1 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, October 2015.

The ‚holy grail‘ of heavy-ion physics: Study of the phase transition from hadronic to partonic matter – Quark-Gluon- Plasma Study of the phase transition from hadronic to partonic matter – Quark-Gluon- Plasma Search for the critical point Search for the critical point Study of the in-medium properties of hadrons at high baryon density and temperature Study of the in-medium properties of hadrons at high baryon density and temperature The phase diagram of QCD

The QGP in Lattice QCD Lattice QCD: energy density versus temperature energy density versus temperature Quantum Chromo Dynamics : predicts strong increase of the energy density e at critical temperature T C ~160 MeV  Possible phase transition from hadronic to partonic matter (quarks, gluons) at critical energy density  C ~0.5 GeV/fm 3 Critical conditions -  C ~0.5 GeV/fm 3, T C ~160 MeV - can be reached in heavy-ion experiments at bombarding energies > 5 GeV/A lQCD: Wuppertal-Budapest group Y. Aoki et al., JHEP 0906 (2009) 088.

‚Little Bangs‘ in the Laboratory time Initial State Hadronization Au+Au Quark-Gluon-Plasma ? quarks and gluons hadron degrees of freedom hadron degrees of freedom How can we proove that an equilibrium QGP has been created in central heavy-ion collisions ?!

Multi-strange particle enhancement in A+A Multi-strange particle enhancement in A+A Charm suppression Charm suppression Collective flow (v 1, v 2 ) Collective flow (v 1, v 2 ) Thermal dileptons Thermal dileptons Jet quenching and angular correlations Jet quenching and angular correlations High p T suppression of hadrons High p T suppression of hadrons Nonstatistical event by event fluctuations and correlations Nonstatistical event by event fluctuations and correlations Experiment: measures final hadrons and leptons Signals of the phase transition: How to learn about physics from data? Compare with theory!

Statistical models: 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] [ -: no dynamics] Ideal hydrodynamical models: Ideal hydrodynamical models: basic assumption: conservation laws + equation of state; assumption of local thermal and chemical equilibrium [ -: - simplified dynamics] [ -: - simplified dynamics] Transport models: Transport models: based on transport theory of relativistic quantum many-body systems - Actual solutions: Monte Carlo simulations [+: full dynamics | -: very complicated] Basic models for heavy-ion collisions  Microscopic transport models provide a unique dynamical description of nonequilibrium effects in heavy-ion collisions

Models of heavy-ion collisions transport hydro thermal+expansion thermal model final initial

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

99 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: is the single particle phase-space distribution function - probability to find the particle at position r with momentum p at time t  self-generated Hartree-Fock mean-field potential: Ludwig Boltzmann collision term: elastic and inelastic reactions Probability including Pauli blocking of fermions: Gain term: 3+4  1+2 Loss term: 1+2  3+4 Collision term for 1+2  3+4 (let‘s consider fermions) :  Collision term for 1+2  3+4 (let‘s consider fermions) :

10 Theoretical description of strongly interecting system Many-body theory: Strong interaction  large width = short life-time  broad spectral function  quantum object  broad spectral function  quantum object  How to describe the dynamics of broad strongly interacting quantum states in transport theory? Barcelona / Valencia group  (1783)N -1 and  (1830)N -1 exitations  semi-classical BUU  generalized transport equations first order gradient expansion of quantum Kadanoff-Baym equations  In-medium effects = changes of particle properties in the hot and dense baryonic medium; example – vector mesons, strange mesons  Strongly interacting QGP

1111 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  Quantum field theory  Kadanoff-Baym dynamics for resummed single-particle Green functions S < (1962) Leo Kadanoff Gordon Baym Green functions S < / self-energies  : Integration over the intermediate spacetime How to describe strongly interacting systems?!

1212 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: Backflow term incorporates the off-shell behavior in the particle propagation Backflow term incorporates the off-shell behavior in the particle propagation ! vanishes in the quasiparticle limit A XP   (p 2 -M 2 ) ! vanishes in the quasiparticle limit A XP   (p 2 -M 2 )  Spectral function: – ‚width‘ of spectral function = reaction rate of particle (at space-time position X) – ‚width‘ of spectral function = reaction rate of particle (at space-time position X) 4-dimentional generalizaton of the Poisson-bracket: W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445  GTE: Propagation of the Green‘s function iS < XP =A XP N XP, which carries information not only on the number of particles ( N XP ), but also on their properties, interactions and correlations (via A XP ) drift term Vlasov term collision term = ‚gain‘ - ‚loss‘ term backflow term Generalized transport equations (GTE):  Life time

1313 General testparticle 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 Cassing‘s off-shell equations of motion for the time-like particles: with W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

14 Collision term in off-shell transport models Collision term for reaction 1+2->3+4: Collision term for reaction 1+2->3+4: with The trace over particles 2,3,4 reads explicitly for fermions for bosons 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! additional integration ‚loss‘ term ‚gain‘ term ‚gain‘ term

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:  QGP phase: hydro with QGP EoS  hadronic freeze-out: after burner - hadron-string transport model  Hybrid-UrQMD  microscopic transport description of the partonic and hadronic phase in terms of strongly interacting dynamical quasi-particles and off-shell hadrons  PHSD pQCD based models:  QGP phase: pQCD cascade  hadronization: quark coalescence  AMPT, HIJING, BAMPS

16 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) Parton-Hadron-String-Dynamics (PHSD) QGP phase described by Dynamical QuasiParticle Model DQPM Dynamical QuasiParticle Model (DQPM)  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 A. Peshier, W. Cassing, PRL 94 (2005) ; A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007 ) Cassing, NPA 791 (2007) 365: NPA 793 (2007 ) W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3

Interacting quasiparticles Entropy density of interacting bosons and fermions (G. Baym 1998): gluons quarks antiquarks with d g = 16 for 8 transverse gluons and d q = 18 for quarks with 3 colors, 3 flavors and 2 spin projections Bose distribution function: Bose distribution function: Fermi distribution function: Fermi distribution function: Gluon propagator: Δ -1 =P 2 - Π gluon self-energy: Π=M 2 -i2γ g ω Quark propagator S q -1 = P 2 - Σ q quark self-energy: Σ q =m 2 -i2γ q ω Simple approximations  DQPM: (scalar)

18 DQPM describes QCD properties in terms of ‚resummed‘ single-particle Green‘s functions – in the sense of a two-particle irreducible (2PI) approach: A. Peshier, W. Cassing, PRL 94 (2005) ; A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) Dynamical QuasiParticle Model (DQPM) - Basic ideas:  the resummed properties are specified by complex self-energies which depend on temperature: -- the real part of self-energies (Σ q, Π) describes a dynamically generated mass (M q,M g ); -- the imaginary part describes the interaction width of partons (  q,  g ) -- the real part of self-energies (Σ q, Π) describes a dynamically generated mass (M q,M g ); -- the imaginary part describes the interaction width of partons (  q,  g )  space-like part of energy-momentum tensor T  defines the potential energy density and the mean-field potential (1PI) for quarks and gluons (U q, U g )  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 Gluon propagator: Δ -1 =P 2 - Π gluon self-energy: Π=M g 2 -i2  g ω Quark propagator: S q -1 = P 2 - Σ q quark self-energy: Σ q =M q 2 -i2  q ω

19 The Dynamical QuasiParticle Model (DQPM) Properties of interacting quasi-particles: massive quarks and gluons (g, q, q bar ) with Lorentzian spectral functions : DQPM: Peshier, Cassing, PRL 94 (2005) ; DQPM: Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) with 3 parameters: T s /T c =0.46; c=28.8; =2.42 (for pure glue N f =0)  fit to lattice (lQCD) results (e.g. entropy density)  running coupling (pure glue): N c = 3, N f =3 mass: width:  gluons:  quarks: lQCD: pure glue  Modeling of the quark/gluon masses and widths  HTL limit at high T

DQPM thermodynamics (N f =3) and lQCD entropy  pressure P energy density: interaction measure: DQPM gives a good description of lQCD results ! DQPM gives a good description of lQCD results ! lQCD: Wuppertal-Budapest group Y. Aoki et al., JHEP 0906 (2009) T C =160 MeV  C =0.5 GeV/fm 3 equation of state N f =3

Time-like and space-like quantities Separate time-like and space-like single-particle quantities by  (+P 2 ),  (-P 2 ): Time-like: Θ(+P 2 ): particles may decay to real particles or interact Space-like: Θ(-P 2 ): particles are virtuell and appear as exchange quanta in interaction processes of real particles gluons quarks antiquarks q q e+e+ e-e- ** e-e- e-e- q q * Cassing, NPA 791 (2007) 365: NPA 793 (2007) Examples:

Time-like and ‚space-like‘ energy densities space-like energy density dominates for gluons;  space-like energy density dominates for gluons;  space-like parts are identified with potential energy densities: x: gluons, quarks, antiquarks Cassing, NPA 791 (2007) 365: NPA 793 (2007)

23 The Dynamical QuasiParticle Model (DQPM) Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007)  Quasiparticle properties:  large width and mass for gluons and quarks DQPM matches well lattice QCD DQPM matches well lattice QCD DQPM provides mean-fields (1PI) for gluons and quarks as well as effective 2-body interactions (2PI) 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 DQPM gives transition rates for the formation of hadrons  PHSD  fit to lattice (lQCD) results (e.g. entropy density) * BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073 T C =158 MeV  C =0.5 GeV/fm 3 23

 Formation of QGP stage if  >  critical : dissolution of pre-hadrons  (DQPM)  dissolution of pre-hadrons  (DQPM)   massive quarks/gluons + mean-field potential U q  massive quarks/gluons + mean-field potential U q 24 Parton-Hadron-String-Dynamics (PHSD)  Hadronic phase: hadron-hadron interactions – off-shell HSD W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3  Initial A+A collisions – HSD: N+N  string formation  decay to pre-hadrons N+N  string formation  decay to pre-hadrons  (quasi-) elastic collisions:  inelastic collisions:  Partonic stage – QGP : based on the Dynamical Quasi-Particle Model (DQPM)  Hadronization (based on DQPM):

Fluctuations in-equilibrium QGP using PHSD

The goal:  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) Properties of parton-hadron matter in-equilibrium Realization:  Initialize the system in a finite box with periodic boundary conditions with some energy density ε and chemical potential μ q  Evolve the system in time until equilibrium is achieved V. Ozvenchuk et al., PRC 87 (2013) , arXiv: V. Ozvenchuk et al., PRC 87 (2013) , arXiv:

Properties of parton-hadron matter – shear viscosity T=T C :  /s shows a minimum (~0.1) close to the critical temperature   T=T C :  /s shows a minimum (~0.1) close to the critical temperature  T>T C : QGP - pQCD limit at higher temperatures  T<T C : 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 QGP in PHSD = strongly-interacting liquid  /s using Kubo formalism and the relaxation time approximation (‚kinetic theory‘) Virial expansion: S. Mattiello, W. Cassing, Eur. Phys. J. C 70, 243 (2010). V. Ozvenchuk et al., PRC 87 (2013) QGP 27

Bulk viscosity (mean-field effects)  bulk viscosity in relaxation time approximation with mean-field effects: Chakraborty, Kapusta, Phys. Rev.C 83, (2011). use DQPM results for masses for m q =0:  significant rise in the vicinity of the critical temperature  in line with the ratio from lQCD calculations lQCD: Meyer, Phys. Rev. Lett. 100, (2008); Sakai,Nakamura, Pos LAT2007, 221 (2007). PHSD using the relaxation time approximation: V. Ozvenchuk et al., PRC 87 (2013) Cf. Gabriel Denicol

Properties of parton-hadron matter – electric conductivity  the QCD matter even at T~ T c is a much better electric conductor than Cu or Ag (at room temperature) by a factor of 500 !  The response of the strongly-interacting system in equilibrium to an external electric field eE z defines the electric conductivity s 0 : W. Cassing et al., PRL 110(2013)

30 Charm spatial diffusion coefficient D s in the hot medium D s for heavy quarks as a function of T for  q =0 and finite  q  D s for heavy quarks as a function of T for  q =0 and finite  q  Continuous transition at T C ! H. Berrehrah et al, PRC 90 (2014) , arXiv: T < T c : hadronic D s  T < T c : hadronic D s L. Tolos, J. M. Torres-Rincon, PRD 88 (2013) V. Ozvenchuk et al., PRC90 (2014) Cf. talk by Laura Tolos, Tu, 17:00

31 ‚ Bulk‘ properties in Au+Au

32 Time evolution of energy density R. Marty et al, 2014 PHSD: 1 event Au+Au, 200 GeV, b = 2 fm time  (x,y,z=0)  (x=0,y,z)  V:  x=  y=1fm,  z=1/  fm

Partonic energy fraction in central A+A  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) Time evolution of the partonic energy fraction vs energy

Transverse mass spectra from SPS to RHIC Central Pb + Pb at SPS energies  PHSD gives harder m T 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 Central Au+Au at RHIC W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215 E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162

Elliptic flow v 2 vs. collision energy for Au+Au 35 v 2 in PHSD is larger than in HSD due to the repulsive scalar mean- field potential U s (ρ) for partons  v 2 in PHSD is larger than in HSD due to the repulsive scalar mean- field potential U s (ρ) for partons  v 2 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)

36 V n (n=2,3,4,5) of charged particles from PHSD at LHC V. Konchakovski, W. Cassing, V. Toneev, arXiv:  PHSD: increase of v n (n=2,3,4,5) with p T  v 2 increases with decreasing centrality  v n (n=3,4,5) show weak centrality dependence symbols – ALICE PRL 107 (2011) lines – PHSD (e-by-e)

Messages from the study of spectra and collective flow  Anisotropy coefficients v n as a signal of the QGP:  quark number scaling of v 2 at ultrarelativistic energies – signal of deconfinement  growing of v 2 with energy – partonic interactions generate a larger pressure than the hadronic interactions  v n, n=3,.. – sensitive to QGP  PHSD gives harder m T 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 ?! 37

38 Thermodynamic and transport properties of sQGP in equilibrium at finite temperature and chemical potential Hamza Berrehrah et al. Hamza Berrehrah et al.

39 The Dynamical QuasiParticle Model (DQPM) at finite T Properties of interacting quasi-particles: massive quarks and gluons (g, q, q bar ) with Lorentzian spectral functions : DQPM: Peshier, Cassing, PRL 94 (2005) ; DQPM: Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) with 3 parameters: T s /T c =0.46; c=28.8; =2.42 (for pure glue N f =0)  fit to lattice (lQCD) results (e.g. entropy density)  running coupling (pure glue): N c = 3, N f =3 mass: width:  gluons:  quarks: lQCD: pure glue  Modeling of the quark/gluon masses and widths  HTL limit at high T

40 DQPM at finite (T,  q ): scaling hypothesis  Scaling hypothesis for the effective temperature T* for N f = N c = 3  Coupling constant:  Critical temperature T c (  q ) : obtained by requiring a constant energy density  for the system at T=T c (  q ) where  at T c (  q =0)=158 GeV is fixed by lQCD at  q =0 ! Consistent with lattice QCD: lQCD: C. Bonati et al., PRC90 (2014) lQCD H. Berrehrah et al. arXiv:

41 DQPM at finite (T,  q ): quasiparticle masses and widths  Quark and gluon masses:  Coupling constant:  Quark and gluon widths:

42 DQPM: thermodynamics at finite (T,  q ) Entropy density at finite (T,  q )  Entropy density at finite T  Energy density at finite T H. Berrehrah et al. arXiv: Energy density at finite (T,  q )

43 DQPM: q, qbar, g elastic scattering at finite (T,  q ) Hamza Berrehrah et al. arXiv:

44 I. DQPM: transport properties at finite (T,  q ) :  /s Shear viscosity  /s at finite (T,  q ) Shear viscosity  /s at finite T PHSD in a box: V. Ozvenchuk et al., PRC 87 (2013) Virial expansion: S. Mattiello, W. Cassing, EPJ C70 (2010) 243 NJL: R. Marty et al., PRC 88 (2013)  /s:  q =0  finite  q : smooth increase as a function of (T,  q ) H. Berrehrah et al. arXiv:

45 II. DQPM: transport properties at finite (T,  q ):  e /T Electric conductivity  e /T at finite (T,  q ) Electric conductivity  e /T at finite T PHSD in a box: W. Cassing et al., PRL 110(2013) NJL: R. Marty et al., PRC 88 (2013)  e /T :  q =0  finite  q : smooth increase as a function of (T,  q ) H. Berrehrah et al. arXiv:

46 Charm spatial diffusion coefficient D s in the hot medium D s for heavy quarks as a function of T for  q =0 and finite  q  D s for heavy quarks as a function of T for  q =0 and finite  q  Continuous transition at T C ! H. Berrehrah et al, PRC 90 (2014) , arXiv: T < T c : hadronic D s L. Tolos, J. M. Torres-Rincon, Phys. Rev. D 88, (2013)  T < T c : hadronic D s L. Tolos, J. M. Torres-Rincon, Phys. Rev. D 88, (2013)

47 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,  /s,  e /T, D s show minima around T C at  q =0 and finite  q  Outlook Implementation into PHSD: from  q =0  finite T,  q Lattice data at finite  q are needed!

48 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 Thanks to: PHSD group

Thank you!

Chiral magnetic effect and evolution of the electromagnetic field in relativistic heavy-ion collisions

Charge separation in HIC: CP violation signal 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) Magnetic field through the axial anomaly induces a parallel electric field which will separate different charges 51  Combination of intense B-field and deconfinement is needed for a spontanuous parity violation signal !

52 Charge separation in RHIC experiments STAR Collaboration, PRL 103 (2009) Combination of intense B and deconfinement is needed for a spontaneous parity violation signal 200 GeV 62 GeV

53 PHSD with electromagnetic fields  Generalized transport equations in the presence of electromagnetic fields*: V. Voronyuk, et al., Phys.Rev. C83 (2011)  retarded Lienard-Wiechert electric and magnetic potentials:  A general solution of the wave equations * Realized in the PHSD for hadrons and quarks

54 Magnetic field evolution Au+Au (200 GeV) b=10 fm V.Voronyuk, et al., Phys.Rev. C83 (2011)

55 Time dependence of eB y 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 Δt~0.2 fm/c, then the field goes down exponentially HSD: V.Voronyuk, et al., PRC83 (2011) V.Voronyuk, et al., Phys.Rev. C83 (2011)

Angular correlation wrt. reaction plane  Angular correlation is of hadronic origin up to s 1/2 = 11 GeV ! V. D. Toneev et al., PRC 85 (2012) , PRC 86 (2012)

Compensation of magnetic and electric forces  strong magnetic and electric forces compensate each other! Momentum increment: (for p Z >0) V. D. Toneev et al., PRC 85 (2012) , PRC 86 (2012) Au+Au, s 1/2 = 11 GeV, b=10 fm

58 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 √s NN = 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 at √s NN = GeV  indication for CME? Summary for CME – angular correlations