ulrich heinz, the ohio state university · u. heinz kapusta-fest 3(32) the qcd phase transition(s)...
TRANSCRIPT
Quark-gluon plasma – the perfect liquid∗
Ulrich Heinz, The Ohio State University
Symposium on Contemporary Subatomic Physics (Joe-Kapusta-Fest)McGill University, June 21-14, 2012
∗Work supported by the U.S. Department of Energy
The Little Bang
Gyulassy RBRC/BNL 12/16/04 11
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U. Heinz Kapusta-Fest 1(32)
Ideal fluids don’t exist!
AdS/CFT universal lower viscosity bound conjecture:η
s>∼
h
4πkB
Kovtun, Son, Starinets, PRL 94 (2005) 111601
1 10 100 1000T, K
0
50
100
150
200
Helium 0.1MPaNitrogen 10MPaWater 100MPa
Viscosity bound
4π ηsh
Similar limit from the uncertainty relation derived by Danielewicz and Gyulassy in 1995.
U. Heinz Kapusta-Fest 2(32)
The connection with phase transitions
L. Csernai, J. Kapusta,L. McLerran, Phys. Rev.Lett. 97 (2006) 152303
Hard to calculate.
Can we measure (η/s)QGP and its temperature dependence?
U. Heinz Kapusta-Fest 3(32)
The QCD phase transition(s)
U. Heinz Kapusta-Fest 4(32)
Elliptic Flow
In non-central collisions the over-
lap region is elliptically deformed
=⇒ anisotropic pressure gradients
=⇒ anisotropic (“elliptic”) collec-
tive flow.
Elliptic flow→ peaks at midrapidity
→ driven by spatial deformation of reaction zone at thermalization
→ magnitude of signal probes degree and time of thermalization
→ “self-quenching”: it shuts itself off as dynamics reduces deformation (H. Sorge)
→ sensitive to Equation of State during first ∼ 5 fm/c
v2(y, pT , b) = 〈cos(2φ)〉y,pT ,b =
∫dφ cos(2φ) dN
dy pTdpT dφ(b)∫dφ dN
dy pTdpT dφ(b)
U. Heinz Kapusta-Fest 5(32)
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 εn
• Each event develops its individual hydrodynamic flow, characterized by a set of harmonic flow
coefficients vn and flow angles ψn
• At small impact parameters fluctuations (“hot spots”) dominate over geometric overlap effects
(Alver & Roland, PRC81 (2010) 054905; Qin, Petersen, Bass, Muller, PRC82 (2010) 064903)
U. Heinz Kapusta-Fest 6(32)
Panta rhei: “soft ridge”=“Mach cone”=flow!ATLAS (J. Jia), Quark Matter 2011 ALICE (J. Grosse-Oetringhaus), QM11
• anisotropic flow coefficients vn and flow angles ψn 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 v3>v2=⇒ prominent “Mach cone”-like structure!
=⇒ event-by-event eccentricity fluctuations dominate!
U. Heinz Kapusta-Fest 7(32)
Event-by-event shape and flow fluctuations rule!
ALICE (A. Bilandzic) Quark Matter 2011
• in the 1% most central collisions v3>v2 =⇒ 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
U. Heinz Kapusta-Fest 8(32)
“The Little Bang”
The Movie
Featuring the QGP in one of itsfinest performances
Producer: Chun Shen
U. Heinz Kapusta-Fest 9(32)
(η/s)QGP
U. Heinz Kapusta-Fest 10(32)
How to use elliptic flow for measuring (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
U. Heinz Kapusta-Fest 11(32)
How to use elliptic flow for measuring (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, UH, PRC83 (2011) 024912) Note: this paper shows that UrQMD 6= viscous hydro!
U. Heinz Kapusta-Fest 12(32)
Extraction of (η/s)QGP from AuAu@RHICH. Song, S.A. Bass, UH, 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, UH, PRC84 (2011) 024911
U. Heinz Kapusta-Fest 13(32)
Global description of AuAu@RHIC spectra and v2
VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (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 wellfor charged hadron, pion and proton spectra and v2(pT ) at all collision centralities
• Note: Tchem=165MeV reproduces the proton spectra from STAR, but not fromPHENIX! =⇒ Slightly incorrect chemical composition in hadronic phase? Not enoughpp annihilation in UrQMD?
U. Heinz Kapusta-Fest 14(32)
Global description of AuAu@RHIC spectra and v2
VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (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 )) (C. Shen et al., PRC84 (2011) 044903)
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 1.05 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
U. Heinz Kapusta-Fest 15(32)
Pre- and postdictions for PbPb@LHCVISHNU with MC-KLN (Song, Bass, UH, PRC83 (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 (C. Shen et al., PRC84 (2011) 044903)
• but: At LHC significant sensitivity of v2 to initialization of viscous pressure tensor πµν (Navier-Stokes
or zero) =⇒ need pre-equilibrium model.
=⇒ QGP at LHC not much more viscous than at RHIC!
U. Heinz Kapusta-Fest 16(32)
Why is vch2 (pT) the same at RHIC and LHC?
Answer: Pure accident! (Kestin & UH EPJC61 (2009) 545; Shen & UH, PRC85 (2012) 054902)
C. Shen, UH, P. Huovinen, H. Song, PRC84 (2011) 044903
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, NJP13 (2011) 075004)
U. Heinz Kapusta-Fest 17(32)
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 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?U. Heinz Kapusta-Fest 18(32)
Successful prediction of v2(pT) for identified hadrons inPbPb@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:
U. Heinz Kapusta-Fest 19(32)
v2(pT) in PbPb@LHC: ALICE vs. VISHNUData: 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
0.1
0.2
0.3
5−10%
v2
ALICE Preliminary
π+
K+
p
10−20%
(η/s)QGP = 0.16VISHNU
20−30%
η/s = 0.20VISH2+1
0 1.0 2.0 00
0.1
0.2
0
30−40%
pT (GeV)
v2
0 1.0 2.0 040−50%
pT (GeV)0 1.0 2.0 3.0
50−60%
pT (GeV)
VISHNU yields correct magnitude and centrality dependence of v2(pT ) for pions, kaons and protons!
Same (η/s)QGP =0.16 (for MC-KLN) at RHIC and LHC!
U. Heinz Kapusta-Fest 20(32)
Back to the“elephant in the room”:
How to eliminate the largemodel uncertainty
in the initial eccentricity?
U. Heinz Kapusta-Fest 21(32)
Two observations:
I. Shear viscosity suppresses higher flow harmonics more strongly
Alver et al., PRC82 (2010) 034913
(averaged initial conditions)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.08 0.16
v n/ε
n
η/s
v2/ε2v3/ε3v4/ε4v5/ε5
Schenke et al., arXiv:1109.6289
(event-by-event hydro)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1 2 3 4 5 6v n
(vis
cous
)/v n
(idea
l)
n
20-30% vn(η/s=0.08)/vn(ideal) vn(η/s=0.16)/vn(ideal)
=⇒ Idea: Use simultaneous analysis of elliptic and triangular flow to constrain initial state models
(see also Bhalerao, Luzum Ollitrault, PRC 84 (2011) 034910)
U. Heinz Kapusta-Fest 22(32)
Two observations:
II. ε3 is ≈ model independentZhi Qiu, UH, PRC84 (2011) 024911
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, but
similar ε5 and almost identical ε3 asMC-Glauber
• Angles of ε2 and ε4 are correlated
with reaction plane by geometry,whereas those of ε3 and ε5 are
random (purely fluctuation-driven)
• While v4 and v5 have mode-couplingcontributions from ε2, v3 is
almost pure response to ε3 andv3/ε3 ≈ const. over a wide range of
centralities
=⇒ Idea: Use total charged hadron vch3 to determine (η/s)QGP,
then check vch2 to distinguish between MC-KLN and MC-Glauber!
U. Heinz Kapusta-Fest 23(32)
Combined v2 & v3 analysis: η/s is small!Zhi Qiu, C. Shen, UH, PLB707 (2012) 151 (VISH2+1)
0
0.1
0.2
0.3
0.4
v2/ε2
(a)
ALICE v2{2}/ε2{2}
ALICE v2{4}/ε2{4}
MC-KLN v2/ε2
0 10 20 30 40 50 60 700
0.1
0.2
0.3
Centrality (%)
v3/ε3
MC-KLN η/s = 0.20 (b)
ALICE v3{2}/ε3{2}
MC-KLN v3/ε3
0
0.2
0.4
v2/ε2
(c)
ALICE v2{2}/ε2{2}
ALICE v2{4}/ε2{4}
MC-Glb. v2/ε2
0 10 20 30 40 50 60 700
0.1
0.2
0.3
Centrality (%)
v3/ε3
MC-Glb. η/s = 0.08 (d)
ALICE v3{2}/ε3{2}
MC-Glb. v3/ε3
• Both MC-KLN with η/s=0.2 and MC-Glauber with η/s=0.08 give very gooddescription of v2/ε2 at all centralities.
• Only η/s=0.08 (with MC-Glauber initial conditions) describes v3/ε3!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 v3 measured at RHIC and LHC requires small (η/s)QGP ≃ 1/(4π) unlessthe fluctuations predicted by both models are completely wrong and ε3 is really 50%larger than we presently believe!
U. Heinz Kapusta-Fest 24(32)
Conclusions• The QGP is the most perfect liquid ever measured. Its specific shear viscosity at RHIC and
LHC energies is
(η/s)QGP(Tc<T<2Tc) =1
4π± 50%
A moderate increase between 2Tc and 3Tc can at present not be excluded but is not mandated
by the data.
• Ingredients that matter at the 50% level and are under control:
– relativistic viscous fluid dynamics
– realistic EOS with correct non-equilibrium composition in HG phase
– microscopic description of the highly dissipative hadronic stage, including all resonance decays
– fluctuating initial conditions, simultaneous study of v2 and v3
• Ingredients that matter at the < 25% level and require further study:
– bulk viscosity
– temperature dependence of (η/s)QGP
– pre-equilibrium flow
– event-by-event hydro evolution vs. single-shot hydro with averaged initial profiles
– (3+1)-d vs. (2+1)-d evolution
– study of higher harmonics; influence of nucleon growth with√s on fluctuations
– flow fluctuations and flow angle correlations for different harmonics
The ultimate theoretical question:Why is (η/s)QGP as small as it is?
U. Heinz Kapusta-Fest 25(32)
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
U. Heinz Kapusta-Fest 26(32)
The fluctuation “power spectrum” of the Little BangStaig & Shuryak, JPG38 (2011) 124039
• 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, NPA872 (2011) 161)
• 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!U. Heinz Kapusta-Fest 27(32)
Higher order event plane correlations in PbPb@LHCData: ATLAS Coll., J. Jia et al., Hard Probes 2012
Event-by-event hydrodynamics: Zhi Qiu (VISH2+1, MC-Glauber, (η/s)QGP=0.08)
0
0.2
0.4
0.6
0.8
1
cos(4ΨEP2 −4ΨEP
4 )
0
0.2
0.4
0.6
0.8
1
cos(8ΨEP2 −8ΨEP
4 )
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6 cos(12ΨEP2 −12ΨEP
4 )
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
cos(6ΨEP2 −6ΨEP
3 )
0 100 200 300 400−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6cos(6ΨEP
2 −6ΨEP6 )
0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6 cos(6ΨEP3 −6ΨEP
6 )
0 100 200 300 400−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
cos(12ΨEP3 −12ΨEP
4 )
0 100 200 300 400
−0.1
−0.05
0
0.05
0.1
0.15cos(10ΨEP
2 −10ΨEP5 )
Viscous hydro, MC-Glauber, η/s = 0.08
ATLAS dataNpart
Very preliminary assessment:
VISH2+1 reproduces qualitative features of the centrality dependence of all measured event-plane
correlations but is quantitatively off by up to 50%
U. Heinz Kapusta-Fest 28(32)
Higher order event plane correlations in PbPb@LHCData: ATLAS Coll., J. Jia et al., Hard Probes 2012
Event-by-event hydrodynamics: Zhi Qiu (VISH2+1, MC-Glauber, (η/s)QGP=0.08)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
cos(2ΨEP2 + 3ΨEP
3 −5ΨEP5 )
−0.1
−0.05
0
0.05
0.1
cos(−8ΨEP2 + 3ΨEP
3 + 5ΨEP5 )
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
cos(2ΨEP2 + 4ΨEP
4 −6ΨEP6 )
0 100 200 300 400−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
cos(−10ΨEP2 + 4ΨEP
4 + 6ΨEP6 )
0 100 200 300 400−0.2
−0.1
0
0.1
cos(2ΨEP2 −6ΨEP
3 + 4ΨEP4 )
0 100 200 300 400−0.1
−0.05
0
0.05
0.1
cos(−10ΨEP2 + 6ΨEP
3 + 4ΨEP4 )
Viscous hydro, MC-Glauber, η/s = 0.08
ATLAS dataNpart
Very preliminary assessment:
VISH2+1 reproduces qualitative features of the centrality dependence of all measured event-plane
correlations but is quantitatively off by up to 50%
U. Heinz Kapusta-Fest 29(32)
Higher order event plane correlations in PbPb@LHCData: ATLAS Coll., J. Jia et al., Hard Probes 2012
Event-by-event hydrodynamics: Zhi Qiu (VISH2+1, MC-KLN, (η/s)QGP=0.2)
0
0.2
0.4
0.6
0.8
1
cos(4ΨEP2 −4ΨEP
4 )
0
0.2
0.4
0.6
0.8
1
cos(8ΨEP2 −8ΨEP
4 )
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6 cos(12ΨEP2 −12ΨEP
4 )
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
cos(6ΨEP2 −6ΨEP
3 )
0 100 200 300 400−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6cos(6ΨEP
2 −6ΨEP6 )
0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6 cos(6ΨEP3 −6ΨEP
6 )
0 100 200 300 400−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
cos(12ΨEP3 −12ΨEP
4 )
0 100 200 300 400
−0.1
−0.05
0
0.05
0.1
0.15cos(10ΨEP
2 −10ΨEP5 )
Viscous hydro, MC-KLN, η/s = 0.2
ATLAS dataNpart
Very preliminary assessment:
VISH2+1 reproduces qualitative features of the centrality dependence of all measured event-plane
correlations but is quantitatively off by up to 50%
U. Heinz Kapusta-Fest 30(32)
Higher order event plane correlations in PbPb@LHCData: ATLAS Coll., J. Jia et al., Hard Probes 2012
Event-by-event hydrodynamics: Zhi Qiu (VISH2+1, MC-KLN, (η/s)QGP=0.2)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
cos(2ΨEP2 + 3ΨEP
3 −5ΨEP5 )
−0.1
−0.05
0
0.05
0.1
cos(−8ΨEP2 + 3ΨEP
3 + 5ΨEP5 )
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
cos(2ΨEP2 + 4ΨEP
4 −6ΨEP6 )
0 100 200 300 400−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
cos(−10ΨEP2 + 4ΨEP
4 + 6ΨEP6 )
0 100 200 300 400−0.2
−0.1
0
0.1
cos(2ΨEP2 −6ΨEP
3 + 4ΨEP4 )
0 100 200 300 400−0.1
−0.05
0
0.05
0.1
cos(−10ΨEP2 + 6ΨEP
3 + 4ΨEP4 )
Viscous hydro, MC-KLN, η/s = 0.2
ATLAS dataNpart
Very preliminary assessment:
VISH2+1 reproduces qualitative features of the centrality dependence of all measured event-plane
correlations but is quantitatively off by up to 50%
U. Heinz Kapusta-Fest 31(32)
Happy Birthday, Joe!
U. Heinz Kapusta-Fest 32(32)
Supplements
U. Heinz Kapusta-Fest 33(32)
Global description of AuAu@RHIC spectra and v2
VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC83 (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
U. Heinz Kapusta-Fest 34(32)
Pre- and postdictions for PbPb@LHCVISHNU with MC-KLN (Song, Bass, UH, PRC83 (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 (C. Shen et al., PRC84 (2011) 044903)
• but: At LHC significant sensitivity of v2 to initialization of viscous pressure tensor πµν (Navier-Stokes
or zero) =⇒ need pre-equilibrium model.
=⇒ QGP at LHC not much more viscous than at RHIC!
U. Heinz Kapusta-Fest 35(32)
Why is vch2 (pT) the same at RHIC and LHC?
Answer: Pure accident! (Kestin & UH EPJC61 (2009) 545; Shen & UH, PRC85 (2012) 054902)
C. Shen, UH, P. Huovinen, H. Song, PRC84 (2011) 044903
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, NJP13 (2011) 075004)
U. Heinz Kapusta-Fest 36(32)
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 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?U. Heinz Kapusta-Fest 37(32)
Successful prediction of v2(pT) for identified hadrons inPbPb@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:
U. Heinz Kapusta-Fest 38(32)
v2(pT) in PbPb@LHC: ALICE vs. VISHNUData: 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
0.1
0.2
0.3
5−10%
v2
ALICE Preliminary
π+
K+
p
10−20%
(η/s)QGP = 0.16VISHNU
20−30%
η/s = 0.20VISH2+1
0 1.0 2.0 00
0.1
0.2
0
30−40%
pT (GeV)
v2
0 1.0 2.0 040−50%
pT (GeV)0 1.0 2.0 3.0
50−60%
pT (GeV)
VISHNU yields correct magnitude and centrality dependence of v2(pT ) for pions, kaons and protons!
Same (η/s)QGP =0.16 (for MC-KLN) at RHIC and LHC!
U. Heinz Kapusta-Fest 39(32)
PbPb@LHC pT -spectra: ALICE vs. VISH2+1 and VISHNU:
10−1
100
101
102
103 0~5%
dN
/(d
ydp
T)
ALICE Preliminaryπ+
K+
p
5~10%
(η/s )QGP = 0 .16
VISHNU
10~20%
η/s = 0 .20
VISH2+1
20~30%
0 1.0 2.0 010
−1
100
101
102
103 30~40%
pT (GeV)
dN
/(d
ydp
T)
0 1.0 2.0 0
40~50%
pT (GeV)0 1.0 2.0 0
50~60%
pT (GeV)0 1.0 2.0 3.0
60~70%
pT (GeV)
• Good description also of identified hadron spectra for centralities < 50%
• VISHNU better than VISH2+1 in central collisions (more radial flow)
• Both models give too much radial flow in peripheral collisions =⇒ initial conditions?
• Both models overpredict proton yield by 50-70%!?U. Heinz Kapusta-Fest 40(32)
The new “proton anomaly”: disagreement with the thermal modelData: 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” Tchem =164MeV reproduces strange hadrons but overpredicts (anti-)protons by 50%!
• pp annihilation in UrQMD not strong enough to repair this
• Similar problem already seen at RHIC but not taken seriously (STAR/PHENIX disagreement)
???U. Heinz Kapusta-Fest 41(32)
Comparison of ALICE PbPb@LHC v2 data with VISH2+1
Data: ALICE (Snellings, Krzewicki, Quark Matter 2011)
Prediction: C. Shen et al., PRC84 (2011) 044903 (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
pT (GeV)
30%~40%
pT (GeV)
40%~50%
pT (GeV)
50%~60%
U. Heinz Kapusta-Fest 42(32)
PbPb@LHC pT -spectra: Glauber vs. KLN
10−1
100
101
102
103 0~5%
dN
/(dydp
T)
[email protected] TeVALICE Preliminary
π+
K+
p
5~10%
η/s = 0 .20MC−KLN
10~20%
η/s = 0 .08MC−Glb
20~30%
0 1.0 2.0 010
−1
100
101
102
103 30~40%
pT (GeV)
dN
/(dydp
T)
0 1.0 2.0 0
40~50%
pT (GeV)0 1.0 2.0 0
50~60%
pT (GeV)0 1.0 2.0 3.0
60~70%
pT (GeV)
• In central collisions no difference between the models.
• In peripheral collisions pT -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 pT -spectra in peripheral collisions, due to hot spots
U. Heinz Kapusta-Fest 43(32)
Smearing effects from nucleon growth at high energiesU. Heinz & Scott Moreland, PRC84 (2011) 054905
-6-4-2 0 2 4 6
x (fm)
-6 -4 -2 0 2 4 6y (fm)
200 GeV Disk
0
10
20
30
40
50
60
-6-4-2 0 2 4 6
x (fm)
-6 -4 -2 0 2 4 6y (fm)
200 GeV Gauss
0 5 10 15 20 25 30 35 40 45 50
-6-4-2 0 2 4 6
x (fm)
-6 -4 -2 0 2 4 6y (fm)
2.76 TeV Gauss
0 10 20 30 40 50 60 70 80 90 100
23.5 GeV
-8-6-4-2 0 2 4 6 8
y (
fm)
0 2 4 6 8 10 12 14 16
200 GeV
0 5 10 15 20 25 30 35 40 45 50
2.76 TeV
-8 -6 -4 -2 0 2 4 6 8x (fm)
-8-6-4-2 0 2 4 6 8
y (
fm)
0 10 20 30 40 50 60 70 80 90 100
7 TeV
-8 -6 -4 -2 0 2 4 6 8x (fm)
0
20
40
60
80
100
120
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
U. Heinz Kapusta-Fest 44(32)
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!
U. Heinz Kapusta-Fest 45(32)
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
U. Heinz Kapusta-Fest 46(32)