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We study the influence of the baryon chemical potential $\mu_B$ on the properties of the Quark-Gluon-Plasma (QGP) in and out-of equilibrium. The description of the QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature $T_c$ from lattice Quantum Chromodynamics (QCD). We calculate the transport coefficients such as the ratio of shear viscosity $\eta$ and bulk viscosity $\zeta$ over entropy density $s$, i.e., $\eta/s$ and $\zeta/s$ in the $(T,\mu_B)$ plane and compare to other model results available at $\mu_B =0$. The out-of equilibrium study of the QGP is performed within the Parton-Hadron-String Dynamics (PHSD) transport approach extended in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections (based on the DQPM propagators and couplings) evaluated at the actual temperature $T$ and baryon chemical potential $\mu_B$ in each individual space-time cell of the partonic scattering. The traces of their $\mu_B$ dependences are investigated in different observables for relativistic heavy-ion collisions with a focus on the directed and elliptic flow coefficients $v_1, v_2$ in the energy range 7.7 GeV $\le \sqrt{s_{NN}}\le 200$ GeV., Comment: 11 pages, 4 figures, contribution to the Proceedings of the 36th Winter Workshop on Nuclear Dynamics, 1-7 March 2020, Puerto Vallarta, Maxico. arXiv admin note: substantial text overlap with arXiv:2001.05395

We present calculations for the shear viscosity of the hot and dense quark-gluon plasma (QGP) using the partonic scattering cross sections as a function of temperature $T$ and baryon chemical potential $\mu_B$ from the dynamical quasiparticle model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. To this aim we calculate the collisional widths for the partonic degrees of freedom at finite $T$ and $\mu_B$ in the time-like sector and conclude that the quasiparticle limit holds sufficiently well. Furthermore, the ratio of shear viscosity $\eta$ over entropy density $s$, i.e. $\eta/s$, is evaluated using these collisional widths and are compared to lQCD calculations for $\mu_B$ = 0 as well. We find that the ratio $\eta/s$ is in agreement with the results of calculations within the original DQPM on the basis of the Kubo formalism. Furthermore, there is only a very modest change of $\eta/s$ with the baryon chemical $\mu_B$ as a function of the scaled temperature $T/T_c(\mu_B)$., Comment: 4 pages, 1 figure,to be published in the Proceedings of the 18th International Conference on Strangeness in Quark Matter (SQM 2019), June 9-15 2019, Bari, Italy

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

The quark rearrangement model for baryon-antibaryon annihilation and reproduction ($B\bar B\leftrightarrow 3M$) - incorporated in the Parton-Hadron-String Dynamics (PHSD) transport approach - is extended to the strangeness sector. A derivation of the transition probabilities for the three-body processes is presented and a strangeness suppression factor for the invariant matrix element squared is introduced to account for the higher mass of the strange quark compared to the light up and down quarks. In simulations of the baryon-antibaryon annihilation and reformation in a box with periodic boundary conditions we demonstrate that our numerical implementation fulfills detailed balance on a channel-by-channel basis for more than 2000 individual $2 \leftrightarrow 3$ channels. Furthermore, we study central Pb+Pb collisions within PHSD from 11.7$A$ GeV to 158$A$ GeV and investigate the impact of the additionally implemented reaction channels in the strangeness sector. We find that the new reaction channels have a visible impact essentially only on the rapidity spectra of antibaryons. The spectra with the additional channels in the strangeness sector are closer to the experimental data than without for all antihyperons. Due to the chemical redistribution between baryons/antibaryons and mesons we find a slightly larger production of antiprotons thus moderately overestimating the available experimental data. We additionally address the question if the antibaryon spectra (with strangeness) from central heavy-ion reactions at these energies provide further information on the issue of chiral symmetry restoration and deconfinement. However, by comparing transport results with/without partonic phase as well as including/excluding effects from chiral symmetry restoration we find no convincing signals in the strange antibaryon sector for either transition due to the strong final-state interactions., Comment: 19 pages, 19 figures

It is proposed to identify a strong electric field - created during relativistic collisions of asymmetric nuclei - via the observation of pseudorapidity and transverse momentum distributions of hadrons with the same mass but opposite charge. The results of detailed calculations within the Parton-Hadron String Dynamics (PHSD) approach for the charge-dependent directed flow $v_1$ are presented for semi-central Cu+Au collision at $\sqrt{s_{NN}}=200$ GeV incorporating the inverse Landau-Pomeranchuk-Migdal (iLPM) effect, which accounts for a delay in the electromagnetic interaction with the charged degree of freedom. Including the iLPM effect we achieve a reasonable agreement of the PHSD results for the charge splitting in $v_1(p_T)$ in line with the recent measurements of the STAR Collaboration for Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV while an instant appearance and coupling of electric charges at the hard collision vertex overestimates the splitting by about a factor of 10. We predict that the iLPM effect should practically disappear at energies of $\sqrt{s_{NN}} \approx$9 GeV, which should lead to a significantly larger charge splitting of $v_1$ at the future FAIR/NICA facilities., Comment: 5 pages, 6 figures

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

The heavy quark collisional scattering on partons of the quark gluon plasma (QGP) is studied in a QCD medium at finite temperature and chemical potential. We evaluate the effects of finite parton masses and widths, finite temperature $T$ and quark chemical potential $\mu_q$ on the different elastic cross sections for dynamical quasi-particles (on- and off-shell particles in the QGP medium as described by the dynamical quasi-particles model "DQPM") using the leading order Born diagrams. Our results show clearly the decrease of the $qQ$ and $gQ$ total elastic cross sections when the temperature and the quark chemical potential increase. These effects are amplified for finite $\mu_q$ at temperatures lower than the corresponding critical temperature $T_c (\mu_q)$. Using these cross sections we, furthermore, estimate the energy loss and longitudinal and transverse momentum transfers of a heavy quark propagating in a finite temperature and chemical potential medium. Accordingly, we have shown that the transport properties of heavy quarks are sensitive to the temperature and chemical potential variations. Our results provide some basic ingredients for the study of charm physics in heavy-ion collisions at Beam Energy Scan (BES) at RHIC and CBM experiment at FAIR., Comment: 19 pages, 28 figures

The Parton-Hadron-String-Dynamics (PHSD) transport model is used to study the influence of the initial size of spatial fluctuations of the interacting system on flow observables in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV for different centralities. While the flow coefficients $v_2$, $v_3$, $v_4$ and $v_5$ are reasonably described in comparison to the data from the ALICE Collaboration for different centralities within the default setting, no essential sensitivity is found with respect to the initial size of spatial fluctuations even for very central collisions where the flow coefficients are dominated by the size of initial state fluctuations. We attribute this lack of sensitivity partly to the low interaction rate of the degrees-of-freedom in this very early phase of order $\sim$ 0.3 fm/c which is also in common with the weakly interacting color glass condensate (CGC) or glasma approach. Moreover, since the event shape in the transverse plane is approximately the same for different size of spatial fluctuations very similar eccentricities $\epsilon_n$ are transformed to roughly the same flow coefficients $v_n$ in momentum space., Comment: 15 pages, 8 figures. arXiv admin note: text overlap with arXiv:1401.4409

The directed flow of identified hadrons is studied within the parton-hadron-string-dynamics (PHSD) approach for the asymmetric system Cu+Au in non-central collisions at $\sqrt{s_{NN}}$ = 200 GeV. It is emphasized that due to the difference in the number of protons of the colliding nuclei an electric field emerges which is directed from the heavy to the light nucleus. This strong electric field is only present for about 0.25 fm/c at $\sqrt{s_{NN}}$ = 200 GeV and leads to a splitting of the directed flow $v_1$ for particles with the same mass but opposite electric charges in case of an early presence of charged quarks and antiquarks. The microscopic calculations of the directed flow for $\pi^\pm, K^\pm, p$ and $\bar{p}$ are carried out in the PHSD by taking into account the electromagnetic field induced by the spectators as well as its influence on the hadronic and partonic quasiparticle trajectories. It is shown that the splitting of the directed flow as a function of pseudorapidity $\eta$ and in particular as a function of the transverse momentum $p_t$ provides a direct access to the electromagnetic response of the very early (nonequilibrium) phase of relativistic heavy-ion collisions and allows to shed light on the presence (and number) of electric charges in this phase., Comment: 8 pages, 12 figures

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

The interactions of heavy quarks with the partonic environment at finite temperature $T$ and finite quark chemical potential $\mu_q$ are investigated in terms of transport coefficients within the Dynamical Quasi-Particle model (DQPM) designed to reproduce the lattice-QCD results (including the partonic equation of state) in thermodynamic equilibrium. These results are confronted with those of nuclear many-body calculations close to the critical temperature $T_c$. The hadronic and partonic spatial diffusion coefficients join smoothly and show a pronounced minimum around $T_c$, at $\mu_q=0$ as well as at finite $\mu_q$. Close and above $T_c$ its absolute value matches the lQCD calculations for $\mu_q=0$. The smooth transition of the heavy quark transport coefficients from the hadronic to the partonic medium corresponds to a cross over in line with lattice calculations, and differs substantially from perturbative QCD (pQCD) calculations which show a large discontinuity at $T_c$. This indicates that in the vicinity of $T_c$ dynamically dressed massive partons and not massless pQCD partons are the effective degrees-of-freedom in the quark-gluon plasma., Comment: 4 pages, 4 figures

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 and HSD) transport models and a 3-fluid hydrodynamics (3FD) approach. Both versions of the kinetic approach, HSD and PHSD, 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 data. The hydrodynamic results are obtained for two equations of state (EoS), a pure hadronic EoS and an EoS with a crossover type transition. The latter case is favored by the STAR experimental data. Special attention is paid to the description of antiproton directed flow based on the balance of $p\bar{p}$ annihilation and the inverse processes for $p\bar{p}$ pair creation from multimeson interactions. Generally, the semiqualitative agreement between the measured data and the model results supports the idea of a crossover type of quark-hadron transition that softens the nuclear EoS but shows no indication of a first-order phase transition., Comment: 12 pages, 11 figures

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'

We study the properties of strongly interacting massive quantum fields in space-time as resulting from a parametric decay of the fields with a large decay width $\gamma$. The resulting imaginary part of the retarded and advanced propagators in this case is of Lorentzian form and the theory conserves microcausality, i.e. the commutator between the fields vanishes for space-like distances in space-time. However, when considering separately space-like and time-like components of the spectral function in momentum space we find microcausality to be violated for each component separately. This implies that the modeling of effective field theories for strongly interacting systems has to be considered with great care and restrictions to time-like four momenta in case of broad spectral functions have to be ruled out. Furthermore, when employing effective propagators with a width $\gamma({\bf p}^2)$ depending explicitly on three-momentum ${\bf p}$ the commutator of the fields no longer vanishes for $r>t$ since the related field theory becomes nonlocal and violates microcausality., Comment: 7 pages, 5 figures, submitted to Phys. Rev. D

The Parton-Hadron-String-Dynamics (PHSD) transport model is employed for p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV and compared to recent experimental data from the LHC as well as to alternative models. We focus on the question of initial state dynamics, i.e. if the initial state might be approximated by a superposition of independent nucleon-nucleon collisions or should be considered as a coherent gluon field as predicted within the color glass condensate (CGC) framework. We find that the PHSD approach provides correlations between the charged particle multiplicity at midrapidity and the number of participant nucleons close to results from the CGC and differs substantially from results calculated with independent Glauber initial conditions. However, a sizeable difference is found between the PHSD approach and CGC models with respect to the rapidity dependence of the average transverse momentum. Accordingly, related measurements at LHC should allow to prove or disprove the presence of coherent colour fields in the initial phase of the collisions., Comment: 16 pages, 8 figures

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 study the electric conductivity as well as the magnetic response of hot QCD matter at various temperatures $T$ and chemical potentials $\mu_q$ within the off-shell Parton-Hadron-String Dynamics (PHSD) transport approach for interacting partonic systems in a finite box with periodic boundary conditions. The response of the strongly-interacting system in equilibrium to an external electric field defines the electric conductivity $\sigma_0$ whereas the response to a moderate external magnetic field defines the induced diamagnetic moment $\mu_L$ ($T, \mu_q$) as well as the spin susceptibility $\chi_S(T, \mu_q)$. We find a sizeable temperature dependence of the dimensionless ratio $\sigma_0/T$ well in line with calculations in a relaxation time approach for $T_c \! < \! T < \! 2.5 \!\, T_c$ as well as an increase of $\sigma_0$ with $\mu_q^2/T^2$. Furthermore, the frequency dependence of the electric conductivity $\sigma(\Omega)$ shows a simple functional form well in line with results from the Dynamical QuasiParticle Model (DQPM). The spin susceptibility $\chi_S(T,\mu_q)$ is found to increase with temperature $T$ and to rise $\sim \mu_q ^2/T^2$, too. The actual values for the magnetic response of the QGP in the temperature range below 250 MeV show that the QGP should respond diamagnetically in actual ultra-relativistic heavy-ion collisions since the maximal magnetic fields created in these collisions are smaller than $B_c(T)$ which defines a boundary between diamagnetism and paramagnetism., Comment: 11 pages, 14 figures. arXiv admin note: text overlap with arXiv:1302.0906, matches published version

Within the aim of a dynamical study of on- and off-shell heavy quarks Q in the quark gluon plasma (QGP) - as produced in relativistic nucleus-nucleus collisions - we study the heavy quark collisional scattering on partons of the QGP. The elastic cross sections $\sigma_{q,g-Q}$ are evaluated for perturbative partons (massless on-shell particles) and for dynamical quasi-particles (massive off-shell particles as described by the dynamical quasi-particles model "DQPM") using the leading order Born diagrams. We demonstrate that the finite width of the quasi-particles in the DQPM has little influence on the cross sections $\sigma_{q,g-Q}$ except close to thresholds. We, furthermore, calculate the heavy quark relaxation time as a function of temperature T within the different approaches using these cross sections., Comment: 4 pages, 5 figures, International Conference on Strangeness in Quark Matter 2013 (SQM 2013)

We calculate the centrality dependence of direct photons produced in Au+Au collisions at sqrt{s}=200GeV and their transverse momentum spectra 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->rho+gamma, rho+pi->pi+gamma, meson-meson bremsstrahlung m+m->m+m+gamma, meson-baryon bremsstrahlung m+B->m+B+gamma), the decays of phi and a_1 mesons and the photons produced in the initial hard collisions ('pQCD'). We find that the pT spectra of the 'thermal' photons (i.e. the direct photons after the pQCD contribution is subtracted) deviate from exponential distributions and, consequently, observe a strong dependence of the inverse slope parameter T_eff on the fitting range in pT. On the other hand, all the obtained 'effective temperatures' are well above the critical temperature for the deconfinement phase transition even for peripheral collisions, reflecting primarily a 'blue shift' due to radial collective motion of hadrons. 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=1.5, whereas the partonic contribution scales with an exponent alpha_p=1.75. Additionally, we provide predictions for the centrality dependence of the direct photon elliptic flow v_2(pT). 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 the final hadrons., Comment: 8 pages, 7 plots, in the new version one plot is added (v2 in min bias collisions), discussion extended

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 heavy quark scattering on partons of the quark gluon plasma (QGP) being especially interested in the collisional (elastic) scattering processes of heavy quarks on quarks and gluons. We calculate the different cross sections for perturbative partons (massless on-shell particles in the vacuum) and for dynamical quasi-particles (off-shell particles in the QGP medium as described by the dynamical quasi-particles model "DQPM") using the leading order Born diagrams. Our results show clearly the effect of a finite parton mass and width on the perturbative elastic $(q(g) Q \rightarrow q (g) Q)$ cross sections which depend on temperature $T$, energy density $\epsilon$, the invariant energy $\sqrt{s}$ and the scattering angle $\theta$. Our detailed comparisons demonstrate that the finite width of the quasi-particles in the DQPM - which encodes the multiple partonic scattering - has little influence on the cross section for $q Q \rightarrow q Q$ as well as $g Q \rightarrow g Q$ scattering except close to thresholds. Thus when studying the dynamics of energetic heavy quarks in a QGP medium the spectral width of the degrees-of-freedom may be discarded. We have, furthermore, compared the cross sections from the DQPM with corresponding results from hard-thermal-loop (HTL) approaches. The HTL inspired models - essentially fixing the regulators by elementary vacuum cross sections and decay amplitudes instead of properties of the QGP at finite temperature - provide quite different results especially w.r.t. the temperature dependence of the $qQ$ and $gQ$ cross sections (in all settings). Accordingly, the transport properties of heavy quarks will be very different as a function of temperature when compared to DQPM results., Comment: 28 pages, 32 figures

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 dynamics of color fields as generated by simple configurations of relativistic particles with Abelian and non-Abelian (SU(2)) charges in the classical limit. We find that chromodynamic (non-Abelian) systems generally show Coulomb-like features by analogy with electrodynamics. A peculiar feature in the non-Abelian case is the additional strength of the chromoelectric and chromomagnetic fields caused by the contribution of changing the color charge. This change of color SU(2) charges results in a rotation of the color vector which is getting very fast at close partonic distances. The presence of this non-Abelian additional term in the chromoelectric and chromomagnetic fields creates a 'color charge glow', which is manifested as a distinct color wave disturbance arising due to the finite distance at which the color interaction becomes active. This situation may be relevant to the hadronization phase in ultrarelativistic heavy-ion collisions, where the partonic state is governed by strong local color fluctuations., Comment: 21 pages, 13 figures; discussion improved according to referee's remarks, results and conclusions not changed

We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary conditions. The response of the strongly interacting system in equilibrium to an external electric field defines the electric conductivity sigma_0. We find a sizable temperature dependence of the ratio sigma_0/T well in line with calculations in a relaxation time approach for Tc

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

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