vishnu – a dynamical evolution model for heavy-ion collisions...v 2 2 /s = 0.16 t dec = 140 mev 0...

VISHNU – a dynamical evolution

model for heavy-ion collisions∗

Ulrich HeinzDepartment of Physics

The Ohio State University191 West Woodruff Avenue

Columbus, OH 43210

presented at

HI Workshop II, 2011 RHIC & AGS Annual Users’ Meeting,Brookhaven National Laboratory, June 20–24, 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)

Prologue: How to measure (η/s)QGP

Hydrodynamics convertsspatial deformation of initial state =⇒momentum anisotropy of final state,through anisotropic pressure gradients

Shear viscosity degrades conversion efficiency

εx=〈〈y2−x2〉〉〈〈y2+x2〉〉

=⇒ εp=〈Txx−T yy〉〈Txx+T yy〉

of the fluid; the suppression of εp is monoto-nically related to η/s. 0 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

(fm/c)

ideal /s = 0.08 /s = 0.16 /s = 0.24

Au+Au RHIC20~30%

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

2 :

εp=〈T xx−T yy〉

〈T xx+T yy〉⇐⇒

∑i

∫pTdpT

∫dφp p

2T cos(2φp)

dNidypTdpTdφp∑

i

∫pTdpT

∫dφp p2T

dNidypTdpTdφp

⇐⇒ vch2

Ulrich Heinz RHIC&AGS Users’ Meeting, 6/20/2011 1(18)

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

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

⇒ vch2 ≈ not affected by details of hadronic rescattering below Tc

but: v(i)2 (pT ),

dNidyd2pT

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 hadronicdynamics affects not only the distribution of εp over hadronic species and in pT , buteven 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 realisticmicroscopic 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 6= viscous hydro!


s95p-PCE: A realistic, lattice-QCD-based EOSHuovinen, 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 6.00.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

p (G

eV/fm

3 )

s95p-PCE SM-EOS Q EOS L

c2 S

e (GeV/fm3)

High T : Lattice QCD (latest

hotQCD results)

Low T : Chemically frozen HRG

(Tchem = 165MeV)

No softest point!


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

Huovinen, Petreczky, NPA 837 (2010) 26Shen, 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 3.00.000.020.040.060.080.100.120.140.160.180.200.22

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

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

TdpT)

PHENIX data s95p-PCE SM-EOS Q EOS L

p/10

Au+Au 20~30% (b = 7.5 fm)

v 2

/s = 0.16Tdec = 140 MeV

0 = 0.4 fm/cCGC initialization

Au+Au 20~30% (b = 7.5 fm)

v 2

pT (GeV)

charged hadrons

s95p-PCE without f SM-EOS Q without f EOS L without f

Au+Au 20~30% (b = 7.5 fm)

v 2

pT (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


H2O: Hydro-to-OSCAR converter

Monte-Carlo interface that samples hydrodynamic Cooper-Frye spectra (including viscouscorrection δf) on conversion surface to generate particles at positions xµi with momentapµi for subsequent propagation in UrQMD (or any other OSCAR-compatible hadron cascadeafterburner)

Song, Bass, Heinz, PRC 83 (2011) 024912

200 AGeV Au+Au, b = 0

0 2 4 6 8 10r (fm)

0

5

10

15

τ (f

m/c

)

0 5 10 15τ (fm/c)

0

20

40

60

80

dN/d

τ

VISH2+1: hydro resultsH

2O: statistical results

Tdec

= 130 MeV

η/s = 0.08

200 AGeV Au+Au, b = 7 fm

0 0.5 1 1.5 2p

T(GeV)

0

0.05

0.1

0.15

0.2

v 2

VISH2+1: hydrodynamic resultsH

2O: statistical results for 500000 events

π K pAu+Au, b = 7 fm; SM-EOSQ

Tdec

= 130 MeV

η/s = 0.08

(b)


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):



0 0.5 1 1.5 2p

T(GeV)

0.01

1

100

dN/d

ypTdp

T(G

eV-2

) π

p X0.2

140 MeV165 MeV

120 MeV100 MeV

s95p-PCE

hydro + UrQMD; Tsw

(a)

η/s = 0.08


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:



0 0.5 1 1.5 2p

T(GeV)

0.01

1

100

dN/d

ypTdp

T(G

eV-2

)

0 0.5 1 1.5 2 2.5p

T(GeV)

π

p

π

pX0.2 X0.2

140 MeV165 MeV

120 MeV100 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)


100 120 140 160T

sw(MeV)

0.04

0.045

0.05

v2

120 140 160 180T

sw(MeV)

0

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 increasestowards lower temperature


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

Unfortunately NO!


100 120 140 160 180 200 220T (MeV)

0

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 temperaturedepends 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 hydrodynamicsUlrich Heinz RHIC&AGS Users’ Meeting, 6/20/2011 8(18)

Extraction of (η/s)QGP from AuAu@RHICH. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301

0 10 20 30 40(1/S) dN

ch/dy (fm

-2)

0

0.05

0.1

0.15

0.2

0.25

v 2/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/dyGlauber / KLN(fm/c) max.

0.16 0.9 8100.24 1.2 810

0.08 0.6 8100.0 0.4 810

η/s0.0

0.08

0.16

0.24

0 10 20 30(1/S) dN

ch/dy (fm

-2)

0

0.05

0.1

0.15

0.2

0.25

v 2/ε

0 10 20 30 40(1/S) dN

ch/dy (fm

-2)

hydro (η/s) + UrQMD hydro (η/s) + UrQMDMC-GlauberMC-KLN0.00.08

0.16

0.24

0.0

0.08

0.16

0.24

η/sη/s

v2{2} / ⟨ε2

part⟩1/2

Gl

(a) (b)

⟨v2⟩ / ⟨ε

part⟩Gl

v2{2} / ⟨ε2

part⟩1/2

KLN

⟨v2⟩ / ⟨ε

part⟩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 aspT -spectra of charged hadrons, pions and protons at all centralities

• vch2 /εx vs. (1/S)(dNch/dy) is “universal”, i.e. depends only onη/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: εGlx vs. εKLN

x −→

• smaller effects: early flow → increasesv2ε by ∼ few% → larger η/s

bulk viscosity → affects vch2 (pT ), but ≈ not vch2

Zhi Qiu, U. Heinz, arXiv:1104.0650


Extraction of (η/s)QGP from AuAu@RHICH. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301

0 10 20 30 40(1/S) dN

ch/dy (fm

-2)

0

0.05

0.1

0.15

0.2

0.25

v 2/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/dyGlauber / KLN(fm/c) max.

0.16 0.9 8100.24 1.2 810

0.08 0.6 8100.0 0.4 810

η/s0.0

0.08

0.16

0.24

0 10 20 30(1/S) dN

ch/dy (fm

-2)

0

0.05

0.1

0.15

0.2

0.25

v 2/ε

0 10 20 30 40(1/S) dN

ch/dy (fm

-2)

hydro (η/s) + UrQMD hydro (η/s) + UrQMDMC-GlauberMC-KLN0.00.08

0.16

0.24

0.0

0.08

0.16

0.24

η/sη/s

v2{2} / ⟨ε2

part⟩1/2

Gl

(a) (b)

⟨v2⟩ / ⟨ε

part⟩Gl

v2{2} / ⟨ε2

part⟩1/2

KLN

⟨v2⟩ / ⟨ε

part⟩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 aspT -spectra of charged hadrons, pions and protons at all centralities

• vch2 /εx vs. (1/S)(dNch/dy) is “universal”, i.e. depends only onη/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: εGlx vs. εKLN

x

• smaller effects: early flow → increasesv2ε by ∼ few% → larger η/s

bulk viscosity → affects vch2 (pT ), but ≈ not vch2

e-by-e hydro → decreasesvch2ε by <

∼ 5% → smaller η/s

Zhi Qiu, U, Heinz, arXiv:1104.0650

0 2 4 6 8 10 12 140.1

0.15

0.2

0.25

0.3

0.35

π+

p

b (fm)

v2/ε2

ideal hydro, MC−KLN

one-shot: v2/ε̄part (π+)e-by-e: 〈v2〉/ε̄part (π+)one-shot: v2/ε̄part (proton)e-by-e: 〈v2〉/ε̄part (proton)


Global description of AuAu@RHIC spectra and v2

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

0.0 0.5 1.0 1.5 2.010-11

10-9

10-7

10-5

10-3

10-1

101

103

105

107

0.0 0.5 1.0 1.5 2.010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

/s = 0.0 (ideal hydro)

/s = 0.08 /s = 0.16 /s = 0.24

40%~60%/10

20%~40%

10%~20%*10

0%~10%*102

PHENIX STAR MC-KLN MC-Glauber

pT (GeV)

+

70%~80%/106

60%~70%/105

50%~60%/104

40%~50%/103

30%~40%/102

20%~30%/10

15%~20%*1

10%~15%*10

5%~10%*102

0%~5%*103

(a)

60%~80%/102

dN/(2

dy

p T dp T) (

GeV

-2)

dN/(2

dy

p T dp T) (

GeV

-2)

pT (GeV)

p

(b)0.0 0.4 0.8 1.2 1.60

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/

pT (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

pT (GeV)

VISHNU PHENIX v2{EP}

• (η/s)QGP = 0.08 for MC-Glauber and (η/s)QGP = 0.16 for MC-KLN work well forcharged hadron, pion and proton spectra and v2(pT ) at all collision centralities




0.0 0.5 1.0 1.5 2.010-11

10-9

10-7

10-5

10-3

10-1

101

103

105

107

0.0 0.5 1.0 1.5 2.010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103


/s = 0.08 /s = 0.16 /s = 0.24

40%~60%/10

20%~40%

10%~20%*10

0%~10%*102


pT (GeV)

+

70%~80%/106

60%~70%/105

50%~60%/104

40%~50%/103

30%~40%/102

20%~30%/10

15%~20%*1

10%~15%*10

5%~10%*102

0%~5%*103

(a)

60%~80%/102

dN/(2

dy

p T dp T) (

GeV

-2)

dN/(2

dy

p T dp T) (

GeV

-2)

pT (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 v2{2}



VISHNU

Au + Au 200 A GeV s = 0.16 /s = 0.24

v 2/

pT (GeV)


p

p

pT (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 protonspectra 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 forcentrality dependence of proton v2(pT ))

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


Pre- and postdictions for PbPb@LHCVISHNU with MC-KLN (Song, Bass, Heinz, PRC 83 (2011) 054912)

0 100 200 300 400N

part

0

2

4

6

8

(dN

ch/d

η)/

(Npart/2

)

LHC: η/s=0.16LHC: η/s=0.20LHC:η/s=0.24RHIC: η/s=0.16

0 100 200 300 400N

part

0

2

4

6

8

(dN

ch/d

η)/

(Npart/2

)

Au+Au 200 A GeV: STARPb+Pb 2.76 A TeV: ALICE

Au+Au 200 A GeV: PHOBOS

MC-KLNreaction plane

(b)

0 0.5 1 1.5 2p

T(GeV)

0

0.1

0.2

0.3

0.4

v2

RHIC: η/s=0.16LHC: η/s=0.16LHC: η/s=0.20LHC: η/s=0.24

STARALICE

VISHNU

MC-KLN

10-20%

20-30%

30-40%

40-50%

+0.3

+0.1

+0.2

reaction plane

v2{4}

0 20 40 60 80centrality

0

0.02

0.04

0.06

0.08

0.1

v2

RHIC: η/s=0.16LHC: η/s=0.16LHC: η/s=0.20LHC: η/s=0.24

STAR

ALICEv

2{4}

MC-KLNReaction 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!


Why is vch2 (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

pT (GeV)

RHIC LHC

20~30%

AuAu@ PbPb@ MC-KLN, /s = 0.20

vπ2 (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 prediction of hydrodynamics! (See also Nagle, Bearden, Zajc, arXiv:1102.0680)


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

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

Perfect fit in semi-peripheral collisions, but not enough proton radial flow in centralcollisions =⇒ hadronic cascade (VISHNU) may help


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

Zhi Qiu and U. Heinz, arXiv:1104.0650

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

b (fm)

ε 3

(b)〈ε3(e)〉 (MC-KLN)〈ε3(s)〉 (MC-KLN)〈ε3(e)〉 (MC-Glb)〈ε3(s)〉 (MC-Glb)

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

b (fm)

ε 4

(c)〈ε4(e)〉 (MC-KLN)〈ε4(s)〉 (MC-KLN)〈ε4(e)〉 (MC-Glb)〈ε4(s)〉 (MC-Glb)

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

b (fm)

ε 5

(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, butsimilar ε5 and almost identical ε3 as

MC-Glauber

• Angles of ε2 and ε4 are correlatedwith reaction plane by geometry,

whereas those of ε3 and ε5 arerandom (purely fluctuation-driven)

• While v4 and v5 have mode-couplingcontributions from ε2, v3 is almost pu-re response to ε3 and v3/ε3 ≈ const.

over a wide range of centralities(for details see arXiv:1104.0650)

=⇒ Idea: Use total charged hadron vch3 to determine (η/s)QGP,

then check vch2 to distinguish between MC-KLN and MC-Glauber!


Shooting the elephant

Zhi Qiu and U. Heinz, to be published

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

pT (GeV)

v 2(%

)

Au+Au @ RHIC, 20-30%

MC-KLN, η/s = 0.20MC-KLN-like, η/s = 0.217 ± 0.005MC-Glb.-like, η/s = 0.111 ± 0.001MC-Glb.-like, η/s = 0.224 ± 0.005

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

pT (GeV)

v 3(%

)

Au+Au @ RHIC, 20-30%

MC-KLN-like, η/s = 0.217MC-Glb.-like, η/s = 0.224 ± 0.005MC-Glb.-like, η/s = 0.111 ± 0.001

Proof of principle calculation:

• Take ensemble of sum of deformed Gaussian profiles,s(r⊥) = s2(r⊥; ε̃2, ψ2) + s3(r⊥; ε̃3, ψ3), with

1. equal Gaussian radii R22 = R2

3 = 8 fm2 to reproduce 〈r2⊥〉 of MC-KLN

source for 20-30% AuAu2. ε̃2 and ε̃3 adjusted such that

- ε̄2,3 = 〈ε2,3〉20−30%KLN

(“MC-KLN-like”)

- ε̄2,3 = 〈ε2,3〉20−30%Gl

(“MC-Glauber-like”)3. ψ2 = 0, ψ3 (direction of triangularity) distributed randomly

• Use vπ2 (pT ) from VISH2+1 for η/s = 0.20 with MC-KLN initial conditions

for 20-30% AuAu as “mock data”

• Fit mock vπ2 (pT ) data with VISH2+1 for “MC-Glauber-like” or “MC-KLN-

like” Gaussian initial conditions with both elliptic and triangular deformationsby adjusting η/s=⇒ (η/s)KLN = 0.217± 0.005 for “MC-KLN-like”,

(η/s)Gl = 0.111± 0.001 for “MC-Glauber-like”

• Compute vπ3 (pT ) for “MC-KLN-like” fit with (η/s)Gl=0.217 and repro-duce it with “MC-Glauber-like” initial condition by readjusting η/s=⇒ (η/s)

v3Gl

= 0.224± 0.005 for “MC-Glauber-like”

• Compute vπ2 (pT ) for “MC-Glauber-like” initial profiles with readjusted

(η/s)v3Gl

= 0.224 and compare with “MC-Glauber-like” fit to originalmock data =⇒ clearly visible (and measurable) difference!

This exercise proves: (i) Fitting v3(pT ) data with MC-Glauber and MC-KLN initial conditions yields the

same η/s (within narrow error band); (ii) The corresponding v2(pT) fits are quite different, and only one

(more precisely: at most one!) of the models will fit the corresponding v2(pT ) data.


Conclusions

• Hybrid codes (e.g. VISHNU) that couple viscous hydro evolution of QGPto microscopic hadron cascade now allow a determination of (η/s)QGP withO(25%) precision if the initial fireball eccentricity is known to better than5% relative accuracy

• With VISHNU good global fits that describe all single-particle observablesfor soft hadron production (spectra, elliptic flow) at all but the mostperipheral AuAu collision centralities are obtained, for both MC-Glauber andMC-KLN initial conditions, by using (η/s)QGP = 0.08 for MC-Glauber and(η/s)QGP = 0.16−0.20 for MC-Glauber

• Event-by-event hydrodynamics with fluctuating initial conditions yields some-what less v2/ε2 than single-shot hydro with smooth average initial profiles =⇒this will bring (η/s)QGP from charged hadrons down by ∼ 0.02 − 0.03. Forproton v2, event-by-event hydro matters a lot.

• While MC-Glauber and MC-KLN give ε2 that differ by 20-25%, they givealmost identical ε3 (which is not geometric but fluctuatiuon-driven). Only oneof them will be able to fit simultaneously both v2 and v3.

• This may be enable us to gain the necessary control over initial conditions tomake a precise (i.e. better than factor 2) measurement of (η/s)QGP.


Supplements




0.0 0.5 1.0 1.5 2.010-11

10-9

10-7

10-5

10-3

10-1

101

103

105

107

0.0 0.5 1.0 1.5 2.010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103


/s = 0.08 /s = 0.16 /s = 0.24

40%~60%/10

20%~40%

10%~20%*10

0%~10%*102


pT (GeV)

+

70%~80%/106

60%~70%/105

50%~60%/104

40%~50%/103

30%~40%/102

20%~30%/10

15%~20%*1

10%~15%*10

5%~10%*102

0%~5%*103

(a)

60%~80%/102

dN/(2

dy

p T dp T) (

GeV

-2)

dN/(2

dy

p T dp T) (

GeV

-2)

pT (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/

pT (GeV)

MC-Glauber initialization200 A GeV Au+Au charged hadrons


(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

pT (GeV)

VISHNU STAR v2{EP}

• (η/s)QGP = 0.08 for MC-Glauber and (η/s)QGP = 0.16 for MC-KLN works well forcharged hadron, pion and proton spectra and v2(pT ) at all collision centralities


vishnu – a dynamical evolution model for heavy-ion collisions...v 2 2 /s = 0.16 t dec = 140 mev 0...

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