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We present the basic ideas of the Parton-Hadron-String Dynamics (PHSD) transport approach which is a microscopic covariant dynamical model for strongly interacting systems formulated on the basis of Kadanoff-Baym equations for Green's functions in phase-space representation (in 1st order gradient expansion beyond the quasi-particle approximation). The approach consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the strongly-interacting quark-gluon plasma (sQGP) as well as hadronization and the subsequent interactions in the expanding hadronic phase. The PHSD approach has been applied to p+p, p+A and A+A collisions from lower SIS to LHC energies and been successful in describing a large number of experimental data including single-particle spectra, collective flow and electromagnetic probes. Some highlights of recent PHSD results will be presented., Comment: 17 pages, 6 figures, to be published in the Proceedings of the Indo-French Seminar on "Multi-fragmentation, collective flow and subthreshold partice production in heavy ion reactions", February 4-6 2019, Punjab University, Chandigarh, India

In this contribution we briefly give an overview of the theoretical models used to describe experimental data from heavy-ion collisions from $\sqrt{s_{NN}} \approx $ 4 GeV to ultra-relativistic energies of $\sqrt{s_{NN}} \approx $ 5 TeV. We highlight the successes and problems of statistical or hadron-resonance gas models, address the results of macroscopic approaches like hydrodynamics (in different hybrid combinations) as well as the results from microscopic transport approaches in comparison to experimental data. Finally, the transport coefficients like shear $\eta$ and bulk viscosity $\zeta$ - entering the macroscopic models - are confronted with results from lattice QCD in thermal equilibrium for vanishing chemical potential., Comment: Contribution to the Proceedings of the ICPPA conference: The 3rd International Conference on Particle Physics and Astrophysics (ICPPA-2017), Moscow, Russia, 2-5 October 2017

We study the effect of the chiral symmetry restoration (CSR) on heavy-ion collisions observables in the energy range $\sqrt{s_{NN}}$=3-20 GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach. The PHSD includes the deconfinement phase transition as well as essential aspects of CSR in the dense and hot hadronic medium, which are incorporated in the Schwinger mechanism for the hadronic particle production. We adopt different parametrizations of the nuclear equation of state from the non-linear $\sigma-\omega$ model, which enter in the computation of the quark scalar density for the CSR mechanism, in order to estimate the uncertainty in our calculations., Comment: 22 pages, 19 figures

In this review we address the dynamics of relativistic heavy-ion reactions and in particular the information obtained from electromagnetic probes that stem from the partonic and hadronic phases. The out-of-equilibrium description of strongly interacting relativistic fields is based on the theory of Kadanoff and Baym. For the modeling of the partonic phase we introduce a dynamical quasiparticle model (DQPM) for QCD in equilibrium. The widths and masses of the quasiparticles are controlled by transport coefficients in comparison to lattice QCD results. The resulting off-shell transport approach - denoted by Parton-Hadron-String Dynamics (PHSD) - also includes covariant dynamical hadronization and keeps track of the hadronic interactions in the final phase. We show that PHSD captures the bulk dynamics of heavy-ion collisions from SPS to LHC energies and provides a basis for the evaluation of the electromagnetic emissivity, using the same dynamical parton propagators as for the system evolution. Direct photon production in elementary processes and heavy-ion reactions at RHIC and LHC energies is investigated and the status of the photon v2 puzzle - a large elliptic flow of the direct photons observed in A+A collisions - is addressed. We discuss the roles of hadronic and partonic sources for the photon spectra and the flow coefficients v2 and v3 and also the possibility to subtract the QGP signal from observables. Furthermore, the production of dilepton pairs is addressed from SIS to LHC energies. The low-mass dilepton yield is enhanced due to the in-medium modification of the rho-meson and at the lowest energy also due to a multiple regeneration of Delta-resonances. In addition, a signal of the partonic degrees-of-freedom is found in the intermediate dilepton mass regime (1.2GeV

We study the production of strange hadrons in nucleus-nucleus collisions from 4 to 160 A GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach that is extended to incorporate essentials aspects of chiral symmetry restoration (CSR) in the hadronic sector (via the Schwinger mechanism) on top of the deconfinement phase transition as implemented in PHSD. Especially the $K^+/\pi^+$ and the $(\Lambda+\Sigma^0)/\pi^-$ ratios in central Au+Au collisions are found to provide information on the relative importance of both transitions. The modelling of chiral symmetry restoration is driven by the pion-nucleon $\Sigma$-term in the computation of the quark scalar condensate $$ that serves as an order parameter for CSR and also scales approximately with the effective quark masses $m_s$ and $m_q$. Furthermore, the nucleon scalar density $\rho_s$, which also enters the computation of $$, is evaluated within the nonlinear $\sigma-\omega$ model which is constraint by Dirac-Brueckner calculations and low energy heavy-ion reactions. The Schwinger mechanism (for string decay) fixes the ratio of strange to light quark production in the hadronic medium. We find that above $\sim$80 A GeV the reaction dynamics of heavy nuclei is dominantly driven by partonic degrees-of-freedom such that traces of the chiral symmetry restoration are hard to identify. Our studies support the conjecture of 'quarkyonic matter' in heavy-ion collisions from about 5 to 40 A GeV and provide a microscopic explanation for the maximum in the $K^+/\pi^+$ ratio at about 30 A GeV which only shows up if a transition to partonic degrees-of-freedom is incorporated in the reaction dynamics and is discarded in the traditional hadron-string models., Comment: 12 pages, 7 figures

We study charm production in ultra-relativistic heavy-ion collisions by using the Parton-Hadron-String Dynamics (PHSD) transport approach. The initial charm quarks are produced by the PYTHIA event generator tuned to fit the transverse momentum spectrum and rapidity distribution of charm quarks from Fixed-Order Next-to-Leading Logarithm (FONLL) calculations. The produced charm quarks scatter in the quark-gluon plasma (QGP) with the off-shell partons whose masses and widths are given by the Dynamical Quasi-Particle Model (DQPM), which reproduces the lattice QCD equation-of-state in thermal equilibrium. The relevant cross sections are calculated in a consistent way by employing the effective propagators and couplings from the DQPM. Close to the critical energy density of the phase transition, the charm quarks are hadronized into $D$ mesons through coalescence and/or fragmentation. The hadronized $D$ mesons then interact with the various hadrons in the hadronic phase with cross sections calculated in an effective lagrangian approach with heavy-quark spin symmetry. The nuclear modification factor $R_{AA}$ and the elliptic flow $v_2$ of $D^0$ mesons from PHSD are compared with the experimental data from the STAR Collaboration for Au+Au collisions at $\sqrt{s_{NN}}$ =200 GeV and to the ALICE data for Pb+Pb collisions at $\sqrt{s_{NN}}$ =2.76 TeV. We find that in the PHSD the energy loss of $D$ mesons at high $p_T$ can be dominantly attributed to partonic scattering while the actual shape of $R_{AA}$ versus $p_T$ reflects the heavy-quark hadronization scenario, i.e. coalescence versus fragmentation. Also the hadronic rescattering is important for the $R_{AA}$ at low $p_T$ and enhances the $D$-meson elliptic flow $v_2$., Comment: 8 pages, 3 figures, to be published in the Proceedings of the 15th International Conference on Strangeness in Quark Matter (SQM2015), 6-11 July 2015, JINR, Dubna, Russia

The direct photon spectra and flow ($v_2$, $v_3$) in heavy-ion collisions at SPS, RHIC and LHC energies are investigated within a relativistic transport approach incorporating both hadronic and partonic phases -- the Parton-Hadron-String Dynamics (PHSD). In the present work, four extensions are introduced compared to our previous calculations: (i) going beyond the soft-photon approximation (SPA) in the calculation of the bremsstrahlung processes $meson+meson\to meson+meson+\gamma$, (ii) quantifying the suppression due to the Landau-Pomeranchuk-Migdal (LPM) coherence effect, (iii) adding the additional channels $V+N\to N+\gamma$ and $\Delta\to N+\gamma$ and (iv) providing predictions for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The first issue extends the applicability of the bremsstrahlung calculations to higher photon energies in order to understand the relevant sources in the region $p_T=0.5-1.5$ GeV, while the LPM correction turns out to be important for $p_T<0.4$ GeV in the partonic phase. The results suggest that a large elliptic flow $v_2$ of the direct photons signals a significant contribution of photons produced in interactions of secondary mesons and baryons in the late (hadronic) stage of the heavy-ion collision. In order to further differentiate the origin of the direct photon azimuthal asymmetry (late hadron interactions vs electromagnetic fields in the initial stage), we provide predictions for the triangular flow $v_3(p_T)$ of direct photons. Additionally, we illustrate the magnitude of the photon production in the partonic and hadronic phases as functions of time and local energy density. Finally, the 'cocktail' method for an estimation of the background photon elliptic flow, which is widely used in the experimental works, is supported by the calculations within the PHSD transport approach., Comment: 28 pages, 24 figures, v3: recent ALICE data added onto the plots on top of our predictions, final version accepted for publication

Direct photon spectra and elliptic flow v2 in heavy-ion collisions at RHIC and LHC energies are investigated within a relativistic transport approach incorporating both hadronic and partonic phases - the Parton-Hadron-String Dynamics (PHSD). The results suggest that a large v2 of the direct photons - as observed by the PHENIX Collaboration - signals a significant contribution of photons produced in interactions of secondary mesons and baryons in the late stages of the collision. In order to further differentiate the origin of the direct photon azimuthal asymmetry, we compare our predictions for the centrality dependence of the direct photon yield to the recent measurements by the PHENIX Collaboration and provide predictions for Pb+Pb collisions at LHC energies with respect to the direct photon spectra and v2(pT) for 0-40% centrality., Comment: 11 pages, 6 figures, talk at the XXII International Baldin Seminar on High Energy Physics Problems, 15-20 September, 2014, JINR, Dubna, Russia

We investigate the properties of the QCD matter across the deconfinement phase transition in the scope of the parton-hadron string dynamics (PHSD) transport approach. We present here in particular the results on the electromagnetic radiation, i.e. photon and dilepton production, in relativistic heavy-ion collisions. By comparing our calculations for the heavy-ion collisions to the available data, we determine the relative importance of the various production sources and address the possible origin of the observed strong elliptic flow $v_2$ of direct photons. We argue that the different centrality dependence of the hadronic and partonic sources for direct photon production in nucleus-nucleus collisions can be employed to shed some more light on the origin of the photon $v_2$ "puzzle". While the dilepton spectra at low invariant mass show in-medium effects like an enhancement from multiple baryonic resonance formation or a collisional broadening of the vector meson spectral functions, the dilepton yield at high invariant masses (above 1.1 GeV) is dominated by QGP contributions for central heavy-ion collisions at ultra-relativistic energies. This allows to have an independent view on the parton dynamics via their electromagnetic massive radiation., Comment: 12 pages, Proceedings of the 3rd International Conference on 'New Frontiers in Physics 2014', Kolymbari, Crete

Recent STAR data for the directed flow of protons, antiprotons and charged pions obtained within the beam energy scan program are analyzed within the Parton-Hadron-String-Dynamics (PHSD/HSD) transport models. Both versions of the kinetic approach are used to clarify the role of partonic degrees of freedom. The PHSD results, simulating a partonic phase and its coexistence with a hadronic one, are roughly consistent with the STAR data. Generally, the semi-qualitative agreement between the measured data and model results supports the idea of a crossover type of quark-hadron transition which softens the nuclear EoS but shows no indication of a first-order phase transition. Furthermore, the directed flow of kaons and antikaons is evaluated in the PHSD/HSD approachesfrom $\sqrt{s_{NN}} \approx$ 3 - 200 GeV which shows a high sensitivity to hadronic potentials in the FAIR/NICA energy regime $\sqrt{s_{NN}} \le$ 8 GeV., Comment: 12 pages, Proceedings of the 3rd International Conference on New Frontiers in Physics, Kolymbari, Crete, July 28th - Aug. 6th

We discuss the latest theoretical results on direct photon and dilepton production from relativistic heavy-ion collisions. While the dilepton spectra at low invariant mass show in-medium effects like a collisional broadening of the vector meson spectral functions, the dilepton yield at high invariant masses (above 1.1 GeV) is dominated by QGP contributions for central heavy-ion collisions at relativistic energies. The present status of the photon $v_2$ "puzzle" - a large elliptic flow $v_2$ of the direct photons experimentally observed at RHIC and LHC energies - is also addressed. The role of hadronic and partonic sources for the photon spectra and $v_2$ is considered as well as the possibility to subtract the QGP signal from the experimental observables., Comment: 8 pages, 4 figures, Proceedings of the XXIV Quark Matter conference, May 19-24 2014, Darmstadt (Germany)

In this study we investigate the dynamics of strongly interacting parton-hadron matter by calculating the centrality dependence of direct photons produced in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach. As sources for 'direct' photons, we incorporate the interactions of quarks and gluons as well as hadronic interactions ($\pi+\pi\to\rho+\gamma$, $\rho+\pi\to\pi+\gamma$, meson-meson bremsstrahlung $m+m\to m+m+\gamma$, meson-baryon bremsstrahlung $m+B\to m+B+\gamma$), the decays of $\phi$ and $a_1$ mesons and the photons produced in the initial hard collisions ('pQCD'). Our calculations suggest that the channel decomposition of the observed spectrum changes with centrality with an increasing (dominant) contribution of hadronic sources for more peripheral reactions. Furthermore, the 'thermal' photon yield is found to scale roughly with the number of participant nucleons as $N_{part}^\alpha$ with $\alpha \approx$ 1.5, whereas the partonic contribution scales with an exponent $\alpha_p \approx1.75$. Additionally, we provide predictions for the centrality dependence of the direct photon elliptic flow $v_2(p_T)$. The direct photon $v_2$ is seen to be larger in peripheral collisions compared to the most central ones since the photons from the hot deconfined matter in the early stages of the collision carry a much smaller elliptic flow than those from the final hadronic interactions., Comment: 4 pages, 4 figures, Proceedings of 'Hard Probes 2013'

The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD approach is applied to nucleus-nucleus collisions from low SPS to LHC energies. The traces of partonic interactions are found in particular in the elliptic flow of hadrons and in their transverse mass spectra. We investigate also the equilibrium properties of strongly-interacting infinite parton-hadron matter characterized by transport coefficients such as shear and bulk viscosities and the electric conductivity in comparison to lattice QCD results., Comment: 6 pages, 7 figures, Proceedings of the STARS2013 and SMFNS2013 conferences, 4-10 May 2013, Havana/Varadero, Cuba

We investigate the properties of the QCD matter across the deconfinement phase transition. In the scope of the parton-hadron string dynamics (PHSD) transport approach, we study the strongly interacting matter in equilibrium as well as the out-of equilibrium dynamics of relativistic heavy-ion collisions. We present here in particular the results on the electromagnetic radiation, i.e. photon and dilepton production, in relativistic heavy-ion collisions and the relevant correlator in equilibrium, i.e. the electric conductivity. By comparing our calculations for the heavy-ion collisions to the available data, we determine the relative importance of the various production sources and address the possible origin of the observed strong elliptic flow $v_2$ of direct photons., Comment: 4 pages, talk at the International Nuclear Physics Conference (INPC 2013), published version

We study the shear and bulk viscosities of partonic and hadronic matter - as well as the electric conductivity - as functions of temperature $T$ within the Parton-Hadron-String Dynamics (PHSD) off-shell transport approach. Dynamical hadronic and partonic systems in equilibrium are studied by the PHSD simulations in a finite box with periodic boundary conditions. The ratio of the shear viscosity to entropy density $\eta(T)/s(T)$ from PHSD shows a minimum (with a value of about 0.1) close to the critical temperature $T_c$. For $T

We study the transverse momentum spectrum and the elliptic flow v2 of photons produced in Au+Au collisions at sqrt(s)=200 GeV using the Parton-Hadron-String Dynamics (PHSD) transport approach. As sources for photon production, we incorporate the interactions of off-shell quarks and gluons in the strongly interacting quark-gluon plasma (q+qbar->g+gamma and q/qbar+g->q/qbar+gamma), the decays of hadrons (pi->gamma+gamma, eta->gamma+gamma, omega->pi+gamma, eta'->rho+gamma, phi->eta+gamma, a_1->pi+gamma) as well as their interactions (pi+pi->rho+gamma, rho+pi->pi+gamma, bremsstrahlung m+m->m+m+gamma). The PHSD calculations reproduce the transverse momentum spectrum, the effective temperature T_eff and the elliptic flow v2 of both inclusive and direct photons as measured by the PHENIX Collaboration. The photons produced in the QGP contribute slightly less then 50% to the observed spectrum, but have small v2. We find that the large direct photon v2 - comparable to that of hadrons - can be attributed to the intermediate hadronic scattering channels not subtracted from the data when following the same extraction procedure for v2 as in the PHENIX experiment. On the other hand the v2 of direct photons - as evaluated by the weighted average of direct photon channels - gives a lower signal. The difference between the two extraction procedures for the direct photon v2 can be attributed to different definitions for the yield ratio of direct photons to the background photons. The QGP phase causes the strong elliptic flow of photons indirectly, by enhancing the v2 of final hadrons due to the partonic interaction in terms of explicit parton collisions and the mean-field potentials. We also show that the presence of the QGP radiation is manifest in the slope of the direct photon spectrum, leading to a slope parameter T_eff far above the critical temperature for the deconfinement phase transition., Comment: 12 pages, 13 figures, section on the direct photon v2 extended, conclusions unchanged

The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD model reproduces a large variety of observables from SPS to LHC energies, e.g. the quark-number scaling of elliptic flow, transverse mass and rapidity spectra of charged hadrons, dilepton spectra, open and hidden charm production, collective flow coefficients etc., which are associated with the observation of a sQGP. The highlights of the latest results on collective flow are presented and open questions/perspectives are discussed., Comment: 8 pages, 4 figures, contribution to the Proceedings of the Kruger-2012 International Workshop on Discovery Physics at the LHC (Kruger National park in South Africa, December 3-7, 2012)

We study the dilepton production in heavy-ion collisions at energies of 1-2 AGeV as well as in proton induced pp, pn, pd and p+A reactions from 1 GeV up to 3.5 GeV. For the analysis we employ three different transport models - the microscopic off-shell Hadron-String-Dynamics (HSD) transport approach, the Isospin Quantum Molecular Dynamics (IQMD) approach as well as the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. We confirm the experimentally observed enhancement of the dilepton yield (normalized to the multiplicity of neutral pions $N_{\pi^0}$) in heavy-ion collisions with respect to that measured in $NN = (pp+pn)/2$ collisions. We identify two contributions to this enhancement: a) the $pN$ bremsstrahlung which scales with the number of collisions and not with the number of participants, i.e. pions; b) the dilepton emission from intermediate $\Delta$'s which are part of the reaction cycles $\Delta \to \pi N ; \pi N \to \Delta$ and $NN\to N\Delta; N\Delta \to NN$. With increasing system size more generations of intermediate $\Delta$'s are created. If such $\Delta$ decays into a pion, the pion can be reabsorbed, however, if it decays into a dilepton, the dilepton escapes from the system. Thus, experimentally one observes only one pion (from the last produced $\Delta$) whereas the dilepton yield accumulates the contributions from all $\Delta$'s of the cycle. We show as well that the Fermi motion enhances the production of pions and dileptons in the same way. Furthermore, employing the off-shell HSD approach, we explore the influence of in-medium effects like the modification of self-energies and spectral functions of the vector mesons due to their interactions with the hadronic environment., Comment: 46 pages, 48 figures, version to be published in Phys. Rev. C

We study the shear and bulk viscosities of partonic and hadronic matter as functions of temperature T within the parton-hadron-string dynamics (PHSD) off-shell transport approach. Dynamical hadronic and partonic systems in equilibrium are studied by the PHSD simulations in a finite box with periodic boundary conditions. The ratio of the shear viscosity to entropy density \eta(T)/s(T) from PHSD shows a minimum (with a value of about 0.1) close to the critical temperature T_c, while it approaches the perturbative QCD limit at higher temperatures in line with lattice QCD (lQCD) results. For T

In terms of the parton-hadron-string-dynamics (PHSD) approach - including the retarded electromagnetic field - we investigate the role of fluctuations of the correlation function in the azimuthal angle $\psi$ of charged hadrons that is expected to be a sensitive signal of local strong parity violation. For the early time we consider fluctuations in the position of charged spectators resulting in electromagnetic field fluctuations as well as in the position of participant baryons defining the event plane. For partonic and hadronic phases in intermediate stages of the interaction we study the possible formation of excited matter in electric charge dipole and quadrupole form as generated by fluctuations. The role of the transverse momentum and local charge conservation laws in the observed azimuthal asymmetry is investigated, too. All these above-mentioned effects are incorporated in our analysis based on event-by-event PHSD calculations. Furthermore, the azimuthal angular correlations from Au+Au collisions observed in the recent STAR measurements within the RHIC Beam-Energy-Scan (BES) program are studied. It is shown that the STAR correlation data at the collision energies of $\sqrt{s_{NN}}$ = 7.7 and 11.5 GeV can be reasonably reproduced within the PHSD. At higher energies the model fails to describe the $\psi$ correlation data resulting in an overestimation of the partonic scalar field involved. We conclude that an additional transverse anisotropy fluctuating source is needed which with a comparable strength acts on both in- and out-of-plane components., Comment: 20 pages, 19 figures, to be published in Phys. Rev. C

We study e^+e^- pair production in proton-proton and central Pb+Pb collisions at sqrt(s_NN)=2.76 TeV within two models: an extended statistical hadronization model (SHM) and the Parton-Hadron-String Dynamics (PHSD) transport approach. We find that the PHSD calculations roughly agree with the dilepton spectrum from hadronic sources with the 'cocktail' estimates from the statistical hadronization model matched to available data at LHC energies. The dynamical simulations within the PHSD show a moderate increase of the low mass dilepton yield essentially due to the in-medium modification of the rho-meson. Furthermore, pronounced traces of the partonic degrees of freedom are found in the PHSD results in the intermediate mass regime. The dilepton production from the strongly interacting quark-gluon plasma (sQGP) exceeds that from the semi-leptonic decays of open charm and bottom mesons. Additionally, we observe that a transverse momentum cut of 1 GeV/c further suppresses the relative contribution of the heavy meson decays to the dilepton yield, such that the sQGP radiation strongly dominates the spectrum for masses from 1 to 3 GeV, allowing a closer look at the electromagnetic emissivity of the partonic plasma in the early phase of Pb+Pb collisions., Comment: 16 pages, 10 figures

The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach which incorporates explicit partonic degrees-of-freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ of charged hadrons with collision energy is successfully described in terms of the PHSD approach. The analysis of higher-order harmonics $v_3$ and $v_4$ in the azimuthal angular distribution shows a similar tendency of growing deviations between partonic and purely hadronic models with increasing collision energy. This demonstrates that the excitation functions of azimuthal anisotropies reflect the increasing role of quark-gluon degrees of freedom in the early phase of relativistic heavy-ion collisions. Furthermore, the specific variation of the ratio $v_4/(v_2)^2$ with respect to bombarding energy, centrality and transverse momentum is found to provide valuable information on the underlying partonic dynamics., Comment: Proceedings of 28th Winter Workshop on Nuclear Dynamics in Dorado del Mar, Puerto Rico, 7-14 April, 2012. 9 pages, 4 figures

We study e+e- pair production in proton-proton and in nucleus-nucleus collisions from SIS to LHC energies within the parton-hadron-string dynamics (PHSD) approach which incorporates explicit partonic degrees-of-freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. We find a visible in-medium effect in the low mass dilepton sector from dynamical vector-meson spectral functions from SIS to SPS energies whereas at RHIC and LHC energies such medium effects become more moderate. In the intermediate mass regime from 1.1 to 3 GeV pronounced traces of the partonic degrees of freedom are found at SPS and RHIC energies which superseed the hadronic (multi-meson) channels as well as the correlated and uncorrelated semi-leptonic D-meson decays. The dilepton production from the strongly interacting quark gluon plasma (sQGP) becomes already visible at top SPS energies and more pronounced at RHIC and LHC energies., Comment: 8 pages, 5 figures, to be published in the proceedings of the 28th Winter Workshop on Nuclear Dynamics, Dorado del Mar, Puerto Rico, April 7-14, 2012

The recently proposed two families of strongly intensive measures of fluctuations and correlations are studied within Hadron-String-Dynamics (HSD) transport approach to nucleus-nucleus collisions. We consider the measures $\Delta^{K\pi}$ and $\Sigma^{K\pi}$ for kaon and pion multiplicities in Au+Au collisions in a wide range of collision energies and centralities. These strongly intensive measures appear to cancel the participant number fluctuations. This allows to enlarge the centrality window in the analysis of event-by-event fluctuations up to at least of 10% most central collisions. We also present a comparison of the HSD results with the data of NA49 and STAR collaborations. The HSD describes $\Sigma^{K\pi}$ reasonably well. However, the HSD results depend monotonously on collision energy and do not reproduce the bump-deep structure of $\Delta^{K\pi}$ observed from the NA49 data in the region of the center of mass energy of nucleon pair $\sqrt{s_{NN}}= 8\div 12$ GeV. This fact deserves further studies. The origin of this `structure' is not connected with simple geometrical or limited acceptance effects, as these effects are taken into account in the HSD simulations.

We study the kinetic and chemical equilibration in "infinite" parton matter within the parton-hadron-string dynamics off-shell transport approach, which is based on a dynamical quasiparticle model (DQPM) for partons matched to reproduce lattice QCD results-including the partonic equation of state-in thermodynamic equilibrium. The "infinite" parton matter is simulated by a system of quarks and gluons within a cubic box with periodic boundary conditions, at different energy densities, initialized slightly out of kinetic and chemical equilibrium. We investigate the approach of the system to equilibrium and the time scales for the equilibration of different observables. We, furthermore, study particle distributions in the strongly interacting quark-gluon plasma (sQGP) including partonic spectral functions, momentum distributions, abundances of the different parton species and their fluctuations (scaled variance, skewness, and kurtosis) in equilibrium. We also compare the results of the microscopic calculations with the ansatz of the DQPM. It is found that the results of the transport calculations are in equilibrium well matched by the DQPM for quarks and antiquarks, while the gluon spectral function shows a slightly different shape due to the explicit interaction of partons. The time scales for the relaxation of fluctuation observables are found to be shorter than those for the average values. Furthermore, in the local subsystem, a strong change of the fluctuation observables with the size of the local volume is observed. These fluctuations no longer correspond to those of the full system and are reduced to Poissonian distributions when the volume of the local subsystem becomes much smaller than the total volume., Comment: 21 pages, 20 figures

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. The PHSD approach is applied to nucleus-nucleus collisions from low SIS to RHIC energies. The traces of partonic interactions are found in particular in the elliptic flow of hadrons as well as in their transverse mass spectra., Comment: To be published by Springer in Proceedings of the International Symposium on `Exciting Physics', Makutsi-Range, South Africa, 13-20 November, 2011

The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic parton-hadron-string dynamics (PHSD) transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation of state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ of charged hadrons with collision energy is successfully described in terms of the PHSD approach. The PHSD scaling properties of various collective observables are confronted with experimental data as well as with hydrodynamic predictions. The analysis of higher-order harmonics $v_3$ and $v_4$ in the azimuthal angular distribution shows a similar tendency of growing deviations between partonic and purely hadronic models with increasing collision energy. This demonstrates that the excitation functions of azimuthal anisotropies reflect the increasing role of quark-gluon degrees of freedom in the early phase of relativistic heavy-ion collisions. Furthermore, the specific variation of the ratio $v_4/(v_2)^2$ with respect to bombarding energy, centrality and transverse momentum is found to provide valuable information on the underlying dynamics., Comment: 15 pages, 19 figures

In terms of the hadron-string-dynamics (HSD) approach we investigate the correlation function in the azimuthal angle $\psi$ of charged hadrons that is expected to be sensitive to a signal of local strong parity violation. Our analysis of Au+Au collisions is based on the recent STAR data within the RHIC Beam-Energy-Scan (BES) program. The HSD model reasonably reproduces STAR data for $\sqrt{s_{NN}}=$7.7 GeV, while there are some deviations from the experiment at the collision energy of 11.5 GeV and an increase of deviations between theory and experiment at $\sqrt{s_{NN}}=$39 GeV. For reference, the results for $\sqrt{s_{NN}}=$ 200 GeV are given as well. The role of the retarded electromagnetic field is discussed and a compensation effect for the action of its electric and magnetic components is pointed out. We conclude that the recent RHIC BES data at $\sqrt{s_{NN}}=$7.7 and 11.5 GeV can be understood on the hadronic level without involving the idea of a strong parity violation; however, at $\sqrt{s_{NN}}\sim$40 GeV and above one needs to take into consideration explicit partonic (quark-qluon) degrees-of-freedom for a proper treatment of the dynamics., Comment: 6pages, 3 figures, 1 table; title changed by editor, references updated

We address dilepton production in Au+Au collisions at sqrt(s_NN)=200 GeV by employing the parton-hadron-string dynamics (PHSD) off-shell transport approach. Within the PHSD one goes beyond the quasiparticle approximation by solving generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for the Green's functions in the phase-space representation. The approach consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the quark-gluon plasma (QGP) as well as hadronization and to the subsequent interactions in the hadronic phase. {With partons described in the PHSD by the dynamical quasiparticle model (DQPM) - matched to reproduce lattice QCD results in thermodynamic equilibrium} - we calculate, in particular, the dilepton radiation from partonic interactions through the reactions q+qbar->gamma^*, q+qbar->gamma^*+g and q+g->gamma^*+q (qbar+g->gamma^*+qbar) in the early stage of relativistic heavy-ion collisions. By comparing our results to the data from the PHENIX Collaboration, we study the relative importance of different dilepton production mechanisms and point out the regions in phase space where partonic channels are dominant. Furthermore, explicit predictions are presented for dileptons within the acceptance of the STAR detector system and compared to the preliminary data., Comment: 11 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1107.3402

The azimuthal anisotropies of the collective transverse flow of hadrons are investigated in a large range of heavy-ion collision energy within the Parton-Hadron-String Dynamics (PHSD) microscopic transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as dynamical hadronization and hadronic dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ with bombarding energy is successfully described in terms of the PHSD approach in contrast to a variety of other kinetic models based on hadronic interactions. The analysis of higher-order harmonics $v_3$ and $v_4$ shows a similar tendency of growing deviations between partonic and purely hadronic models with increasing bombarding energy. This signals that the excitation functions of azimuthal anisotropies provide a sensitive probe for the underling degrees of freedom excited in heavy-ion collisions., Comment: 4 pages, 3 figures, title changed

Dilepton production in In+In collisions at 158 AGeV is studied within the microscopic parton-hadron-string dynamics (PHSD) transport approach that incorporates explicit partonic degrees-of-freedom, dynamical hadronization as well as the more familiar hadronic dynamics in the final reaction stages. A comparison to the data of the NA60 Collaboration shows that the measured dilepton yield is well described by including the collisional broadening of vector mesons, while simultaneously accounting for the electromagnetic radiation of the strongly coupled quark-gluon plasma (sQGP) via off-shell quark-antiquark annihilation, quark annihilation with additional gluon Bremsstrahlung and the gluon-Compton scattering mechanisms. In particular, the spectra in the intermediate mass range (1 GeV < M < 2.5 GeV) are dominated by quark-antiquark annihilation in the nonperturbative QGP. Also, the observed softening of the transverse mass spectra at intermediate masses (1 GeV < M < 2.5 GeV) is approximately reproduced. Furthermore, for dileptons of low masses (M < 0.6 GeV), we find a sizable contribution from the quark annihilation with additional gluon bremsstrahlung, thus providing another possible window for probing the properties of the sQGP., Comment: 16 pages, 14 figures

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results -- including the partonic equation of state -- in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. In order to explore the space-time regions of 'partonic matter' the PHSD approach is applied to nucleus-nucleus collisions from SPS to RHIC energies. Detailed comparisons are presented for hadronic rapidity spectra and transverse mass distributions. The traces of partonic interactions are found in particular in the elliptic flow of hadrons as well as in an approximate quark-number scaling at the top RHIC energy., Comment: Talk presented at the 27th Winter Workshop on Nuclear Dynamics (WWND) in Colorado, USA on February 6 - 13, 2011

The hadron string dynamics (HSD) model is generalized to include the creation and evolution of retarded electromagnetic fields as well as the influence of the magnetic and electric fields on the quasiparticle propagation. The time-space structure of the fields is analyzed in detail for non-central Au+Au collisions at $\sqrt{s_{NN}}=$200 GeV. It is shown that the created magnetic field is highly inhomogeneous but in the central region of the overlapping nuclei it changes relatively weakly in the transverse direction. For the impact parameter $b=$10 fm the maximal magnetic field - perpendicularly to the reaction plane - is obtained of order $eB_y/m_\pi^2\sim$5 for a very short time $\sim$ 0.2 fm/c, which roughly corresponds to the time of a maximal overlap of the colliding nuclei. We find that at any time the location of the maximum in the $eB_y$ distribution correlates with that of the energy density of the created particles. In contrast, the electric field distribution, being also highly inhomogeneous, has a minimum in the center of the overlap region. Furthermore, the field characteristics are presented as a function of the collision energy and the centrality of the collisions. To explore the effect of the back reaction of the fields on hadronic observables a comparison of HSD results with and without fields is exemplified. Our actual calculations show no noticeable influence of the electromagnetic fields - created in heavy-ion collisions - on the effect of the electric charge separation with respect to the reaction plane., Comment: 17 pages, 22 figures, title changed by editor, accepted for PRC

We address the dilepton production from the parton interactions in the early stage of relativistic heavy-ion collisions within the parton-hadron-string dynamics (PHSD) off-shell transport approach. The description of partons in PHSD is based on the dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. According to the DQPM the constituents of the strongly interacting quark-gluon plasma (sQGP) are massive and off-shell quasi-particles (quarks and gluons) with broad spectral functions. In order to address the electromagnetic radiation of the sQGP, we derive off-shell cross sections of q+qbar->gamma*, q+qbar->gamma*+g and q+g->gamma*+q (qbar+g->gamma*+qbar) reactions taking into account the effective propagators for quarks and gluons from the DQPM. Dilepton production in In+In collisions at 158 AGeV and in Au+Au at sqrt(s)=200 GeV is calculated by implementing these off-shell processes into the PHSD transport approach. By comparing to the data of the NA60 and PHENIX Collaborations, we study the relative importance of different dilepton production mechanisms and point out the regions in phase space where partonic channels are dominant., Comment: Talk presented at the International Nuclear Physics Conference (INPC 2010) in Vancouver, Canada on July 4 - 9, 2010, to be published in J.Phys.Conf.Ser

The novel Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. The PHSD approach is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results from the Wuppertal-Budapest group in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Our dynamical studies for heavy-ion collisions at relativistic collider energies are compared to earlier results from the Hadron-String Dynamics (HSD) approach - incorporating no explicit dynamical partonic phase - as well as to experimental data from the STAR, PHENIX, BRAHMS and PHOBOS collaborations for Au+Au collisions at the top RHIC energy of $\sqrt{s}$ = 200 GeV. We find a reasonable reproduction of hadron rapidity distributions and transverse mass spectra and also a fair description of the elliptic flow of charged hadrons as a function of the centrality of the reaction and the transverse momentum $p_T$. Furthermore, an approximate quark-number scaling of the elliptic flow $v_2$ of hadrons is observed in the PHSD results, too., Comment: 27 pages, 15 figures

Dilepton production in relativistic heavy-ion collisions is studied within the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. A comparison to the data of the NA60 Collaboration for In+In collisions at 158 AGeV shows that the dilepton spectra are well described by the sum of hadronic and partonic sources, if a collisional broadening of vector mesons is taken into account as well as the off-shell quark-antiquark annihilation (q+qbar->l^+l^- and q+qbar->gl^+l^-) in the QGP. In particular, the observed softening of the mT spectra at intermediate masses is reproduced. The data of the PHENIX collaboration on dilepton production in Au+Au collisions at sqrt(s)=200 GeV for masses above 1 GeV are found to be dominated by the contributions of the QGP radiation and the charm meson decays, while the measured spectrum is underestimated in the mass range from 0.2 to 0.6 GeV., Comment: Talk given at the 4th International Conference on Hard and Electromagnetic Probes of High Energy Nuclear Collisions (Hard Probes 2010), 10 to 15 of October, 2010, Eilat, Israel

The transition from hadronic to partonic degrees of freedom in the course of a relativistic heavy-ion collision is described by the microscopic covariant Parton-Hadron-String Dynamics (PHSD) transport approach. Studying Pb+Pb reactions from 40 to 158 AGeV and comparing the PHSD results to those of the Hadron-String Dynamics (HSD) approach without a phase transition to the QGP, we observe that the existence of the partonic phase has a sizable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields. Furthermore, we find a significant effect of the QGP on the production of multi-strange antibaryons due to a slightly enhanced ssbar pair production in the partonic phase from massive time-like gluon decay and to a more abundant formation of strange antibaryons in the hadronization process. Another evidence for pre-hadronization dynamics is gained from a study of di-jet correlations in Au+Au collisions at the top RHIC energy of sqrt(S)=200 GeV. Within the HSD transport approach, the reaction of the hadronic medium to the jet energy loss is calculated. In comparison with the data of the STAR, PHOBOS and PHENIX Collaborations differentially in azimuthal angle and pseudorapidity, the HSD results do not show enough suppression for the `away-side' jet. In addition, the HSD results exhibit neither a `Mach-cone' structure for the angular distribution in the away-side jet nor the `ridge' long-range rapidity correlations for the near-side jet as observed by the STAR and PHOBOS Collaborations, thus suggesting a partonic origin of these structures., Comment: Proceedings of the international workshop "Dense Matter 2010", 5-10 April 2010, in Stellenbosch, South Africa. To be published in Particles and Nuclei Letters A: Heavy Ions. 8 pages, 5 figures

Di-jet correlations in nucleus-nucleus collisions are studied within the Hadron-String-Dynamics (HSD) transport approach taking into account the reaction of the medium on the jet energy loss nonperturbatively. A comparison with the STAR and PHENIX data in central Au+Au collisions at the RHIC energy $\sqrt{s}=200$ GeV is performed differentially, i.e. with respect to correlations in azimuthal angle $\Delta \phi$ and pseudorapidity $\Delta \eta$. The HSD results do not show enough suppression for the `away-side' jets in accordance with earlier perturbative studies. Furthermore, the `Mach-cone' structure for the angle distribution in the `away-side' jet as well as `ridge' long rapidity correlations in the `near-side' jet - observed by the STAR and PHOBOS Collaborations - are not seen in the HSD results, thus suggesting a partonic origin., Comment: 7 pages, 3 figures

We study dilepton production in proton-proton, Cu+Cu as well as in Au+Au collisions at the center-of-mass energy 200 GeV per participating nucleon pair within an extended statistical hadronization model. In extension to earlier studies we incorporate transport calculations for an estimate of uncorrelated e+e- -pairs from semileptonic D meson decays. While the invariant mass spectrum of dielectrons is well understood in the p+p collisions, severe discrepancies among different model scenarios based on hadronic degrees of freedom and recent data from the PHENIX Collaboration are found in heavy-ion collisions in the low mass region from 0.15 to 0.6 GeV as well as in the intermediate mass regime from 1.1 to 3 GeV when employing the standard dilepton sources. We investigate, furthermore, the background from correlated dileptons that are not emitted as a pair from a parent hadron but emerge from semileptonic decays of two correlated daughter hadrons. Our calculations suggest a sizeable contribution of such sources in central heavy-ion collisions in the low mass region. However, even the upper limits of our calculations are found to be far below the dilepton mass spectra of the PHENIX Collaboration., Comment: revised version, 17 pages, 13 figures

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. Scalar- and vector-interaction densities are extracted from the DQPM as well as effective scalar- and vector-mean fields for the partons. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant 'pre-hadronic' color-dipole states ($q\bar{q}$ or $qqq$) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. When applying the PHSD approach to Pb+Pb colllisions at 158 A$\cdot$GeV we find a significant effect of the partonic phase on the production of multi-strange antibaryons due to a slightly enhanced $s{\bar s}$ pair production from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process., Comment: 12 pages, 6 figures, to be published in the Proceedings of the 26th Winter Workshop on `Nuclear Dynamics', Ochto Rios, Jamaica, 2-9 January, 2010.

According to the dynamical quasiparticle model (DQPM) -- matched to reproduce lattice QCD results in thermodynamic limit, -- the constituents of the strongly interacting quark-gluon plasma (sQGP) are massive and off-shell quasi-particles (quarks and gluons) with broad spectral functions. In order to address the electromagnetic radiation of the sQGP, we derive off-shell cross sections of $q\bar q\to\gamma^*$, $q\bar q\to\gamma^*+g$ and $qg\to\gamma^*q$($\bar q g\to\gamma^* \bar q$) reactions taking into account the effective propagators for quarks and gluons from the DQPM. Dilepton production in In+In collisions at 158 AGeV is studied by implementing these processes into the parton-hadron-string dynamics (PHSD) transport approach. The microscopic PHSD transport approach describes the full evolution of the heavy-ion collision: from the dynamics of quasi-particles in the sQGP phase (when the local energy density is above $\sim 1$ GeV/fm$^3$) through hadronization and to the following hadron interactions and off-shell propagation after the hadronization. A comparison to the data of the NA60 Collaboration shows that the low mass dilepton spectra are well described by including a collisional broadening of vector mesons, while the spectra in the intermediate mass range are dominated by off-shell quark-antiquark annihilation, quark Bremsstrahlung and gluon-Compton scattering in the nonperturbative QGP. In particular, the observed softening of the $m_T$ spectra at intermediate masses (1 GeV $\le M \le$ 3 GeV) is approximately reproduced., Comment: 8 pages, 8 figures, to be published in the Proceedings of the 26th Winter Workshop on `Nuclear Dynamics', Ochto Rios, Jamaica, 2-9 January, 2010

According to the dynamical quasiparticle model (DQPM) - matched to reproduce lattice QCD results in thermodynamic limit, - the constituents of the strongly interacting quark-gluon plasma (sQGP) are massive and off-shell quasi-particles (quarks and gluons) with broad spectral functions. In order to address the electromagnetic radiation of the sQGP, we derive off-shell cross sections of q+qbar->gamma*, q+qbar->gamma*+glue and q+glue->gamma*+q(qbar+glue->gamma*qbar) reactions taking into account the effective propagators for quarks and gluons from the DQPM. Dilepton production in In+In collisions at 158 AGeV is studied by implementing these processes into the parton-hadron-string dynamics (PHSD) transport approach. The microscopic PHSD transport approach describes the full evolution of the heavy-ion collision: from the dynamics of quasi-particles in the sQGP phase (when the local energy density is above ~1 GeV/fm^3) through hadronization and to the following hadron interactions and off-shell propagation after the hadronization. A comparison to the data of the NA60 Collaboration shows that the low mass dilepton spectra are well described by including a collisional broadening of vector mesons, while the spectra in the intermediate mass range are dominated by off-shell quark-antiquark annihilation, quark Bremsstrahlung and gluon-Compton scattering in the nonperturbative QGP. In particular, the observed softening of the mT spectra at intermediate masses (1 GeV < M < 3 GeV) is approximately reproduced., Comment: Talk given at the XIII International Conference on Hadron Spectroscopy (HADRON 09), November 29 - December 4, 2009, Tallahassee, Florida; two references added in version 2

Particle number fluctuations and correlations in nucleus-nucleus collisions at SPS and RHIC energies are studied within microscopic transport approaches. In this review we focus on the Hadron-String-Dynamics (HSD) and Ultra-relativistic-Quantum-Molecular-Dynamics (UrQMD) models The obtained results are compared with the available experimental data as well as with the statistical models and the model of independent sources. In particular the role of the experimental centrality selection and acceptance is discussed in detail for a variety of experimental fluctuations and correlation observables with the aim to extract information on the critical point in the $(T,\mu_B)$ plane of strongly interacting matter.

The Parton-Hadron-String Dynamics (PHSD) transport approach consistently simulates the full evolution of a relativistic heavy-ion collision from the initial hard scatterings string formation through the dynamical deconfinement phase transition to the quark gluon plasma (QGP), to the hadronization and to subsequent interactions in the hadronic phase. The transport theoretical description of quarks and gluons is based on a dynamical quasiparticle model for partons matched to reproduce recent lattice QCD results in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks). Studying Pb+Pb reactions from 40 to 158 A GeV, we find that at most 40% of the collision energy is stored in the dynamics of the partons. This implies that a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona, is present in these reactions, thus neither hadronic nor purely partonic models can be employed to extract physical conclusions in comparing model results with data. On the other hand, comparing the PHSD results to those of the Hadron-String Dynamics (HSD) approach without the phase transition to QGP, we observe that the existence of the partonic phase has a sizeable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields and initial partonic scattering. Furthermore, we find a significant effect of the QGP on the production of multi-strange antibaryons due to a slightly enhanced s+sbar pair production in the partonic phase from massive time-like gluon decay and to a more abundant formation of strange antibaryons in the hadronization process., Comment: Talk given at the International Conference Strangeness in Quark Matter 2009 (SQM 09)

The multiplicity fluctuations in A+A collisions at SPS and RHIC energies are studied within the HSD transport approach. We find a dominant role of the fluctuations in the nucleon participant number for the final fluctuations. In order to extract physical fluctuations one should decrease the fluctuations in the participants number. This can be done considering very central collisions. The system size dependence of the multiplicity fluctuations in central A+A collisions at the SPS energy range -- obtained in the HSD and UrQMD transport models -- is presented. The results can be used as a `background' for experimental measurements of fluctuations as a signal of the critical point. Event-by-event fluctuations of the $K/\pi$, $K/p$ and $p/\pi$ ratios in A+A collisions are also studied. Event-by-event fluctuations of the kaon to pion number ratio in nucleus-nucleus collisions are studied for SPS and RHIC energies. We find that the HSD model can qualitatively reproduce the measured excitation function for the $K/\pi$ ratio fluctuations in central Au+Au (or Pb+Pb) collisions from low SPS up to top RHIC energies. The forward-backward correlation coefficient measured by the STAR Collaboration in Au+Au collisions at RHIC is also studied. We discuss the effects of initial collision geometry and centrality bin definition on correlations in nucleus-nucleus collisions. We argue that a study of the dependence of correlations on the centrality bin definition as well as the bin size may distinguish between these `trivial' correlations and correlations arising from `new physics'., Comment: To appear in the proceedings of 5th International Workshop on Critical Point and Onset of Deconfinement (CPOD), Brookhaven, Upton, New York, 8-12 Jun 2009

Particle number fluctuations and correlations in nucleus-nucleus collisions at SPS and RHIC energies have been studied within the Hadron-String-Dynamics (HSD) transport approach. Event-by-event fluctuations of pion-to-kaon, proton-to-pion and kaon-to-proton number ratios are calculated for the samples of most central collision events and compared with the available experimental data. It has been found that the HSD model can qualitatively reproduce the measured excitation function for the $K/\pi$ ratio fluctuations in central Au+Au (or Pb+Pb) collisions from low SPS up to top RHIC energies. These predictions impose a challenge for future experiments., Comment: To appear in the proceedings of International Conference on Strangeness in Quark Matter 2009, Buzios, Brazil, Sep.27 - Oct.2, 2009

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is applied to Pb+Pb collisions from 20 to 160 A GeV in order to explore the space-time regions of 'partonic matter'. We find that even central collisions at the top-SPS energy of 158 A GeV show a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona. Furthermore, we observe that the partonic phase has a very low impact on rapidity distributions of hadrons but a sizeable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields. We also find a significant effect on the production of multi-strange antibaryons due to a slightly enhanced $s{\bar s}$ pair production in the partonic phase from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process. All differential hadron spectra are analyzed in comparison to the data of experimental collaborations., Comment: 33 pages, 23 figures, submitted to Nulc. Phys. A

Dilepton production in In+In collisions at 158 AGeV is studied within the microscopic Parton-Hadron-Strings Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. A comparison to the data of the NA60 Collaboration shows that the low mass dilepton spectra are well described by including a collisional broadening of vector mesons, while the spectra in the intermediate mass range are dominated by off-shell quark-antiquark annihilation in the nonperturbative QGP. In particular, the observed softening of the mT spectra at intermediate masses is reproduced., Comment: talk given at the 21st International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2009), to be published in Nucl.Phys.A, 4 pages, 3 figures, elsarticle style