Dynamic Modeling for
Relativistic Heavy Ion Collisions
Huichao Song
Peking University
CPOD2014, Bielefeld, Germany, Nov.17-Nov.21, 2014
11/20/2014
QGP-the most perfect fluid in the world?
BNL News, 2005
How perfect is the QGP fluid?
What is viscosity
Shear viscosity – measures the resistance to flow

act against the buildup of
flow anisotropy
Bulk viscosity – measures the resistance to expansion

act against the buildup of
radial flow
Heat conductivity – measures the ability of heat transfer

Assume:   0, n  0 (RHIC&LHC)
Hydrodynamics & its Hybrid Model
Viscous Hydrodynamics
 T

(x)  0
T



 ( e  p  )u u  ( p  ) g
Evolution equations for shear pressure tensor 
         2


1
2
     (   u ) 
 
 
1
2

T

T





and bulk pressure
 
 

 
u


 T

   
 
u 



T


Assume zero net baryon density & heat conductivity at RHIC and the LHC
Song & Heinz PLB08, PRC08
2+1-d: OSU, INT, Stony Brook,
Pudue, Calcutta (2008), Crakow,
Frankfurt(2010) … …
3+1-d: Mcgill(2011), MSU(2012),
Crakow(2012), Nagoya(2013)… …
Viscous Hydro + Hadron Cascade Hybrid Model
QGP
Initial conditions
viscous hydro
HRG
HRG
hadron cascade
ideal hydro (QGP & HRG)
viscous hydro (QGP & HRG)
viscous hydro (QGP)
+ URQMD (HRG)
H. Song, S. Bass, U. Heinz,
PRC2011
Event-by-event hydrodynamics
Single shot simulations: smoothed initial conditions (before 2010)
E-b-E simulations: fluctuating initial conditions (since 2010)
B. Schenke et al, Phys.Rev. C85, 024901 (2012)
Extracting QGP viscosity from
elliptic flow data – VISHNU results
VISHNU hybrid model & QGP viscosity
H. Song,et.al, PRL2011
MC-KLN
MC-Glauber
1  (1 4  )  ( / s )QGP  2.5  (1 4  )
-Main uncertainties come from initial conditions
-Other uncertainties (much smaller)
-Initial flow, bulk viscosity, single shot vs. e-b-e calculations
(each of them shift V2 by a few percent, partial cancellation among them)
V2 at RHIC and LHC
Song, Bass & Heinz, PRC 2011
The average QGP viscosity is roughly the same at RHIC and LHC
LHC: spectra for identified hadrons
Song, Bass & Heinz,PRC 2014
-a nice fit of spectra for pions, kaons and proton
Spectra of Strange & Multi-strange Hadrons
X.R. Zhu, H. Song et al., in preparation
-a nice fit of spectra for Lambda, Xi, and Omega
V2 ( pT )
for pions, kaons & protons at LHC
VISHNU
Song, Bass & Heinz,PRC 2014
( / s )QGP  0.20
A very nice fit of V2(PT) for all centrality bins at LHC from VISHNU hybrid model
v2 of Strange & Multi-strange Hadrons
X.R. Zhu, H. Song et al., in preparation
-Nice descriptions of Lambda, Xi and Omega V2 at various centralities
Initial State Fluctuations,
Final State Correlations
& the QGP viscosity
Uncertainties from Initial Conditions
H. Song, S. Bass, U. Heinz, T. Hirano, and C. Shen, PRL2011
MC-KLN
MC-Glauber
1  (1 4  )  ( / s )QGP  2.5  (1 4  )
Main uncertainties come from initial conditions
MC-KLN, larger  2
HIGHER value of QGP viscosity
MC-Glauber, smaller  2
LOWER value of QGP viscosity
MC-KLN & MC-Glauber initializations & V3
Pure viscous hydro simulations :
v2 /  2
MC  KLN,  / s  0.20
v3 /  3
MC  KLN,  / s  0.20
V3 prefer lower value of QGP viscosity
Qiu, Shen & Heinz, PLB2012
v2 /  2
MC  Glb,  / s  0.08
v3 /  3
MC  Glb,  / s  0.08
Initialization & Pre-equilibrium: Updates after 2011
-fluctuations of nucleon positions: MC-Glauber, MC-KLN
-fluctuations of color charges (in the framework of CGC):
IP-Glasma: B. Schenke et al., arXiv:1202.6646; 1206.6805 [nucl-th]
Correlated Fluctuation: B. Muller & A. Schafer, arXiv:1111.3347 [hep-ph]
.
-fluctuations of local gluon numbers (in the famework of MC-KLN):
Multiplicity fluctuations: A. Dumitru and Y. Nara, Phys. Rev. C 85, (2012) 034907
-Pre-equilibriums:
URQMD initialization: H.Petersen & M. Bleicher, Phys. Rev. C81, 044906,2010
AMPT initialization: L. Pang, Q.Wang & X.Wang, arXiv:1205.5019[nucl-th]
EPOS/NEXUS initialization: K. Werner et al., Phys. Rev. C83:044915,2011
…… ……
Mostly, the effects of initializations /pre-equilibrium dynamics was studied with ideal
hydro. Their quantitative influences on ( / s)QGP are still unknown.
Flow at RHIC & LHC: results from IP-Glasma + MUSIC
Gale, Jeon ,Schenke, Tribedy &Venugopalan PRL2013
New Observables for Higher Order Flow Harmonics
Luzum & Ollitrault, 2012-10
Qiu & Heinz,12-08
C. Gale et al.
12-09
-They are all sensitive to the QGP viscosity
-A further study of flow data in different aspects, using e-b-e hybrid model
will constrain initialization models, tightening the limit on ( / s ) QGP
Massive Data evaluation
Exp Observables
- particle yields
- spectra
- elliptic flow
- triangular flow & higher order
flow harmonics
- event by event Vn distributions
- higher-order event plane
correlations
… ... … …
Theoretical Inputs:
- type of initial conditions
- initial flow
- starting time
- EoS
- shear viscosity
- bulk viscosity
- relaxation times
- freeze-out/switching cond.
…… ……
Massive data evaluation
Early CHIMERA Results
(Comprehensive Heavy Ion Model
Evaluation and Reporting Algorithm)
Spectra
spectra
elliptic flow
HBT
R. Soltz, et al., PRC2013
Please also refer to the work from MSUDUKE collaboration, arXiv: 1303.5769
Bernhard & Bass, JET collaboration
Massive data evaluation
Bulk Viscosity
Long , but not full lists of articles:
K. Rajagopal et al. JHEP 1003, 018(2008) .
R.Fries et al. Phys.Rev. C78 034913 (2008) .
G.Torrieri et al. Phys.Rev. C78, 021901(2008).
A. Monnai et al. Phys.Rev. C80 054906 (2009)
H.Song and U.WHeinz, Phys. Rev. C81, 024905 (2010)
P. Bozek, Phys. Rev. C81, 034909 (2010)
K.Dusling and T.Schäfer, Phys.Rev.C 85, 044909 (2012)
J.Noronha-Hostler, et.al., Phys.Rev. C 88, 044916 (2013)
J.Noronha-Hostler, J.Noronha and F.Grassi, arXiv:1406.3333 [nucl-th]
M. Habich and P. Romatschke, arXiv:1405.1978 [hep-ph].
… … … …
… …
The interplay between shear and bulk viscosity
ideal
shear visc.
shear+ bulk visc.
QGP
Visc. suppression
of elliptic flow
Song & Heinz PRC09
HRG
Min.
AdS/CF
T
predictio
n
-Bulk viscous effects are much smaller than shear ones due to the critical slowing
down near phase transition (Song & Heinz PRC09)
-One can extract the QGP shear viscosity from exp data without large contamination
from bulk viscosity
Ultracentral Collisions: bulk visc. & NN correlations
Shen, Qiu and Heinz 2013
G. Denicol, QM2014
-MC-Glauber & MC-KLN: can not simultaneously fit V2 and V3
-IP+Glasma + NN correlations + bulk viscosity nicely reproduces Vn in
ultra-central collisions
Soft Particle Yields, Chemical & thermal
Freeze-out at the LHC
J. Stachel,SQM 2013
Tch = 165MeV
v.s.
Tch = 150MeV
dN/dy for identified hadrons (RHIC & LHC)
Song, Bass & Heinz,PRC 2014
RHIC : 200 A GeV Au+Au
LHC : 2.76 A TeV Pb+Pb
-VISHNU nicely describes the multiplicity for pions, kaons & protons
-B-Bbar annihilations plays an important role for a nice fit of the proton data
VISHNU : Tsw= 165MeV
Please also refer to F. Becattini et al., PRC2012
dN/dy for identified hadrons (LHC)
X.R. Zhu, H. Song et al., in preparation
-VISHNU nicely describes the multiplicity for various hadrons at the LHC
dN/dy for identified hadrons (LHC)
X.R. Zhu, H. Song et al., in preparation
VISHNU
most central collisions
Statistical Model vs. VISHNU
Statistical Model
Statistical Model : Tch ~ 150 MeV
VISHNU
VISHNU : Tsw= 165MeV
- Statistical Model: Tch is extracted from final hadron yields; averaged chemical
freeze-out temperature for final stable hadrons
- VISHNU: Tsw corresponds QGP chemical freeze-out; different hadrons may
have different chemical freeze-out temperature.
Chemical freeze-out for various hadrons in UrQMD
X.R. Zhu, H. Song et al., in preparation
Thermal freeze-out for various hadrons in UrQMD
X.R. Zhu, H. Song et al., in preparation
-earlier freeze-out for Xi and Omega!
phi-meson
Elliptic flow for phi at the LHC
Song, Bass & Heinz, PRC 2014
-Hadron cascade: small cross sections
for phi
-mass ordering between phi and
proton are independent of collision
energies, centralities & theoretical
details
200A GeV
Au+Au
T. Hirano
3+1-d ideal hydro+JAM
Elliptic flow for phi at the LHC
Song, Bass & Heinz, PRC 2014
ALICE 2014
Elliptic flow for phi at the LHC
Song, Bass & Heinz, PRC 2014
STAR Preliminary
ALICE 2014
phi V2 in strong & weakly coupling limit
Song, Bass & Heinz, PRC 2014
-hydro + Tdec =165 MeV weakly coupling limit
-hydro + Tdec =100 MeV strong coupling limit
-VISHNU: small cross sections for phi
phi V2 in strong & weakly coupling limit
Song, Bass & Heinz, PRC 2014
-hydro + Tdec =165 MeV
weakly coupling limit
-hydro + Tdec =100 MeV
strong coupling limit
STAR Preliminary
VISHNU:
small cross sections for phi
ALICE 2014
Summary
Summary
-Extraction  / s from elliptic flow data using VISHNU indicates:
1  (1 4  )   / s  2.5  (1 4  )
(MC-Glauber; MC-KLN)
-Slightly larger averaged QGP viscosity at the LHC
-Recent developments on initialization models: color charge fluctuations;
multiplicity fluctuations; initial flow fluctuations … …
-New flow data: triangular flow & higher order flow harmonics, higher-order
event plane correlations e-b-e vn … ...
-To implement e-b-e simulations to further study other flow will help us
to constrain initialization models, tightening the limit on ( / s ) QGP
-massive data evaluation are needed
-VISHNU could nicely describe the yields of various hadrons
-B-Bbar annihilations is important to describe the proton yields at the LHC
VISHNU: an indication of different chemical freeze-out temperature for various hadrons