
100
1
0.01
π
p
(a)
hydro + UrQMD; T sw
η/s = 0.08 165 MeV π
140 MeV
120 MeV
100 MeV
X0.2 p X0.2
s95p-PCE
0 0.5 1 1.5 2
p T
(GeV)
(b)
s95p-PCE
hydro + UrQMD; T sw
(1)
(η/s) (T) 165 MeV
140 MeV
120 MeV
100 MeV
0 0.5 1 1.5 2 2.5
p T
(GeV)
0.05
0.045
0.04
v 2
Glauber initialization 0.4 (a)
(1)
Au+Au, b=7 fm 0.32 (η/s) (T)
s95p-PCE 0.24
0.16
(a)
(b) η/s=0.08
0.08
0
120 140 160 180
T sw
(MeV)
Hydro(η/s) + UrQMD
with different T sw
(b)
100 120 140 160
T sw
(MeV)
Viscous hydro with fixed η/s = 0.08 generates more v 2 below T c than does UrQMD
=⇒ UrQMD is more dissipative
VISH2+1 simulation of UrQMD dynamics requires T-dependent (η/s)(T) that increases
towards lower temperature
Ulrich Heinz CPTEIC, 31 Jan. 2012 52(43)

Is there a switching window in which UrQMD can be simulated by
viscous hydro?
Unfortunately NO!
Song, Bass, Heinz, PRC 83 (2011) 2011
0.4
0.32
HRG QGP
(1)
( η/s) (T)
(2)
( η/s) (T)
(3)
( η/s) (T)
η/s
0.24
0.16
0.08
0
100 120 140 160 180 200 220
T (MeV)
(η/s)(T) extracted by trying to reproduce v 2 independent of switching temperature
depends on δ f input into UrQMD from hadronizing QGP
=⇒ δf relaxes too slowly in UrQMD to be describable by viscous Israel-Stewart hydro
=⇒ extracted (η/s)(T) not a proper UrQMD transport coefficient
=⇒ UrQMD dynamics can’t be described by viscous Israel-Stewart hydrodynamics
Ulrich Heinz CPTEIC, 31 Jan. 2012 53(43)