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QCD and Heavy-Ion Collisions
Elena Bratkovskaya
Institut für Theoretische Physik & FIAS,
Uni. Frankfurt
The international workshop 'Monte Carlo methods in computer simulations of complex systems',
FEFU, Vladivostok, Russia, 12-24 October 2015.
1
The ‚holy grail‘ of heavy-ion physics:
• Search for the critical point
The phase diagram of QCD
• Study of the
phase transition
from hadronic to
partonic matter –
Quark-GluonPlasma
• Study of the in-medium properties of hadrons at high baryon
density and temperature
The QGP in Lattice QCD
Quantum Chromo Dynamics :
Lattice QCD:
energy density versus temperature
predicts strong increase of
the energy density e at critical
temperature TC ~160 MeV
 Possible phase transition from
hadronic to partonic matter (quarks,
gluons) at critical energy density
eC ~0.5 GeV/fm3
lQCD: Wuppertal-Budapest group
Y. Aoki et al., JHEP 0906 (2009) 088.
Critical conditions - eC ~0.5 GeV/fm3 , TC ~160 MeV - can be reached in
heavy-ion experiments at bombarding energies > 5 GeV/A
‚Little Bangs‘ in the Laboratory
Initial State
Hadronization
time
Au+Au
hadron
degrees
of freedom
Quark-Gluon-Plasma ?
quarks and gluons
hadron
degrees
of freedom
How can we proove that an equilibrium QGP has been created in
central heavy-ion collisions ?!
Signals of the phase transition:
• Multi-strange particle enhancement in A+A
• Charm suppression
• Collective flow (v1, v2)
• Thermal dileptons
• Jet quenching and angular correlations
• High pT suppression of hadrons
• Nonstatistical event by event fluctuations and correlations
• ...
Experiment: measures
final hadrons and leptons
How to learn about
physics from data?
Compare with theory!
Basic models for heavy-ion collisions
• Statistical models:
basic assumption: system is described by a (grand) canonical ensemble of
non-interacting fermions and bosons in thermal and chemical equilibrium
[ -: no dynamics]
• Ideal hydrodynamical models:
basic assumption: conservation laws + equation of state; assumption of
local thermal and chemical equilibrium
[ -: - simplified dynamics]
• Transport models:
based on transport theory of relativistic quantum many-body systems Actual solutions: Monte Carlo simulations
[+: full dynamics | -: very complicated]
 Microscopic transport models provide a unique dynamical description
of nonequilibrium effects in heavy-ion collisions
Models of heavy-ion collisions
thermal model
thermal+expansion
initial
hydro
transport
final
Dynamical description of heavy-ion collisions
The goal:
to study the properties of strongly interacting matter
under extreme conditions from a microscopic point
of view
Realization:
dynamical many-body transport models
Semi-classical BUU equation
Boltzmann-Uehling-Uhlenbeck equation (non-relativistic formulation)
- propagation of particles in the self-generated Hartree-Fock mean-field
potential U(r,t) with an on-shell collision term:



 
 

 

p 
 f 


f ( r , p , t )   r f ( r , p , t )   r U ( r , t )  p f ( r , p , t )   
t
m
  t  coll
 
f ( r , p , t ) is the single particle phase-space distribution function
Ludwig Boltzmann
collision term:
elastic and
inelastic reactions
- probability to find the particle at position r with momentum p at time t
 self-generated Hartree-Fock mean-field potential:

U ( r ,t ) 
1
( 2  ) 3
d



3
 
 
r  d 3 p V ( r  r  , t ) f ( r  , p , t )  ( Fock term )
o cc
 Collision term for 1+23+4 (let‘s consider fermions) :
I coll 
   d
4
3
3
3 
d
p
d
p
d

|

|

(
p

p
( 1  2  3  4 ) P
2
3 
12
1
2  p3  p4 ) 
( 2 )3 
d
Probability including Pauli blocking of fermions:
P  f 3 f 4 ( 1  f 1 )( 1  f 2 )  f 1 f 2 ( 1  f 3 )( 1  f 4 )
1
Gain term: 3+41+2
2
Loss term: 1+23+4
t
 12
3
4
9
Theoretical description of strongly interecting system
 In-medium effects = changes of particle properties in the hot and
dense baryonic medium; example – vector mesons, strange mesons
 Strongly interacting QGP
Many-body theory:
Strong interaction  large width = short life-time
 broad spectral function  quantum object
 How to describe the dynamics of
broad strongly interacting quantum
states in transport theory?
L(1783)N-1
and
S(1830)N-1
exitations
 semi-classical BUU
first order gradient
expansion of quantum
Kadanoff-Baym equations
Barcelona /
Valencia
group
 generalized transport equations
10
Dynamical description of strongly interacting systems
 Semi-classical on-shell BUU: applies for small collisional width, i.e. for a weakly
interacting systems of particles
How to describe strongly interacting systems?!
 Quantum field theory 
Kadanoff-Baym dynamics for resummed single-particle Green functions S<
(1962)
Green functions S< / self-energies S:
Integration over the intermediate spacetime

iS xy
 η {Φ  ( y )Φ ( x ) }
ret
c


a
S xy
 S xy
 S xy
 S xy
 S xy
 retarded

iS xy
  {Φ ( y )Φ  ( x ) }
adv
c


a
S xy
 S xy
 S xy
 S xy
 S xy
 advanced
c
iS xy
 T c {Φ ( x )Φ  ( y ) }  causal
   1( bosons / fermions )
a
iS xy
 T a {Φ ( x )Φ  ( y ) }  anticausal
Leo Kadanoff
Ŝ 0 x1   (  x  x  M 02 )
T a ( T c )  ( anti  )time  ordering operator
Gordon Baym
11
From Kadanoff-Baym equations to
generalized transport equations
After the first order gradient expansion of the Wigner transformed Kadanoff-Baym
equations and separation into the real and imaginary parts one gets:
Generalized transport equations (GTE):
drift term
Vlasov term
backflow term
collision term = ‚gain‘ - ‚loss‘ term
Backflow term incorporates the off-shell behavior in the particle propagation
! vanishes in the quasiparticle limit AXP  (p2-M2)
 GTE: Propagation of the Green‘s function iS<XP=AXPNXP , which carries
information not only on the number of particles (NXP), but also on their properties,
interactions and correlations (via AXP)
 Spectral function:
 XP   Im S XPret  2 p0  – ‚width‘ of spectral function
4-dimentional generalizaton of the Poisson-bracket:
= reaction rate of particle (at space-time position X)
c


 Life time

W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445
12
General testparticle off-shell equations of motion
W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445
 Employ testparticle Ansatz for the real valued quantity i S<XP -
insert in generalized transport equations and determine equations of motion !
 General testparticle Cassing‘s off-shell equations of motion
for the time-like particles:
with
13
Collision term in off-shell transport models
Collision term for reaction 1+2->3+4:
‚gain‘ term
‚loss‘ term
with
The trace over particles 2,3,4 reads explicitly
for bosons
for fermions
additional integration
The transport approach and the particle spectral functions are
fully determined once the in-medium transition amplitudes G
are known in their off-shell dependence!
14
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
From SIS to LHC: from hadrons to partons
The goal: to study of the phase transition from hadronic to partonic matter
and properties of the Quark-Gluon-Plasma from microscopic origin
 need a consistent non-equilibrium transport model
 with explicit parton-parton interactions (i.e. between quarks and gluons)
 explicit phase transition from hadronic to partonic degrees of freedom
 lQCD EoS for partonic phase (‚crossover‘ at q=0)
 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)
16
Interacting quasiparticles
Entropy density of interacting bosons and fermions (G. Baym 1998):
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 (  / T )  exp / T   1
Bose distribution function:
1
Fermi distribution function: nF ((   q ) / T )  exp(   q ) / T   1
Simple approximations  DQPM:
Gluon propagator: Δ-1 =P2 - Π
Quark propagator Sq-1 = P2 - Σq
gluon self-energy: Π=M2-i2γgω
quark self-energy: Σq=m2-i2γqω
(scalar)
Dynamical QuasiParticle Model (DQPM) - Basic ideas:
DQPM describes QCD properties in terms of ‚resummed‘ single-particle
Green‘s functions – in the sense of a two-particle irreducible (2PI) approach:
Gluon propagator: Δ-1 =P2 - Π
gluon self-energy: Π=Mg2-i2gω
Quark propagator: Sq-1 = P2 - Σq
quark self-energy: Σq=Mq2-i2qω
 the resummed properties are specified by complex self-energies which depend
on temperature:
-- the real part of self-energies (Σq, Π) describes a dynamically generated mass
(Mq,Mg);
-- the imaginary part describes the interaction width of partons (q, g)
 space-like part of energy-momentum tensor Tn defines the potential energy
density and the mean-field potential (1PI) for quarks and gluons (Uq, Ug)
2PI framework guaranties a consistent description of the system in- and out-off
equilibrium on the basis of Kadanoff-Baym equations with proper states in
equilibrium
A. Peshier, W. Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
18
The Dynamical QuasiParticle Model (DQPM)
Properties of interacting quasi-particles:
4 ω i (T)
A
(

,
T
)

massive quarks and gluons (g, q, qbar)
i
2
2
2
2
2 2
ω

p

M
(T)

4
ω
 i (T)
with Lorentzian spectral functions :
i
( i  q ,q , g )

 Modeling of the quark/gluon masses and widths

 HTL limit at high T
 gluons:
 quarks:
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)
DQPM: Peshier, Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
19
DQPM thermodynamics (Nf=3) and lQCD
entropy
interaction measure:
 pressure P
energy density:
TC=160 MeV
eC=0.5 GeV/fm3
lQCD: Wuppertal-Budapest group
Y. Aoki et al., JHEP 0906 (2009) 088.
0.35
0.30
p/e
0.25
0.20
Nf=3
0.15
0.10
equation of state
0.05
0.00
1
10
100
1000
3
e [GeV/fm ]
DQPM gives a good description of lQCD results !
20
Time-like and space-like quantities
Separate time-like and space-like single-particle quantities by Q(+P2), Q(-P2):
gluons
quarks
antiquarks
Time-like: Θ(+P2): particles may
decay to real particles or interact
Examples:
q
q
g*
e+
Space-like: Θ(-P2): particles are virtuell
and appear as exchange quanta in
interaction processes of real particles
e-
e*
e-
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
q
q
Time-like and ‚space-like‘ energy densities
x: gluons, quarks, antiquarks
energy density / T
4
6
5
4
3
2
00
Tg
1
00
Tg
+
00
Tq

00
Tq
+

0
250
500
750
1000
T [MeV]
 space-like energy density dominates for gluons;
 space-like parts are identified with potential energy densities:
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
The Dynamical QuasiParticle Model (DQPM)
 fit to lattice (lQCD) results (e.g. entropy density)
* BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073
 Quasiparticle properties:
 large width and mass for gluons and quarks
TC=158 MeV
eC=0.5 GeV/fm3
•DQPM matches well lattice QCD
•DQPM provides mean-fields (1PI) for gluons and
quarks as well as effective 2-body interactions (2PI)
•DQPM gives transition rates for the formation of hadrons  PHSD
Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)
23
23
Parton-Hadron-String-Dynamics (PHSD)
 Initial A+A collisions – HSD:
N+N  string formation  decay to pre-hadrons
 Formation of QGP stage if e > ecritical :
dissolution of pre-hadrons  (DQPM) 
 massive quarks/gluons + mean-field potential Uq
 Partonic stage – QGP :
based on the Dynamical Quasi-Particle Model (DQPM)
 (quasi-) elastic collisions:
qqqq
qq qq
q q q q
gq gq
gq  gq
g g g g
 inelastic collisions:
qq  g
g qq
qq  g g
g g g
 Hadronization (based on DQPM):
g  qq,
q  q  meson ( or ' string ' )
q  q  q  baryon ( or ' string ' )
 Hadronic phase: hadron-hadron interactions – off-shell HSD
W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3
24
Fluctuations in-equilibrium QGP
using PHSD
Properties of parton-hadron matter in-equilibrium
The goal:
V. Ozvenchuk et al., PRC 87 (2013) 024901, arXiv:1203.4734
V. Ozvenchuk et al., PRC 87 (2013) 064903, arXiv:1212.5393
 study of the dynamical equilibration of QGP within the non-equilibrium
off-shell PHSD transport approach
 transport coefficients (shear and bulk viscosities) of strongly
interacting partonic matter
 particle number fluctuations (scaled variance, skewness, kurtosis)
Realization:
 Initialize the system in a finite box with
periodic boundary conditions with some
energy density ε and chemical potential μq
 Evolve the system in time until
equilibrium is achieved
26
Properties of parton-hadron matter – 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
QGP
 T<TC: fast increase of the ratio
h/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
Virial expansion: S. Mattiello, W.
Cassing, Eur. Phys. J. C 70, 243 (2010).
QGP in PHSD = strongly-interacting liquid
V. Ozvenchuk et al., PRC 87 (2013) 064903
27
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 mq=0:
PHSD using the relaxation time
approximation:
 significant rise in the vicinity of
the critical temperature
 in line with the ratio from lQCD
calculations
V. Ozvenchuk et al.,
PRC 87 (2013) 064903
Cf. Gabriel Denicol
lQCD: Meyer, Phys. Rev. Lett. 100, 162001 (2008);
Sakai,Nakamura, Pos LAT2007, 221 (2007).
Properties of parton-hadron matter – electric conductivity
The response of the strongly-interacting
system in equilibrium to an external electric
field eEz defines the electric conductivity s0:
 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., PRL 110(2013)182301
29
Charm spatial diffusion coefficient Ds in the hot medium
 Ds for heavy quarks as a function of T for q=0 and finite q
 Continuous transition at TC!
 T < Tc : hadronic Ds
L. Tolos , J. M. Torres-Rincon, PRD 88 (2013) 074019
V. Ozvenchuk et al., PRC90 (2014) 054909
Cf. talk by Laura Tolos, Tu, 17:00
H. Berrehrah et al, PRC 90 (2014) 051901, arXiv:1406.5322
30
‚Bulk‘ properties
in Au+Au
31
Time evolution of energy density
PHSD: 1 event Au+Au, 200 GeV, b = 2 fm
e(x=0,y,z)
time
e(x,y,z=0)
V: x=y=1fm, z=1/g fm
R. Marty et al, 2014
32
Partonic energy fraction in central A+A
partonic energy fraction
Time evolution of the partonic energy fraction vs energy
Pb+Pb, b=1 fm
0.4
Tkin [A GeV]
10
20
40
80
160
0.3
0.2
0.1
0.0
0
3
5
8
10
13
15
18
20
t [fm/c]
 Strong increase of partonic phase with energy from AGS to RHIC
 SPS: 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
 RHIC: Au+Au, 21.3 A TeV: up to 90% - QGP
W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215
V. Konchakovski et al., Phys. Rev. C 85 (2012) 011902
33
Transverse mass spectra from SPS to RHIC
Central Pb + Pb at SPS energies
Central Au+Au at RHIC
 PHSD gives harder mT spectra and works better than HSD (wo QGP) 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
Elliptic flow v2 vs. collision energy for Au+Au
v
in PHSD is larger than in HSD
due to the repulsive scalar meanfield 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
35
Vn (n=2,3,4,5) of charged particles from PHSD at LHC
symbols – ALICE
PHSD: increase of vn (n=2,3,4,5) with pT
 v2 increases with decreasing centrality
PRL 107 (2011) 032301
lines – PHSD (e-by-e)
 vn (n=3,4,5) show weak centrality dependence
V. Konchakovski, W. Cassing, V. Toneev, arXiv:1411.5534
36
Messages from the study of spectra and collective flow
 PHSD gives harder mT spectra than HSD (without QGP) at high
energies – LHC, RHIC, SPS
 at RHIC and LHC the QGP dominates the early stage dynamics
 at low SPS (and low FAIR, NICA) energies the effect of the partonic
phase decreases
 influence of the finite quark chemical potential q ?!
 Anisotropy coefficients vn as a signal of the QGP:
 quark number scaling of v2 at ultrarelativistic energies – signal of
deconfinement
 growing of v2 with energy – partonic interactions generate a larger
pressure than the hadronic interactions
 vn, n=3,.. – sensitive to QGP
37
Thermodynamic and transport
properties of sQGP in equilibrium at finite
temperature and chemical potential
Hamza Berrehrah et al.
38
The Dynamical QuasiParticle Model (DQPM) at finite T
Properties of interacting quasi-particles:
4 ω i (T)
A
(

,
T
)

massive quarks and gluons (g, q, qbar)
i
2
2
2
2
2 2
ω

p

M
(T)

4
ω
 i (T)
with Lorentzian spectral functions :
i
( i  q ,q , g )

 Modeling of the quark/gluon masses and widths

 HTL limit at high T
 gluons:
 quarks:
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)
DQPM: Peshier, Cassing, PRL 94 (2005) 172301;
Cassing, NPA 791 (2007) 365: NPA 793 (2007)
39
DQPM at finite (T, q): scaling hypothesis
 Scaling hypothesis for the effective temperature T* for Nf = Nc = 3
 Coupling constant:
 Critical temperature Tc(q) :
obtained by requiring a constant energy density e
for the system at T=Tc(q) where e at Tc(q=0)=158 GeV
is fixed by lQCD at q=0
! Consistent with lattice QCD:
lQCD: C. Bonati et al., PRC90 (2014) 114025
lQCD
H. Berrehrah et al. arXiv:1412.1017
40
DQPM at finite (T, q): quasiparticle masses and widths
 Coupling constant:
 Quark and gluon masses:
 Quark and gluon widths:
41
DQPM: thermodynamics at finite (T, q)
 Entropy density at finite T
 Energy density at finite T
Entropy density at finite (T, q)
Energy density at finite (T, q)
H. Berrehrah et al. arXiv:1412.1017
42
DQPM: q, qbar, g elastic scattering at finite (T, q)
Hamza Berrehrah et al. arXiv:1412.1017
43
I. DQPM: transport properties at finite (T, q) : /s
Shear viscosity /s at finite T
Shear viscosity /s at finite (T, q)
/s: q=0  finite q:
smooth increase as a function of (T, q)
H. Berrehrah et al. arXiv:1412.1017
PHSD in a box: V. Ozvenchuk et al., PRC 87 (2013) 064903
Virial expansion: S. Mattiello, W. Cassing, EPJ C70 (2010) 243
NJL: R. Marty et al., PRC 88 (2013) 045204
44
II. DQPM: transport properties at finite (T, q): e/T
Electric conductivity e/T at finite T
Electric conductivity e/T at finite (T, q)
e/T : q=0  finite q:
smooth increase as a function of (T, q)
H. Berrehrah et al. arXiv:1412.1017
PHSD in a box: W. Cassing et al., PRL 110(2013)182301
NJL: R. Marty et al., PRC 88 (2013) 045204
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Charm spatial diffusion coefficient Ds in the hot medium
 Ds for heavy quarks as a function of T for q=0 and finite q
 T < Tc : hadronic Ds
 Continuous transition at TC!
L. Tolos , J. M. Torres-Rincon,
Phys. Rev. D 88, 074019 (2013)
H. Berrehrah et al, PRC 90 (2014) 051901, arXiv:1406.5322
46
Summary: DQPM at finite (T, q)
 Extension of the DQPM to finite q using scaling hypothesis for the
effective temperature T*
 q=0  finite q:
 variations in the QGP transport coefficients
 smooth dependence on (T, q)
 /s, z/s, e/T, Ds show minima around TC at q=0 and finite q
 Outlook
Implementation into PHSD: from T,q=0  finite T,q
Lattice data at finite q are needed!
47
Thanks to:
PHSD group
FIAS & Frankfurt University
Elena Bratkovskaya
Hamza Berrehrah
Daniel Cabrera
Taesoo Song
Andrej Ilner
Pierre Moreau
Giessen University
Wolfgang Cassing
Olena Linnyk
Volodya Konchakovski
Thorsten Steinert
Alessia Palmese
Eduard Seifert
External Collaborations
SUBATECH, Nantes University:
Jörg Aichelin
Christoph Hartnack
Pol-Bernard Gossiaux
Vitalii Ozvenchuk
Texas A&M University:
Che-Ming Ko
JINR, Dubna:
Viacheslav Toneev
Vadim Voronyuk
Lyon University:
Rudy Marty
Barcelona University:
Laura Tolos
Angel Ramos
48
Thank you!
Chiral magnetic effect and
evolution of the electromagnetic field
in relativistic heavy-ion collisions
Charge separation in HIC: CP violation signal
Magnetic field through the axial anomaly induces a parallel electric field
which will separate different charges
L or B
Non-zero angular momentum (or
equivalently strong magnetic field) in
heavy-ion collisions make it possible
for P- and CP-odd domains to induce
charge separation
 ‚chiral magnetic effect‘ (CME)
D.Kharzeev, PLB 633 (2006) 260
Electric dipole moment of QCD matter !
Measuring the charge
separation with respect to the
reaction plane - S.Voloshin,
PRC 70 (2004) 057901
 Combination of intense B-field and deconfinement is needed for a spontanuous
parity violation signal !
51
Charge separation in RHIC experiments
STAR Collaboration, PRL 103 (2009) 251601
<cos(φa+φb-2ψRP)>
200 GeV
62 GeV
Combination of intense B and deconfinement is needed
for a spontaneous parity violation signal
52
PHSD with electromagnetic fields
 Generalized transport equations in the presence of electromagnetic fields*:
 A general solution of the wave equations
 retarded Lienard-Wiechert electric and magnetic potentials:
* Realized in the PHSD for
hadrons and quarks
V. Voronyuk, et al., Phys.Rev. C83 (2011) 054911
53
Magnetic field evolution
Au+Au (200 GeV)
b=10 fm
54
V.Voronyuk, et al., Phys.Rev. C83 (2011) 054911
Time dependence of eBy
HSD: V.Voronyuk, et al.,
PRC83 (2011) 054911
Collision of two infinitely
thin layers (pancake-like)
D.E. Kharzeev et al., NPA803,
227 (2008)
 Until t~1 fm/c the induced magnetic field is defined by spectators only
 Maximal magnetic field is reached during nuclear overlapping time
Δt~0.2 fm/c, then the field goes down exponentially
V.Voronyuk, et al., Phys.Rev. C83 (2011) 054911
55
Angular correlation wrt. reaction plane
 Angular correlation is of hadronic origin up to s1/2 = 11 GeV !
V. D. Toneev et al., PRC 85 (2012) 034910, PRC 86 (2012) 064907
56
Compensation of magnetic and electric forces
Au+Au, s1/2 = 11 GeV, b=10 fm
Momentum increment:
(for pZ>0)
 strong magnetic and electric
forces compensate each other!
V. D. Toneev et al., PRC 85 (2012) 034910,
PRC 86 (2012) 064907
57
Summary for CME – angular correlations
The PHSD transport model with retarded electromagnetic fields shows :
 creation of strong electric and magnetic fields at heavy-ion collisions
 strong magnetic and electric forces compensate each other small
effect on observables
 low-energy experiments within the RHIC BES program at √sNN = 7.7 and
11.5 GeV can be explained within hadronic scenario without reference to
the spontaneous local CP violation.
 PHSD doesn’t reproduce the exp. data on angular correlations
<cos(φa+φb-2ψRP)> at √sNN= 39 - 200 GeV  indication for CME?
58