Parton-hadron matter
in and out of equilibrium
Olena Linnyk
‚Little Bangs‘ in the Laboratory
Parton Hadron String Dynamics (PHSD)
Hadronization
Initial State
Au Au
Equilibrium QGP?
hadrons
quarks and gluons
hadrons
From hadrons to partons
In order to study the phase transition from
hadronic to partonic matter – Quark-Gluon Plasma –
we need a consistent non-equilibrium (transport) model with
 explicit interactions between quarks and gluons (beyond strings)
 phase transition from hadronic to partonic degrees of freedom
 lQCD EoS for partonic phase
Transport theory: off-shell Kadanoff-Baym equations for the Green-functions
S<h(x,p) in phase-space representation for the partonic and hadronic phase
Parton-Hadron-String-Dynamics (PHSD)
QGP phase described by
Dynamical QuasiParticle Model (DQPM)
W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;
NPA831 (2009) 215;
W. Cassing, EPJ ST 168 (2009) 3
A. Peshier, W. Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
Boltzmann equation -> off-shell transport
GENERALIZATION
(First order gradient expansion of the Wigner-transformed Kadanoff-Baym equations)
drift term
Vlasov term
backflow term
collision term = ‚loss‘ term - ‚gain‘ term
Backflow term incorporates the off-shell behavior in the particle propagation
! vanishes in the quasiparticle limit AXP = 2 p d(p2-M2)
Propagation of the Green‘s function iS<XP=AXP fXP , which carries information not only on
the number of particles, but also on their properties, interactions and correlations
GXP – width of spectral function = reaction rate of a particle (at phase-space position XP)
W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 4451
Lattice QCD ->
The Dynamical QuasiParticle Model (DQPM)
Quasiparticle properties:
 large width and mass for gluons and quarks
Lorentzian spectral function, HTL limit at high T
interaction measure:
TC=160 MeV
eC=0.5 GeV/fm3
lQCD: Fodor & Katz, (2009)
0.35
0.30
equation of state
p/e
0.25
0.20
Nf=3
0.15
0.10
lQCD: M. Cheng et al.,
PRD 77 (2008) 014511
0.05
S. Borsanyi et al., JHEP 1009, 073
(2010); JHEP 1011, 077 (2010)
0.00
1
10
100
1000
3
e [GeV/fm ]
E.L.Bratkovskaya, W. Cassing, V.P. Konchakovski, O. Linnyk, NPA856 (2011) 162 5
PHSD: Summary of the ideas
DQPM describes QCD properties in terms of „resumed“ single-particle Green‘s
functions in the sense of a two-particle irreducible (2PI) approach.
 2PI framewark guaranties a consistent description of the system in- and out-of
equilibrium on the basis of Kadanoff-Baym equations
 the resumed properties are specified by complex self-energies which depend on
temperature; the real part of self-energies describes a dynamically generated mass;
the imaginary part describes the interaction width of partons
 space-like part of energy-momentum tensor defines the potential energy density
and the mean-field potential (1PI) for quarks and gluons
 3 parameters
of the model (for the resumed coupling) are fitted to QCD
thermodynamics from the lattice
A. Peshier, W. Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
PHSD for HIC (highlights)
10
4
10
2
10
0
10
-2
10
-4
+
p


__
D(c)
+
K
-
AGS
SPS
RHIC
HSD ' 99
K
10
J/
D(c)
-6
10
-1
10
0
10
1
10
2
10
3
10
4
Energy [A GeV]
0.06
dN/dy | y=0 / Nwound
Multiplicity
Au+Au (central)
 +
Pb+Pb, 158 A0.010
GeV, mid-rapidity
0
_
0.05
_

0.008

0.04
0.006
0.03
0.004
0.02
NA57
NA49
0.01
HSD
PHSD
0.002
0.00
0.000
0
100
200
Nwound
300
400
0
100
200
300
400
Nwound
PHSD provides a consistent description of HIC dynamics
Properties of equilibrium QGP
using PHSD
Shear viscosity
/s using Kubo formalism and the relaxation time approximation (‚kinetic theory‘)
 T=TC: /s shows a minimum (~0.1)
close to the critical temperature
 T>TC : QGP - pQCD limit at higher
temperatures
 T<TC: fast increase of the ratio /s for
hadronic matter
lower interaction rate of hadronic system
smaller number of degrees of freedom (or
entropy density) for hadronic matter
compared to the QGP
QGP in PHSD = strongly-interacting liquid
V. Ozvenchuk et al., PRC 87 (2013) 024901; V. Ozvenchuk et al., arXiv:1212.5393 (accepted to PRC)
Electric conductivity
The response of the strongly-interacting system in equilibrium to an external
electric field eEz defines the electric conductivity s0:
 additional force from external electric
field eEz:
Note: pQCD result at leading order :
 the QCD matter even at T~ Tc is a much better electric conductor than Cu or Ag (at
room temperature) by a factor of 500 !
W. Cassing et al., Phys.Rev.Lett. 110 (2013) 182301
Thermal dilepton rates
10
Dileptons from dynamical
off-shell quark and gluon
interactions,
LO and NLO in the coupling
4
dynamical quasiparticels,
lattice QCD,
HTL
Thermal rate
P=0
dR/d P
• Qualitative agreement of
-6
10
-7
10
-8
10
-9
10
-10
10
-11
0
1
2
PHSD (sum):
+ q +q -> e e
+ q +q -> g + e e
lattice QCD
Hard Thermal Loops
Born
Gluon Condensate
3
4
5
6
7
8
M/T
O. Linnyk et al. Phys.Rev. C87 (2013) 014905
Dileptons
Dileptons - an ideal probe to study the
properties of the hot and dense medium
Dilepton sources:
1) from the QGP via partonic (q,qbar, g) interactions:
q
g*
q
l+
q
l-
q
g
g
g*
q
q
g*
g
q
2) from hadronic sources:
•direct decay of vector
mesons (r,w,,J/,‘)
•Dalitz decay of mesons
and baryons (p0,, D,…)
•radiation from secondary meson interaction:
p  p, p  r, p  w, r  r, p + a1
•correlated semi-leptonic decays of Dand B-mesons
+qq
g*
q
Dileptons at SPS: NA60
NA60 data at low M are well described by an inmedium scenario with collisional broadening
 Mass region above 1 GeV is dominated by
partonic radiation
O. Linnyk, E. Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011) 054917,
O. Linnyk, J.Phys.G38 (2011) 025105, NA60 Collaboration, Eur. Phys. J. C 59 (2009) 607; CERN Courier 11/2009
PHENIX: dileptons from QGP
•The excess over the considered mesonic
• The partonic channels fill up the
sources for M=0.15-0.6 GeV is not
explained by the QGP radiation as
incorporated presently in PHSD
discrepancy between the hadronic
contributions and the data for M>1 GeV
O. Linnyk, W. Cassing, J. Manninen, E.Bratkovskaya and C.M. Ko, PRC 85 (2012) 024910
STAR: dilepton mass spectra
 STAR data are well described by the PHSD predictions
 Confirmed by the extended data set at QM2012
O. Linnyk, W. Cassing, J. Manninen, E.Bratkovskaya and C.M. Ko, PRC 85 (2012) 024910
Predictions for LHC
1/2
1/2
Pb+Pb, s =2.76 TeV, b=0.5, |y|<0.88
PHSD
w 
0
10

r

J/, '
DD correlated
DD
BB
2
dN/dM [1/(GeV/c )]
1
10
p
w
QGP (qq )
Sum
-1
10
J/
-2
10
10
2
0
dN/dM [1/(GeV/c )]
2
10
2
e
Pb+Pb, s =2.76 TeV, b=0.5, |y|<0.88, pT >1 GeV
0
1
10
p
w
PHSD
w



BB
DD
QGP (qq )
Sum
0
10
10
-1
10
-2
10
-3
10
-4
r
J/, '
J/
'
-3
10
'
0.0
0.5
1.0
1.5
2.0
2
2.5
3.0
3.5
M [GeV/c ]
QGP(qbar-q) dominates at M>1.2 GeV
0.0
0.5
1.0
1.5
2.0
2
2.5
3.0
3.5
M [GeV/c ]
pT cut enhances the signal of QGP(qbar-q)
D-, B-mesons energy loss from Pol-Bernard Gossiaux and Jörg Aichelin
JPsi and Psi’ nuclear modification from Che-Ming Ko and Taesoo Song
O. Linnyk et al. Phys.Rev. C87 (2013) 014905
Photons
Photons from the hot and dense QCD medium
Photon sources
q the QGP
l+
1) From
g*
via partonic interactions:
q
l-
q
q
g
g
g
q
q
g
g
q
g
q
2) From hadronic sources
•decays of mesons:
•secondary meson interactions:
O. Linnyk et al. arXiv:1304.7030
Photons from the QGP
0.06
g
dv2/dt of q + g
dv2/dt, v2(t)
dv2/dt of q +q
v2(t) of g
0.04
QGP
v2 evolution
QGP
0.02
0.00
 Strong elliptic flow of photons
seen by PHENIX is surprising, if
the origin is the QGP
dN/dt per event
10
4
10
3
10
2
10
Numbers of q +q, q + g collisions
1/2
Au+Au, s =200 GeV, MB, |y|<1
q +q
q + g
PHSD
1
0
5
10
15
20
25
t [fm/c]
O. Linnyk et al. arXiv:1304.7030
Photon spectrum
1/2
PHSD
sum
10
10
2
1
0
10
-1
10
-2
p0

'
w
pp
pr

q +q
q+ g
pQCD
2
2
10
-2 2
3
d N/(2ppTdydpT) [GeV c ]
10
-2 2
d N/(2ppTdydpT) [GeV c ]
Au+Au, sNN =200 GeV, MB, |y|<0.35
0.0
0.5
1.0
1.5
2.0
2.5
pT [GeV/c]
10
1
10
0
10
1/2
Au+Au, sNN =200 GeV, MB, |y|<0.35
PHENIX
PHSD:
hadrons
QGP
pQCD
Sum
-1
10
-2
10
-3
10
-4
10
-5
'
pp
pr
w

a1
pQCD
m+m
0
1
2
3
pT [GeV/c]
 PHSD: PHENIX data are well described,
including the Teff
 QGP sources mandatory to explain the spectrum,
but hadronic sources of ‘direct’ photons are considerable, too
O. Linnyk et al. arXiv:1304.7030
Photon spectrum
Photon spectrum
2
(1/Nevt) dN/dM [1/(GeV/c )]
1/2
10
Au+Au, s =200 GeV
MB, PHENIX acc, 1<pT<1.5 GeV
-2
PHENIX data
PHENIX cocktail:
10
p
w
-3
10
-4
10
-5

'
PHSD:
p
w
D

'
a1
QGP
mm
0.0
0.1
0.2
0.3
2
M [GeV/c ]
0.4
0.5
Inclusive photon elliptic flow
0.3
0.3
inclusive photon v2
v2 of p-mesons
1/2
Au+Au, s =200 GeV, MB, |y|<0.35
1/2
Au+Au, s =200 GeV, MB, |y|<0.35
0.2
0
p
+
-
+
-
0.2
0
p PHSD
PHENIX
p +p STAR
0.1
0.1
0.0
0.0
0.0
0.5
1.0
incl
g
p
PHSD
PHENIX
PHSD
v2
v2
p +p PHENIX
g
1.5
2.0
2.5
3.0
0.0
pT [GeV/c]
0.5
1.0
1.5
2.0
2.5
pT [GeV/c]
 Pion elliptic flow is well under control in the PHSD.
 Also the inclusive photon v2 is reproduced, because the inclusive photons are
dominate by those from the pion decay
O. Linnyk et al. arXiv:1304.7030
Direct photon elliptic flow
0.4
0.4
direct photon v2
v2(g) from various channels
1/2
1/2
g (QGP)
0
v2
0.2
0.3
Au+Au, sNN =200 GeV, MB, |y|<0.35
g (p )
g ( )
PHENIX
PHSD
p
g (w)
g (mm)
0.2
v2
0.3
Au+Au, sNN =200 GeV, MB, |y|<0.35
0.1
0.1
PHSD
0.0
0.0
0.0
0.5
1.0
1.5
pT [GeV/c]
2.0
2.5
0.0
0.5
1.0
1.5
2.0
2.5
pT [GeV/c]
 Strong direct photon v2 is reproduced by the PHSD calculations
 QGP contribution is very small; v2 of photons from hadronic sources is large
 Observed elliptic flow of direct photons is reproduced, if the same calculation
procedure as in the experiment is used
PHENIX, Adare et al., Phys.Rev.Lett. 109 (2012) 122302; O. Linnyk et al., arXiv:1304.7030
•
•
•
•
•
Conclusions
Parton-Hadron-String-Dynamics (PHSD) transport model provides a
consistent description of the phase transition to the QGP in heavy-ion
collisions. The dynamical quasiparticle model (DQPM) defines the partonic
phase in line with lattice QCD.
Distributions and the collective flow of particles produced in heavy ion
collisions are reproduced from AGS to LHC energies.
The properties of the sQGP in equilibrium are calculated: sheer viscosity,
bulk viscosity, electric conductivity, thermal dilepton rate.
Dilepton data provide evidence for off-shell dynamics of vector mesons.
Yield of dilepton pairs at masses above 1 GeV is described by the q+q
interaction in the QGP.
The enhanced yield and the elliptic flow of produced photons (inclusive and
direct) are explained by the combination of partonic and hadron sources.
Wolfgang Cassing (Giessen U)
Elena Bratkovskaya (FIAS & ITP Frankfurt U)
Volodya Konchakovski (Giessen U)
Thorsten Steinert (Giessen U)
Vitalii Ozvenchuk (FIAS & ITP Frankfurt U)
Rudy Marty (FIAS, Frankfurt U)
Hamza Berrehrah (FIAS, Frankfurt U)
Daniel Cabrera (ITP&FIAS, Frankfurt U)
Taesoo Song (FIAS, Frankfurt U)
Che-Ming Ko
Jörg Aichelin
Pol Bernard Gossiaux
Christoph Hartnack
Mark I. Gorenstein
Viatcheslav D. Toneev
Vadym Voronyuk
Laura Tolos
Angel Ramos
Sergei Voloshin
Back up slides
Flow harmonics (v1, v2, v3, v4)
Increase of v2 with impact parameter but flat v3 and v4
v2/ε = const, indicates near ideal hydrodynamic flow !
Expected since η/s is very small in the DQPM and PHSD.
E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162;
V. P. Konchakovski et al., PRC 85 (2012) 044922
Electro-magnetic fields
PHSD - transport model with electromagnetic fields.
Generalized transport equations:
Magnetic field evolution in HSD/PHSD :
V. Voronyuk et al., Phys.Rev. C83 (2011) 054911
PHENIX: pT spectra
• The lowest and highest mass bins are described very well
• Underestimation of pT data for 100<M<750 MeV bins consistent with dN/dM
• The ‘missing source’(?) is located at low pT !
O. Linnyk, W. Cassing, J. Manninen, E.B. and C.-M. Ko, PRC 85 (2012) 024910
Centrality dependent NA60 data
In+In, 158 A GeV, central (b<3.5)
10
-7
(dN /dMdy)/(dNch/dy) (20 MeV)
-1
10
-6
10
Dominant rho-channel at low
and quark annihilation at
intermediate masses !
-8
10
-6
10
-7
10
-8
10
-9
In+In, 158 A GeV, semi-central (3.5<b<5.5)
In+In, 158 A GeV, semi-periferal (5.5<b<8.5)
r (broadened)
2
PHSD predictions versus
preliminary data
NA60
PHSD
10
-6
10
-7
10
-8
10
-9
+ -
q+qbar-> 
+ q+qbar->  +g
0.5
2
1.0
1.5
M [GeV/c ]
O. Linnyk, E. Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011) 054917
PHENIX: mass spectra
 Peripheral collisions (and pp) are well described, however, central fail!
O. Linnyk, W. Cassing, J. Manninen, E.B. and C.-M. Ko, PRC 85 (2012) 024910
Parton-Hadron-String Dynamics (PHSD)
Description of heavy-ion collisions
as well as p+p, p+A, d+A, p+A reactions.
Features:

Unified description of collisions at all energies from AGS to LHC.

Non-equilibrium approach: applicable to far from equilibrium configurations
as explosion-like heavy-ion collisions as well as to equilibrated matter („in the
box“).

Dynamics: mean fields (hadronic and partonic), scattering (elastic, inelastic,
2<->2, 2<->n), resonance decays, retarded electro-magnetic fields.

Phase transition (cross over) according to the lattice QCD equation of state,
hadronic and partonic degrees of freedom, spacial co-existance, dynamical
hadronisation.

Off-shell transport: takes into account 2-particle correlations beyond the oneparticle distributions.
Can we go back in time ?
Goal: microscopic transport description
of the partonic and hadronic phase
Problems:


How to model a QGP phase in line with lQCD data?
How to solve the hadronization problem?
Ways to go:
‚Hybrid‘ models:
pQCD based models:
QGP phase: hydro with QGP EoS
 QGP phase: pQCD cascade
 hadronization: quark coalescence
 hadronic freeze-out: after burner
- hadron-string transport model
 BAMPS, AMPT, HIJING
 Hybrid-UrQMD
 microscopic transport description of the partonic
and hadronic phase in terms of strongly interacting
dynamical quasi-particles and off-shell hadrons
 PHSD
Parton-Hadron-String Dynamics
Main goal – description of heavy-ion collisions and properties of matter at high
temperature and density as well as of p+p and p(d)+A reactions.

Unified description of collisions at all energies from AGS to LHC.

Non-equilibrium: applicable to far from equilibrium configurations as explosionlike heavy-ion collisions as well as to equilibrated matter („in the box“).

Universal: dileptons, charm, flow (v1, v2, v3, v4), chiral magnetic effect, spin, …

Dynamics: mean fields (hadronic and partonic), scattering (elastic, inelastic, 2<>2, 2<->n), resonance decays, retarded electro-magnetic fields.

Microscopic phase transition (cross over) according to the lattice QCD equation
of state, hadronic and partonic degrees of freedom, spacial co-existance,
dynamical hadronisation.

Off-shell transport: takes into account 2-particle correlations beyond the oneparticle distributions.
Off-shell equations of motion
Employ testparticle Ansatz for the real valued quantity i S<XP -
insert in generalized transport equations and determine equations of motion !
General testparticle off-shell equations of motion:
with
W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445
PHSD: hadronization
Based on DQPM; massive, off-shell quarks and gluons with broad spectral
functions hadronize to off-shell mesons and baryons:
gluons  q + qbar
q + qbar  meson
q + q +q  baryon
Parton-parton recombination rate =
Wm - Gaussian in phase space with
Hadronization happens when the effective interactions |v| become attractive,
approx. for parton densities 1 < rP < 2.2 fm-3
<= from DQPM
W. Cassing, E.L. Bratkovskaya, PRC 78 (2008) 034919; W. Cassing, EPJ ST 168 (2009) 3
RHIC:Dileptons in pp and in heavy ions
PHENIX: pp
PHENIX: Au+Au
‚excess‘
Dilepton cocktail provides a good description of pp data as well as
peripheral Au+Au data, however, fails in describing the central bins!
Phys.Rev.C81 (2010) 034911
PHSD
Unified transport description of partonic and hadronic phases
Initial A+A collisions: string formation and decay to pre-hadrons
Fragmentation of pre-hadrons into quarks using the quark spectral functions
from the Dynamical Quasi-Particle Model
Partonic phase: quarks and gluons with constituent mass and broad spectral
functions defined by DQPM. Elastic and inelastic parton-parton interactions
 q + qbar <=> gluon <=> s + sbar
 gluon + gluon <=> gluon
 q + qbar (color neutral) <=> hadron resonances
Hadronization: massive, off-shell quarks and gluons with broad spectral
functions hadronize to off-shell hadrons:
 gluons  q + qbar; q + qbar  off-shell meson or ‚string‘;
 q + q +q  baryon or ‚string‘;
Hadronic phase: hadron-hadron interaction, propagation and decays
W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;
NPA831 (2009) 215; EPJ ST 168 (2009) 3; NPA856 (2011) 162
Interacting quasiparticles
Entropy density of interacting bosons and fermions (G. Baym 1998):
(2PI)
gluons
quarks
antiquarks
with dg = 16 for 8 transverse gluons and dq = 18 for quarks with 3 colors, 3 flavors and 2
spin projections
-1
nB ( w / T )  expw / T  - 1
Bose distribution function:
-1
nF (( w -  q ) / T )  exp( w -  q ) / T   1
Fermi distribution function:
Simple approximations  DQPM:
Gluon propagator: Δ-1 =P2 - Π
gluon self-energy: Π=Mg2-i2Ggω
Quark propagator Sq-1 = P2 - Σq
quark self-energy: Σq=Mq2-i2Gqω
(scalar)
The Dynamical QuasiParticle Model (DQPM)
Properties of interacting quasi-particles
- massive quarks and gluons (g, q, qbar) with spectral functions :
ρi (w ,T ) 

4 ωG i (T)

2
2
2
2
ω - p - M i (T)  4 ω2 G i (T)
2
 quarks
( i  q ,q , g )
 gluons:
mass:
width:
Nc = 3, Nf=3
 running coupling (pure glue):
 fit to lattice (lQCD) results (e.g. entropy density)
lQCD: pure glue
with 3 parameters: Ts/Tc=0.46; c=28.8; l=2.42 (for
pure glue Nf=0)
 quasiparticle properties (mass, width)
DQPM: Peshier, Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
44
PHSD: Hadronization details
Local covariant off-shell transition rate for q+qbar fusion
=> meson formation
using
Nj(x,p) is the phase-space density of parton j at space-time position x and 4momentum p
 Wm is the phase-space distribution of the formed ‚pre-hadrons‘:
(Gaussian in phase space)

is the effective quark-antiquark interaction from the DQPM

Cassing, Bratkovskaya, PRC 78 (2008) 034919; Cassing, EPJ ST 168 (2009) 3
45
Goal: microscopic transport description of the
partonic and hadronic phase
Problems:
 How to model a QGP phase in line with lQCD data?

How to solve the hadronization problem?
Ways to go:
pQCD based models:
‚Hybrid‘ models:
 QGP phase: pQCD cascade
QGP phase: hydro with QGP EoS
 hadronization: quark coalescence
 hadronic freeze-out: after burner hadron-string transport model
 AMPT, HIJING, BAMPS
 Hybrid-UrQMD
 microscopic transport description of the partonic and
hadronic phase in terms of strongly interacting dynamical
quasi-particles and off-shell hadrons
 PHSD
Bulk viscosity (mean-field effects)
 bulk viscosity in relaxation time approximation with mean-field effects:
Chakraborty, Kapusta, Phys. Rev.C 83, 014906 (2011).
use DQPM results for masses for q=0:
PHSD using the relaxation time
approximation:
 significant rise in the vicinity of
critical temperature
 in line with the ratio from lQCD
calculations
lQCD: Meyer, Phys. Rev. Lett. 100, 162001 (2008);
Sakai,Nakamura, Pos LAT2007, 221 (2007).
V. Ozvenchuk et al., arXiv:1212.5393
Bulk to shear viscosity ratio and specific sound
Bulk to shear viscosity ratio z/ as a
function of temperature T
Specific sound channel (+3z/4)/s as
a function of temperature T
lQCD: H. Meyer
 z/ without mean-field effects almost temperature independent behavior
z/ with mean-field effects  strong increase close to the critical
temperature
 (+3z/4)/s: both the shear and bulk viscosities contribute to the damping of sound
waves in the medium and provide a further constraint on the viscosities
V. Ozvenchuk et al., arXiv:1212.5393
Scaled variance
 scaled variance:
where μ is the mean value of the
observable x averaged over N events:
σ2 is the sample variance:
 scaled variances reach a plateau in time for all observables
 equilibrium values are less than 1 (as in GCE) for all w  MCE
 particle number fluctuations are flavor blind
V. Ozvenchuk et al., PRC 87 (2013) 024901, arXiv:1203.4734
Skewness
 skewness
 skewness characterizes the asymmetry of the distribution function with
respect to its average value
V. Ozvenchuk et al., PRC 87 (2013) 024901, arXiv:1203.4734
Kurtosis
 kurtosis:
 b2 is equal to 3 for normal distribution  excess kurtosis
 Kurtosis as a probe of deconfinement:
lQCD: Ejiri, Karsch, Redlich, Phys. Lett. B 633, 275 (2006)
PHSD
 Kurtosis in PHSD is compatible with
lQCD for QGP
V. Ozvenchuk et al., PRC 87 (2013) 024901, arXiv:1203.4734
Data vs. models
‚Cocktail‘
Hydro
model –
Dusling/
Zahed
Fireball
model –
Rapp/Hees
PHSD model,
in-medium
effects: coll.
broadening
Large discrepances between the models and PHENIX data in the invariant mass
region from 0.2 to 0.7 GeV in central Au+Au collisions.
-> PHENIX dilepton puzzle?
Phys.Rev.C81 (2010) 034911
Bulk properties
Application to nucleus-nucleus collisions
energy balance
Pb+Pb, b=1 fm
0.4
Tkin [A GeV]
10
20
40
80
160
0.3
0.2
0.1
Pb+Pb, 158 A GeV, b=1 fm
4000
Etot
Em
3000
# [GeV]
partonic energy fraction
partonic energy fraction vs energy
Ep
EB
2000
1000
0
0.0
0
3
5
8
10
13
15
18
20
0
3
5
8
10
13
15
18
20
t [fm/c]
t [fm/c]
 Dramatic decrease of partonic phase with decreasing energy
 Pb+Pb, 160 A GeV: only about 40% of the converted energy goes to partons; the rest
is contained in the large hadronic corona and leading partons!
(hadronic corona effect, cf. talk by J. Aichelin)
Cassing & Bratkovskaya, NPA 831 (2009) 215
54
PHSD: Transverse mass spectra
Central Pb + Pb at SPS energies
Central Au+Au at RHIC
 PHSD gives harder mT spectra and works better than HSD at high energies
– RHIC, SPS (and top FAIR, NICA)
 however, at low SPS (and low FAIR, NICA) energies the effect of the partonic phase
decreases due to the decrease of the partonic fraction
W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215
E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856
(2011) 162
55
Anisotropy coefficients
Non central Au+Au collisions :
 interaction between constituents leads to a pressure gradient
=> spatial asymmetry is converted to an asymmetry in
momentum space => collective flow
from S. A. Voloshin, arXiv:1111.7241
v2 > 0 indicates in-plane emission of particles
v2 < 0 corresponds to a squeeze-out perpendicular to the
reaction plane (out-of-plane emission)
Collective flow: v2 excitation functions
PHSD
The excitation function for v2 of charged particles from
string-hadron transport models – UrQMD:
QGP
Influence of hadron potentials  EoS
0.20
0.15
Au+Au, mid-rapidity, semi-central
protons
RBUU (Munich), potential
RBUU (Giessen), potential
RBUU (Giessen), cascade
GiBUU, potential
GBUU, cascade
0.10
v2
0.05
0.00
-0.05
-0.10
-0.15
EOS/ E895/ E877
FOPI/ Plastic Ball/ LAND/ MSU
0.1
1
Ebeam [GeV]
10
Excitation function of elliptic flow
Excitation function of elliptic flow is not described by hadron-string or purely
partonic models (hadronic corona effect, cf. talk by J. Aichelin) !
Elliptic flow v2 vs. collision energy for Au+Au
v
in PHSD is larger than in HSD due to the
repulsive scalar mean-field potential Us(ρ) for
partons
2
 v2 grows with bombarding energy due to the
increase of the parton fraction
V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev.
C 85 (2012) 011902
59
Development of azimuthal anisotropies in time
Time evolution of vn for Au + Au collisions at s 1/2 = 200 GeV with impact
parameter b = 8 fm.
 Flow coefficients reach their asymptotic values by the time of 6–8 fm/c after the
beginning of the collision
V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev.
C 85 (2012) 011902
60
Scaling properties: quark number scaling
 The mass splitting at low pT is approximately reproduced as well as the
meson-baryon splitting for pT > 2 GeV/c !
 The scaling of v2 with the number of constituent quarks nq is roughly in line
with the data at RHIC.
E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856
(2011) 162
61
NA60: differential spectrum
Acceptance corrected NA60 data
Parton dominance at M>1 GeV and rho broadening confirmed by the differencial data
O. Linnyk, E.Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011) 054917
Off-shell propagation
The off-shell spectral function becomes on-shell in the vacuum dynamically!
2
10
collisional broadening
1
10
0
1
2
3
5
0
A(M)
gluon
r/r
r meson
10
-1
10
-2
10
-3
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2
M [GeV/c ]
E.L. Bratkovskaya, W. Cassing, V. P. Konchakovski, O. Linnyk, NPA856(2011) 162; E.L. Bratkovskaya, W. Cassing, NPA 807 (2008) 214;