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The quark-gluon plasma shear viscosity from RHIC to LHC Ulrich Heinz Department of Physics The Ohio State University 191 West Woodruff Avenue Columbus, OH 43210 presented at University of Crete, Heraklion, Sep. 4, 2011

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SLIDE 1

The quark-gluon plasma shear viscosity from RHIC to LHC∗

Ulrich Heinz

Department of Physics The Ohio State University 191 West Woodruff Avenue Columbus, OH 43210

presented at

University of Crete, Heraklion, Sep. 4, 2011

——————————————————– Work done in collaboration with S.A. Bass, T. Hirano, P. Huovinen, Zhi Qiu, Chun Shen, and H. Song

∗Supported by the U.S. Department of Energy (DOE)

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SLIDE 2

Prologue: How to measure (η/s)QGP

Hydrodynamics converts spatial deformation of initial state = ⇒ momentum anisotropy of final state, through anisotropic pressure gradients Shear viscosity degrades conversion efficiency εx =

y2−x2

  • y2+x2

=

⇒ εp = T xx−T yy

T xx+T yy

  • f the fluid; the suppression of εp is monoto-

nically related to η/s.

1 2 3 4 5 6 7 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 p (f m /c) ideal /s = 0.08 /s = 0.16 /s = 0.24 Au+Au RHIC 20~30%

The observable that is most directly related to the total hydrodynamic momentum anisotropy εp is the total (pT-integrated) charged hadron elliptic flow vch

2 :

εp = T xx−T yy T xx+T yy ⇐ ⇒

  • i
  • pTdpT
  • dφp p2

T cos(2φp) dNi dypT dpT dφp

  • i
  • pTdpT
  • dφp p2

T dNi dypT dpT dφp

⇐ ⇒ vch

2

Ulrich Heinz Heraklion, Sep.4, 2011 1(15)

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SLIDE 3

Prologue: How to measure (η/s)QGP (ctd.)

  • If εp saturates before hadronization (e.g. in PbPb@LHC (?))

⇒ vch

2 ≈ not affected by details of hadronic rescattering below Tc

but: v(i)

2 (pT), dNi dyd2pT change during hadronic phase (addl. radial flow!), and these

changes depend on details of the hadronic dynamics (chemical composition etc.) ⇒ v2(pT) of a single particle species not a good starting point for extracting η/s

  • If εp does not saturate before hadronization (e.g. AuAu@RHIC), dissipative hadronic

dynamics affects not only the distribution of εp over hadronic species and in pT, but even the final value of εp 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, Heinz, PRC83 (2011) 024912) Note: this paper shows that UrQMD = viscous hydro!

Ulrich Heinz Heraklion, Sep.4, 2011 2(15)

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SLIDE 4

Extraction of (η/s)QGP from AuAu@RHIC

  • H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301

10 20 30 40 (1/S) dNch/dy (fm

  • 2)

0.05 0.1 0.15 0.2 0.25

v2/ε

0.0 0.4 810 0.08 0.6 810 0.16 0.9 810 0.24 0.9 810

. . . . hydro (η/s)+UrQMD

η/s τ0 dN/dy

Glauber / KLN

(fm/c) max.

0.16 0.9 810 0.24 1.2 810 0.08 0.6 810 0.0 0.4 810

η/s 0.0 0.08 0.16 0.24

10 20 30 (1/S) dNch/dy (fm

  • 2)

0.05 0.1 0.15 0.2 0.25

v2/ε

10 20 30 40 (1/S) dNch/dy (fm

  • 2)

hydro (η/s) + UrQMD hydro (η/s) + UrQMD

MC-Glauber MC-KLN

0.0 0.08 0.16 0.24 0.0 0.08 0.16 0.24 η/s η/s v2{2} / 〈ε

2 part〉 1/2 Gl

(a) (b)

〈v2〉 / 〈εpart〉Gl v2{2} / 〈ε

2 part〉 1/2 KLN

〈v2〉 / 〈εpart〉KLN

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 pT -spectra of charged hadrons, pions and protons at all centralities

  • vch

2 /εx vs. (1/S)(dNch/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: εGl

x

  • vs. εKLN

x

− →

  • smaller effects: early flow → increases v2

ε by ∼ few % → larger η/s

bulk viscosity → affects vch

2 (pT ), but ≈ not vch 2

Zhi Qiu & UH, PRC84 (2011) 024911

Ulrich Heinz Heraklion, Sep.4, 2011 3(15)

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SLIDE 5

Extraction of (η/s)QGP from AuAu@RHIC

  • H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301

10 20 30 40 (1/S) dNch/dy (fm

  • 2)

0.05 0.1 0.15 0.2 0.25

v2/ε

0.0 0.4 810 0.08 0.6 810 0.16 0.9 810 0.24 0.9 810

. . . . hydro (η/s)+UrQMD

η/s τ0 dN/dy

Glauber / KLN

(fm/c) max.

0.16 0.9 810 0.24 1.2 810 0.08 0.6 810 0.0 0.4 810

η/s 0.0 0.08 0.16 0.24

10 20 30 (1/S) dNch/dy (fm

  • 2)

0.05 0.1 0.15 0.2 0.25

v2/ε

10 20 30 40 (1/S) dNch/dy (fm

  • 2)

hydro (η/s) + UrQMD hydro (η/s) + UrQMD

MC-Glauber MC-KLN

0.0 0.08 0.16 0.24 0.0 0.08 0.16 0.24 η/s η/s v2{2} / 〈ε

2 part〉 1/2 Gl

(a) (b)

〈v2〉 / 〈εpart〉Gl v2{2} / 〈ε

2 part〉 1/2 KLN

〈v2〉 / 〈εpart〉KLN

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 pT -spectra of charged hadrons, pions and protons at all centralities

  • vch

2 /εx vs. (1/S)(dNch/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: εGl

x

  • vs. εKLN

x

  • smaller effects: early flow → increases v2

ε by ∼ few % → larger η/s

bulk viscosity → affects vch

2 (pT ), but ≈ not vch 2

e-by-e hydro → decreases

vch 2 ε

by <

∼ 5% → smaller η/s

Zhi Qiu & UH, PRC84 (2011) 024911

2 4 6 8 10 12 14 0.1 0.15 0.2 0.25 0.3 0.35

π

p K

b (fm)

v2/ε2

ideal hydro, MC−KLN single-shot, v2/¯ εpart e-by-e, v2/¯ εpart

Ulrich Heinz Heraklion, Sep.4, 2011 4(15)

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SLIDE 6

Global description of AuAu@RHIC spectra and v2

VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC 83 (2011) 054910)

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10 10 1 10 2 10 3 /s = 0.0 (ideal hy dro) /s = 0.08 /s = 0.16 /s = 0.24 40%~60%/10 20%~40% 10%~20%*10 0%~10%*10 2 PHENIX STAR M C-KLN M C-Glauber p T (GeV) + 70%~80%/10 6 60%~70%/10 5 50%~60%/10 4 40%~50%/10 3 30%~40%/10 2 20%~30%/10 15%~20%*1 10%~15%*10 5%~10%*10 2 0%~5%*10 3 (a) 60%~80%/10 2 dN/(2 dy p T dp T ) (GeV
  • 2
) dN/(2 dy p T dp T ) (GeV
  • 2
) p T (GeV) p (b) 0.0 0.4 0.8 1.2 1.6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.0 0.4 0.8 1.2 1.6 2.0 s = 0.08 s = 0.16 v 2 / p T (GeV) MC-Glauber initialization 200 A GeV Au+Au charged hadrons MC-KLN initialization (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%) s = 0.16 s = 0.24 p T (GeV) VISHNU PHENIX v 2 {EP}
  • (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 v2(pT) at all collision centralities

Ulrich Heinz Heraklion, Sep.4, 2011 5(15)

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SLIDE 7

Global description of AuAu@RHIC spectra and v2

VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC 83 (2011) 054910)

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10 10 1 10 2 10 3 /s = 0.0 (ideal hy dro) /s = 0.08 /s = 0.16 /s = 0.24 40%~60%/10 20%~40% 10%~20%*10 0%~10%*10 2 PHENIX STAR M C-KLN M C-Glauber p T (GeV) + 70%~80%/10 6 60%~70%/10 5 50%~60%/10 4 40%~50%/10 3 30%~40%/10 2 20%~30%/10 15%~20%*1 10%~15%*10 5%~10%*10 2 0%~5%*10 3 (a) 60%~80%/10 2 dN/(2 dy p T dp T ) (GeV
  • 2
) dN/(2 dy p T dp T ) (GeV
  • 2
) p T (GeV) p (b) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 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 (5-10%)+ 0.6 (20-30%)+ 0.4 (30-40%)+ 0.2 (40-50%) v 2 / s = 0.08 /s = 0.16 STAR v 2 {2} M C-Glauber initializ ation M C-Glauber initializ ation VISHNU Au + Au 200 A GeV s = 0.16 /s = 0.24 v 2 / p T (GeV) MC-KLN initialization p p p T (GeV) MC-KLN initialization
  • (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 v2(pT ) 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 v2(pT )) = ⇒ Shen et al., arXiv:1105.3226

  • Main difference: VISHNU develops more radial flow in the hadronic phase (larger shear viscosity), pure viscous hydro must

start earlier than VISHNU (τ0 = 0.6 instead of 0.9 fm/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 v2

Ulrich Heinz Heraklion, Sep.4, 2011 6(15)

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SLIDE 8

Pre- and postdictions for PbPb@LHC

VISHNU with MC-KLN (Song, Bass, Heinz, PRC 83 (2011) 054912)

100 200 300 400 Npart 2 4 6 8 (dNch/dη)/(Npart/2) LHC: η/s=0.16 LHC: η/s=0.20 LHC:η/s=0.24 RHIC: η/s=0.16 100 200 300 400 Npart 2 4 6 8 (dNch/dη)/(Npart/2) Au+Au 200 A GeV: STAR Pb+Pb 2.76 A TeV: ALICE Au+Au 200 A GeV: PHOBOS MC-KLN reaction plane (b)

0.5 1 1.5 2 pT(GeV) 0.1 0.2 0.3 0.4 v2

RHIC: η/s=0.16 LHC: η/s=0.16 LHC: η/s=0.20 LHC: η/s=0.24 STAR ALICE VISHNU MC-KLN 10-20% 20-30% 30-40% 40-50% +0.3 +0.1 +0.2 reaction plane v2{4}

20 40 60 80 centrality 0.02 0.04 0.06 0.08 0.1 v2 RHIC: η/s=0.16 LHC: η/s=0.16 LHC: η/s=0.20 LHC: η/s=0.24

STAR ALICE

v2{4}

MC-KLN

Reaction Plane

  • After normalization in 0-5% centrality collisions, MC-KLN + VISHNU (w/o running coupling, but

including viscous entropy production!) reproduces centrality dependence of dNch/dη well in both AuAu@RHIC and PbPb@LHC

  • (η/s)QGP = 0.16 for MC-KLN works well for charged hadron v2(pT) and integrated v2 in

AuAu@RHIC, but overpredicts both by about 10-15% in PbPb@LHC

  • Similar results from predictions based on pure viscous hydro =

⇒ Shen et al., arXiv:1105.3226

  • but: At LHC, we see significant sensitivity of v2 to initialization of viscous pressure tensor πµν (Navier-

Stokes or zero), and it is not excluded that it may be possible to bring down v2 at LHC to the ALICE data without increasing η/s at higher T (requires more study) = ⇒ QGP at LHC perhaps a bit, but not dramatically more viscous than at RHIC!

Ulrich Heinz Heraklion, Sep.4, 2011 7(15)

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SLIDE 9

Why is vch

2 (pT) the same at RHIC and LHC? Answer: Pure accident! (Kestin & Heinz EPJC61 (2009) 545)

  • C. Shen, U. Heinz, P. Huovinen, H. Song, arXiv:1105.3226
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 + p v 2 p T (GeV) RHIC LHC 20~30% AuAu@ PbPb@ MC-KLN, /s = 0.20

vπ

2 (pT ) increases a bit from RHIC to LHC, for heavier hadrons v2(pT ) at fixed pT decreases

(radial flow pushes momentum anisotropy of heavy hadrons to larger pT )

This is a hard (and successful!) prediction of hydrodynamics! (See also Nagle et al., arXiv:1102.0680)

Ulrich Heinz Heraklion, Sep.4, 2011 8(15)

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SLIDE 10

Confirmation of increased mass splitting at LHC

Data: ALICE @ LHC, Quark Matter 2011 (symbols), PHENIX @ RHIC (shaded) Lines: Shen et al.,arXiv:1105.3226 (VISH2+1)

  • Qualitative features of data agree with VISH2+1 predictions
  • VISH2+1 does not push proton v2 strongly enough to higher pT, both at RHIC and LHC
  • At RHIC we know that this is fixed when using VISHNU – is the same true at LHC?

Ulrich Heinz Heraklion, Sep.4, 2011 9(15)

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SLIDE 11

Successful prediction of v2(pT) for identified hadrons in PbPb@LHC

Data: ALICE, Quark Matter 2011 Lines: Shen et al., arXiv:1105.3226 (VISH2+1)

Perfect fit in semi-peripheral collisions! The problem with insufficient proton radial flow exists only in more central collisions = ⇒ hadronic cascade (VISHNU) may help!

Ulrich Heinz Heraklion, Sep.4, 2011 10(15)

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SLIDE 12

Comparison VISH2+1 . . .

Data: ALICE, preliminary (Snellings, Krzewicki, Quark Matter 2011) Lines: C. Shen et al., arXiv:1105.3226 (VISH2+1, MC-KLN, η/s=0.2)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 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 pion kaon anti-proton VISH2+1 ( /s = 0.20) v 2 5%~10% Pb+Pb @ 2.76 A TeV 10%~20% data: ALICE Preliminary 20%~30% v 2 p T (G e V) 30%~40% p T (G e V) 40%~50% p T (G e V) 50%~60%

Ulrich Heinz Heraklion, Sep.4, 2011 11(15)

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SLIDE 13

. . . vs. VISHNU

Data: ALICE, preliminary (Snellings, Krzewicki, Quark Matter 2011) Lines: UH, Shen, Song, arXiv:1108.5323 (VISHNU, MC-KLN, (η/s)QGP=0.2)

0.1 0.2 0.3 0.4 0.5 0.6 v

2/ε

Pb+Pb @ 2.76 A TeV 5%-10% pions kaons protons VISHNU 1 2 Pb+Pb @ 2.76 A TeV 10%-20% pions kaons protons VISHNU 1 2 0.1 0.2 0.3 0.4 0.5 0.6 Pb+Pb @ 2.76 A TeV 20%-30% pions kaons protons VISHNU 1 2

pT

(GeV) 0.1 0.2 0.3 0.4 0.5 0.6 v

2/ε

Pb+Pb @ 2.76 A TeV 30%-40% pions kaons protons VISHNU 1 2

pT

(GeV) Pb+Pb @ 2.76 A TeV 40%-50% pions kaons protons VISHNU 1 2

pT

(GeV) Pb+Pb @ 2.76 A TeV 50%-60% pions kaons protons VISHNU

  • VISHNU yields correct centrality dependence of v2(pT) for pions, kaons and protons!
  • v2(pT) slightly too low (by ∼ 5−10%, increasing with peripherality) for all particle

species = ⇒ (η/s)QGP=0.16 will probably work better

Ulrich Heinz Heraklion, Sep.4, 2011 12(15)

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SLIDE 14

Back to the elephant in the room: How to eliminate the large model uncertainty in the initial eccentricity?

Zhi Qiu and U. Heinz, PRC84 (2011) 024911

5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 b (fm)

ε3

(b) ε3(e) (MC-KLN) ε3(s) (MC-KLN) ε3(e) (MC-Glb) ε3(s) (MC-Glb) 5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 b (fm)

ε4

(c) ε4(e) (MC-KLN) ε4(s) (MC-KLN) ε4(e) (MC-Glb) ε4(s) (MC-Glb) 5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 b (fm)

ε5

(d) ε5(e) (MC-KLN) ε5(s) (MC-KLN) ε5(e) (MC-Glb) ε5(s) (MC-Glb)

Initial eccentricities εn and angles ψn: εneinψn = −

rdrdφ r2einφ e(r,φ)

  • rdrdφ r2 e(r,φ)
  • MC-KLN has larger ε2 and ε4, but

similar ε5 and almost identical ε3 as MC-Glauber

  • Angles of ε2 and ε4 are correlated

with reaction plane by geometry, whereas those

  • f

ε3 and ε5 are random (purely fluctuation-driven)

  • While v4 and v5 have mode-coupling

contributions from ε2, v3 is almost pu- re response to ε3 and v3/ε3 ≈ const.

  • ver a wide range of centralities

(for details see PRC84 (2011) 024911)

= ⇒ Idea: Use total charged hadron vch

3 to determine (η/s)QGP,

then check vch

2 to distinguish between MC-KLN and MC-Glauber! Ulrich Heinz Heraklion, Sep.4, 2011 13(15)

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SLIDE 15

Shooting the elephant

Zhi Qiu & U. Heinz, arXiv:1108.1714

0.2 0.4 0.6 0.8 1.0 2 4 6 8 10 12 14

pT (GeV) v2 (%)

Au+Au @ RHIC, 20-30% MC-KLN-like, , η/s = 0.22 MC-Glb.-like, η/s = 0.11 MC-Glb.-like, η/s = 0.22 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5

pT (GeV) v3(%)

Au+Au @ RHIC, 20-30% MC-KLN-like, η/s = 0.22 MC-Glb.-like, η/s = 0.22 MC-Glb.-like, η/s = 0.11

Proof of principle calculation:

  • Take ensemble of sum of deformed Gaussian profiles,

s(r⊥) = s2(r⊥; ˜ ε2, ψ2) + s3(r⊥; ˜ ε3, ψ3), with

  • 1. equal Gaussian radii R2

2 = R2 3 = 8 fm2 to reproduce r2 ⊥ of MC-KLN

source for 20-30% AuAu

  • 2. ˜

ε2 and ˜ ε3 adjusted such that

  • ¯

ε2,3 = ε2,320−30%

KLN

(“MC-KLN-like”)

  • ¯

ε2,3 = ε2,320−30%

Gl

(“MC-Glauber-like”)

  • 3. ψ2 = 0, ψ3 (direction of triangularity) distributed randomly
  • Use vπ

2 (pT ) from VISH2+1 for η/s = 0.20 with MC-KLN initial conditions

for 20-30% AuAu as “mock data”

  • Fit mock vπ

2 (pT ) data with VISH2+1 for “MC-Glauber-like” or “MC-KLN-

like” Gaussian initial conditions with both elliptic and triangular deformations by adjusting η/s = ⇒ (η/s)KLN = 0.22 for “MC-KLN-like”, (η/s)Gl = 0.11 for “MC-Glauber-like”

  • Compute vπ

3 (pT ) for “MC-KLN-like” fit with (η/s)Gl=0.22 and reproduce

it with “MC-Glauber-like” initial condition by readjusting η/s = ⇒ (η/s)v3

Gl = 0.22 for “MC-Glauber-like”

  • Compute vπ

2 (pT ) for “MC-Glauber-like” initial profiles with readjusted

(η/s)v3

Gl = 0.224 and compare with “MC-Glauber-like” fit to original

mock data = ⇒ clearly visible (and measurable) difference!

This exercise proves: (i) Fitting v3 data with MC-Glauber and MC-KLN initial conditions yields the same η/s (within narrow error band); (ii) The corresponding v2 fits are quite different, and only one (more precisely: at most one!) of the models will fit the corresponding v2(pT) data.

Ulrich Heinz Heraklion, Sep.4, 2011 14(15)

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SLIDE 16

Conclusions

  • Hybrid codes (e.g. VISHNU) that couple viscous hydro evolution of QGP to microscopic hadron

cascade now allow a determination of (η/s)QGP with O(25%) precision if the initial fireball eccentricity is known to better than 5% relative accuracy

  • With VISHNU good global fits that describe all single-particle observables for soft hadron

production (spectra, elliptic flow) at all but the most peripheral AuAu collision centralities are

  • btained, for both MC-Glauber and MC-KLN initial conditions, by using (η/s)QGP = 0.08

for MC-Glauber and (η/s)QGP = 0.16−0.20 for MC-KLN. This appears to carry over to PbPb@LHC.

  • Event-by-event ideal hydrodynamics with fluctuating initial conditions yields somewhat less

v2/ε2 than single-shot hydro with smooth average initial profiles = ⇒ Event-by-event hydro may be necessary for a precise extraction of (η/s)QGP from charged hadron v2. Depending on (η/s)QGP, event-by-event hydro can matter a lot for proton v2.

  • While MC-Glauber and MC-KLN give ε2 that differ by 20-25%, they give almost identical

ε3 (which is not geometric but fluctuation-driven). Only one of them will be able to fit simultaneously both v2 and v3 (analysis in progress).

  • This should enable us to gain the necessary control over initial conditions to make a precise (i.e.

much better than factor 2) measurement of (η/s)QGP.

Ulrich Heinz Heraklion, Sep.4, 2011 15(15)

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SLIDE 17

Supplements

Ulrich Heinz Heraklion, Sep.4, 2011 16(15)

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SLIDE 18

Global description of AuAu@RHIC spectra and v2

VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC 83 (2011) 054910)

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10
  • 1
10 10 1 10 2 10 3 /s = 0.0 (ideal hy dro) /s = 0.08 /s = 0.16 /s = 0.24 40%~60%/10 20%~40% 10%~20%*10 0%~10%*10 2 PHENIX STAR M C-KLN M C-Glauber p T (GeV) + 70%~80%/10 6 60%~70%/10 5 50%~60%/10 4 40%~50%/10 3 30%~40%/10 2 20%~30%/10 15%~20%*1 10%~15%*10 5%~10%*10 2 0%~5%*10 3 (a) 60%~80%/10 2 dN/(2 dy p T dp T ) (GeV
  • 2
) dN/(2 dy p T dp T ) (GeV
  • 2
) p T (GeV) p (b) 0.0 0.4 0.8 1.2 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 0.0 0.4 0.8 1.2 1.6 2.0 s = 0.08 s = 0.16 v 2 / p T (GeV) MC-Glauber initialization 200 A GeV Au+Au charged hadrons MC-KLN initialization (0-5%)+1.6 (5-10%)+1.4 (10-20%)+1.2 (20-30%)+1.0 (30-40%)+0.8 (40-50%)+0.6 (50-60%)+0.4 (60-70%)+0.2 (70-80%) s = 0.16 s = 0.24 p T (GeV) VISHNU STAR v 2 {EP}
  • (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 v2(pT) at all collision centralities

Ulrich Heinz Heraklion, Sep.4, 2011 17(15)

slide-19
SLIDE 19

s95p-PCE: A realistic, lattice-QCD-based EOS

Huovinen, Petreczky, NPA 837 (2010) 26 Shen, Heinz, Huovinen, Song, PRC 82 (2010) 054904

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 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 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 p (GeV/fm 3 ) s95p-PCE SM-EOS Q EOS L c 2 S e (GeV/fm 3 )

High T : Lattice QCD (latest hotQCD results) Low T : Chemically frozen HRG (Tchem = 165 MeV) No softest point!

Ulrich Heinz Heraklion, Sep.4, 2011 18(15)

slide-20
SLIDE 20

s95p-PCE: A realistic, lattice-QCD-based EOS

Huovinen, Petreczky, NPA 837 (2010) 26 Shen, Heinz, Huovinen, Song, PRC 82 (2010) 054904

1E-4 1E-3 0.01 0.1 1 10 100 1000 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 central Au+Au (b = 2.33 fm) 1/2 *dN/(dyp T dp T ) PHENIX data s95p-PCE SM
  • EOS Q
EOS L p/10 Au+Au 20~30% (b = 7.5 fm ) v 2 /s = 0.16 T de c = 140 M eV = 0.4 fm /c CGC initializ ation Au+Au 20~30% (b = 7.5 fm ) v 2 p T (GeV) charged hadrons s95p-PCE with
  • u
t f SM-EOS Q with
  • u
t f EOS L with
  • u
t f Au+Au 20~30% (b = 7.5 fm ) v 2 p T (GeV) p

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 v2

Ulrich Heinz Heraklion, Sep.4, 2011 19(15)

slide-21
SLIDE 21

H2O: 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 xµ

i with momenta

pµ

i for subsequent propagation in UrQMD (or any other OSCAR-compatible hadron cascade

afterburner)

Song, Bass, Heinz, PRC 83 (2011) 024912 200 A GeV Au+Au, b = 0 2 4 6 8 10 r (fm) 5 10 15 τ (fm/c)

5 10 15 τ (fm/c) 20 40 60 80 dN/dτ VISH2+1: hydro results H2O: statistical results

Tdec = 130 MeV η/s = 0.08

200 A GeV Au+Au, b = 7 fm

0.5 1 1.5 2 pT(GeV) 0.05 0.1 0.15 0.2

v

2

VISH2+1: hydrodynamic results H2O: statistical results for 500000 events π

K p Au+Au, b = 7 fm; SM-EOSQ Tdec = 130 MeV η/s = 0.08

(b)

Ulrich Heinz Heraklion, Sep.4, 2011 20(15)

slide-22
SLIDE 22

VISHNU: hydro (VISH2+1) + cascade (UrQMD) hybrid Sensitivity to H2O switching temperature:

With chemically frozen EOS (s95p-PCE), pT-spectra show very little sensitivity to Tsw (Teaney, 2000):

Song, Bass, Heinz, PRC 83 (2011) 024912 200 A GeV Au+Au, b = 7 fm

0.5 1 1.5 2 pT(GeV) 0.01 1 100 dN/dypTdpT(GeV

  • 2)

π p

X0.2 140 MeV 165 MeV 120 MeV 100 MeV

s95p-PCE hydro + UrQMD; Tsw

(a)

η/s = 0.08

Ulrich Heinz Heraklion, Sep.4, 2011 21(15)

slide-23
SLIDE 23

VISHNU: hydro (VISH2+1) + cascade (UrQMD) hybrid Sensitivity to H2O switching temperature:

With chemically frozen EOS (s95p-PCE), pT-spectra show very little sensitivity to Tsw but v2 does:

Song, Bass, Heinz, PRC 83 (2011) 024912 200 A GeV Au+Au, b = 7 fm

0.5 1 1.5 2 pT(GeV) 0.01 1 100 dN/dypTdpT(GeV

  • 2)

0.5 1 1.5 2 2.5 pT(GeV) π p π p

X0.2 X0.2 140 MeV 165 MeV 120 MeV 100 MeV

s95p-PCE hydro + UrQMD; Tsw

165 MeV 120 MeV

hydro + UrQMD; Tsw

(b) (a)

100 MeV 140 MeV

s95p-PCE η/s = 0.08 (η/s) (T)

(1)

200 A GeV Au+Au, b = 7 fm

100 120 140 160 Tsw(MeV) 0.04 0.045 0.05

v2

120 140 160 180 Tsw(MeV) 0.08 0.16 0.24 0.32 0.4

Au+Au, b=7 fm

(η/s) (T)

(1)

s95p-PCE

with different Tsw Hydro(η/s) + UrQMD

(a) (b) (a)

Glauber initialization

η/s=0.08 (b)

Viscous hydro with fixed η/s = 0.08 generates more v2 below Tc 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 Heraklion, Sep.4, 2011 22(15)

slide-24
SLIDE 24

Is there a switching window in which UrQMD can be simulated by viscous hydro?

Unfortunately NO!

Song, Bass, Heinz, PRC 83 (2011) 2011

100 120 140 160 180 200 220

T (MeV)

0.08 0.16 0.24 0.32 0.4

η/s

HRG QGP

η ( /s) (T)

(3)

η ( /s) (T)

(2)

η ( /s) (T)

(1)

(η/s)(T) extracted by trying to reproduce v2 independent of switching temperature depends on δf 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 Heraklion, Sep.4, 2011 23(15)

slide-25
SLIDE 25

Smearing effects from nucleon growth at high energies

  • U. Heinz & Scott Moreland, arXiv:1108.5379
  • 6
  • 4
  • 2

2 4 6 x (fm)

  • 6
  • 4
  • 2

2 4 6 y (fm) 200 GeV Disk 10 20 30 40 50 60

  • 6
  • 4
  • 2

2 4 6 x (fm)

  • 6
  • 4
  • 2

2 4 6 y (fm) 200 GeV Gauss 5 10 15 20 25 30 35 40 45 50

  • 6
  • 4
  • 2

2 4 6 x (fm)

  • 6
  • 4
  • 2

2 4 6 y (fm) 2.76 TeV Gauss 10 20 30 40 50 60 70 80 90 100

23.5 GeV

  • 8
  • 6
  • 4
  • 2

2 4 6 8 y (fm) 2 4 6 8 10 12 14 16 200 GeV 5 10 15 20 25 30 35 40 45 50 2.76 TeV

  • 8 -6 -4 -2 0 2 4 6 8

x (fm)

  • 8
  • 6
  • 4
  • 2

2 4 6 8 y (fm) 10 20 30 40 50 60 70 80 90 100 7 TeV

  • 8 -6 -4 -2 0 2 4 6 8

x (fm) 20 40 60 80 100 120 Between √s = 23.5 and 7,000 GeV, nucleon area grows by factor O(2) = ⇒ significant smoothing of event-by-event density fluctuations from RHIC to LHC

Ulrich Heinz Heraklion, Sep.4, 2011 24(15)