VISHNU – a dynamical evolution model for heavy-ion collisions · VISHNU: hydro (VISH2+1) +...
Transcript of VISHNU – a dynamical evolution model for heavy-ion collisions · VISHNU: hydro (VISH2+1) +...
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, June 20-24, 2011 1(28)
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!
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 2(28)
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!
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 3(28)
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 4(28)
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)
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 5(28)
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 AGeV Au+Au, b = 7 fm
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 6(28)
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 AGeV Au+Au, b = 7 fm
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)
200 AGeV Au+Au, b = 7 fm
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 7(28)
Is there a switching window in which UrQMD can be simulated byviscous hydro?
Unfortunately NO!
Song, Bass, Heinz, PRC 83 (2011) 2011
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, June 20-24, 2011 8(28)
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 → increases
v2ε by ∼ few% → larger η/s
bulk viscosity → affects vch2 (pT ), but ≈ not vch2
Zhi Qiu, U. Heinz, arXiv:1104.0650
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 9(28)
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)
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 10(28)
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 11(28)
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
0.2
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}
MC-Glauber initialization
MC-Glauber initialization
VISHNU
Au + Au 200 A GeV s = 0.16 /s = 0.24
v 2/
pT (GeV)
MC-KLN initialization
p
p
pT (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 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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 12(28)
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!
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 13(28)
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)
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 14(28)
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 15(28)
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!
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 16(28)
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.
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 17(28)
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.
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 18(28)
Supplements
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 19(28)
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 1.6
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
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
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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 20(28)
Panel Discussion
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 21(28)
RHIC data have led to a series of paradigmatic shifts in our under-standing of the Little Bang:
2002-2003 The QGP is not a weakly coupled quark-gluon gas but a stronglycoupled, almost “perfect” liquid
2003-2008 Deviations from local equilibrium (dissipative effects) play an essentialrole and dictate much of the phenomenologyEasier to measure transport coefficients (e.g. η/s, q̂, charm drag anddiffusion) by varying
√s, A, b, φ than thermodynamic properties of the
QGP (e.g. EOS, cs, µD)Differences in transport properties of QGP and HRG more importantthan differences in thermodynamic variables (P , e, s, nB)
2009-2010 “COBE revolution”: Many key experimental phenomena cannot bedescribed by classical evolution of smooth mean field configurations;quantum fluctuations in the initial state play an essential role in anyquantitative understanding of RHIC data
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 22(28)
The fluctuation “power spectrum” of the Little Bang (Mocsy & Sorensen)
nv
-210
-110
|<5, 2.0-3.0 GeV !2<|
0-1%
same charge
opp charge
all
-1b! Ldt = 8 "
ATLAS Preliminary
0 5 10 15n
0 5 10 15-10-505
10
-310"
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 23(28)
The fluctuation “power spectrum” of the Little Bang (Mocsy & Sorensen)n
v
-210
-110
|<5, 2.0-3.0 GeV !2<|
0-1%
same charge
opp charge
all
-1b! Ldt = 8 "
ATLAS Preliminary
0 5 10 15n
0 5 10 15-10-505
10
-310"
Staig & Shuryak, arXiv:1106.3243
2 4 6 8 10 12 14
0.00001
0.0001
0.001
2 4 6 8 10 12 14
0.00001
0.0001
0.001
n
vn
• Relating the measured “anisotropic flow power spectrum” (i.e. vn vs. n) to the “initial fluctuation
power spectrum” (i.e. εn vs. n) provides access to the QGP transport coefficients (likely not only η/s,
but also ζ/s, τπ, τΠ . . .)
• 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
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 24(28)
A comment
(Viscous) hydro works better at higher (RHIC 200, LHC) than atlower energies (RHIC BES, SPS/AGS)
=⇒ breakdown of macroscopic approach at low energies (vπ+
2 6=vπ
−2 , vp2 6= vp̄2) may prove fatal to our attempts to measure thethermodynamic properties of QCD matter near or below Tc. (Thisdoes not invalidate the “sweet spot” argument that RHIC is theonly machine that allows us to move easily in and out of the regionof deconfinement; I am just saying that it will probably not bepossible to understand this transition region primarily in terms ofthe change of thermodynamic characteristics of the matter, butrather in terms of its changing transport properties, caused by achange in degrees of freedom.)
=⇒ limits and breakdown of the hydrodynamic approach requirecareful exploration at RHIC
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 25(28)
Some personal convictions
• To sort out the transport coefficients of the bulk medium and related to hard probes(parton energy loss, heavy quark diffusion, . . . )=⇒ need systematic studies of
√s, A+B, b, and φ dependences
This requires a dedicated program and extensive running time
• To obtain access to T -dependence of transport coefficients=⇒ need large range of
√s from low-energy RHIC to top LHC energies (and it will
still be difficult)
• To sort out parton energy loss mechanism and parton→medium backreaction, neitherRHIC nor LHC alone will be sufficient
• To perform JET of QGP at all length scales, need large range of Q2
Large Q2 only at LHCLower Q2 cleaner at RHIC
• We will only find the correct theory of thermalization after having carefully mappedthermalization times phenomenologically, by analyzing systematic studies of flowpatterns in A+B data at both RHIC and LHC
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 26(28)
Looking into the future > 2018
Question: How would the world-wide heavy-ion program > 2018 lookwithout an active RHIC A+B program?
Answer: Like RHIC 2005-2010, without active SPS and LHC HI programs
Example: The parton energy loss confusion
It is not hard to predict that the LHC will discover hard probe phenomenaat high pT that will find several competing explanations which differ atlow pT where it will be difficult to test them at the LHC, due to largebackgrounds from the fluctuating bulk medium. Will need RHIC data toresolve these ambiguities. I don’t believe that that all the necessary datawill be taken before 2018, simply because we don’t know yet what tolook for.
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 27(28)
Looking into the future > 2018
By not having a RHIC A+A program after 2018, in parallelwith the LHC heavy ion and EIC e+A programs, wewill (at best) delay and (more likely) close the door to atimely and comprehensive understanding of LHC and EICmeasurements.
Need coherence, not only with respect to the RHIC →EIC transition, but also with respect to the worldwideheavy-ion program (which has strong US involvement in allits different components).
Think about optimizing RHIC detector(s) for complementa-rity to LHC A+A and EIC e+A capabilities
Ulrich Heinz RHIC&AGS Users’ Meeting, June 20-24, 2011 28(28)