Dynamical Quasiparticle Model Research Articles

Dilepton production at SPS and RHIC energies within the PHSD off-shell transport approach

The microscopic parton-hadron-string dynamics (PHSD) transport approach describes the full evolution of relativistic heavy-ion collisions: from the initial hard scatterings to the partonic phase in the early hot and dense reaction region (when the local energy density is above ≈1 GeV/fm3) followed by hadronization and off-shell hadron propagation and interactions. The description of quarks and gluons in PHSD is based on the dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. The DQPM describes QCD properties in terms of single-particle Green's functions and leads to the notion of effective quasiparticles which are massive and have broad spectral functions (due to large interaction rates). Dressing the quark and gluon lines with effective propagators provided by the DQPM, we obtain cross sections of dilepton production in the reactions q + q̄ → l+l− (Born mechanism), q + q̄ → l+l− + g (quark annihilation with the gluon Bremsstrahlung in the final state), and q/q̄ + g → l+l− + q/q̄ (gluon Compton scattering) by off-shell quarks and gluons in the strongly interacting partonic phase. After implementing the off-shell cross sections for the partonic processes into the PHSD transport approach, we address the dilepton production from the parton interactions in the early stage of relativistic heavy-ion collisions at SPS and RHIC energies. Dilepton production in In + In collisions at 158 AGeV and in Au + Au at √s = 200 GeV is calculated. 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.

Properties of the partonic phase at RHIC within PHSD

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.

Dilepton production in the strongly interacting quark-gluon plasma

Dilepton production in relativistic heavy ion collisions 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 on the In + In collisions at 158 A⋅GeV 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 + q ¯ → l + l − and q + q ¯ → l + l − g ) in the QGP. In particular, the observed softening of the m T spectra at intermediate masses is reproduced. The data of PHENIX collaboration on dilepton production in Au + Au collisions at s = 200 GeV at masses above 1 GeV/c 2 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/c 2.

Parton–Hadron-String Dynamics at relativistic collider energies

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.

Dilepton production by dynamical quasi-particles in the strongly interacting quark–gluon plasma

We address the dilepton production by the constituents of the strongly interacting quark–gluon plasma (sQGP). In order to make quantitative predictions for dilepton rates at experimentally relevant low dilepton mass (O(1GeV)) and strong coupling (αS ∼ 0.5–1), we take into account non-perturbative spectral functions and self-energies of the quarks, antiquarks and gluons. For this purpose, we use parametrizations of the quark and gluon propagators provided by the dynamical quasi-particle model (DQPM) matched to reproduce lattice quantum chromodynamics (QCD) data. The DQPM describes QCD properties in terms of the single-particle Green's functions and leads to the notion of the constituents of the sQGP being effective quasi-particles, which are massive and have broad spectral functions (due to large interaction rates). By ‘dressing’ the quark and gluon lines with the effective propagators, we derive the off-shell cross sections for dilepton production in the reactions (Born mechanism), (quark annihilation with the gluon bremsstrahlung in the final state), (gluon–Compton scattering), and (virtual gluon decay, virtual quark decay). In contrast to previous calculations of these cross sections, we account for virtualities of all the quarks and gluons. We find that finite masses of the effective quasi-particles not only screen the singularities typical of the perturbative cross sections with massless quarks, but also modify the shape of the dilepton production cross sections, especially at low dilepton mass Q and at the edges of the phase space. Finally, we use the calculated mass-dependent cross sections to identify the dependence of the dilepton rates on the spectral function widths of the initial and final quarks and gluons, which has not been estimated so far. The results demonstrate that the multiple partonic scatterings encoded in the broad spectral functions of the dynamical quasi-particles have considerable effect on the dilepton rates.

Dynamical equilibration in strongly-interacting parton-hadron matter

We study the kinetic and chemical equilibration in 'infinite' parton-hadron matter within the Parton-Hadron-String Dynamics transport approach, which is based on a dynamical quasiparticle model for partons matched to reproduce lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. The 'infinite' matter is simulated within a cubic box with periodic boundary conditions initialized at different baryon density (or chemical potential) and energy density. The transition from initially pure partonic matter to hadronic degrees of freedom (or vice versa) occurs dynamically by interactions. Different thermodynamical distributions of the strongly-interacting quark-gluon plasma (sQGP) are addressed and discussed.

Strangeness production within parton–hadron–string dynamics (PHSD)

Parton-hadron–string dynamics (PHSD) transport approach consistently simulates the full evolution of a relativistic heavy ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to quark gluon plasma (QGP) to the hadronization and to the 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 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 a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona; 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. Furthermore, we find a significant effect of the QGP on the production of multi-strange antibaryons due to a slightly enhanced 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.

Dileptons from the nonequilibrium quark-gluon plasma

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 qq̄ → γ*, qq̄ → γ* + g and qg → γ* q(q̄g → γ*q̄) 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) 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.

Covariant transport approach for strongly interacting partonic systems

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 (qq̄ 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·GeV we find a significant effect of the partonic phase on the production of multi-strange antibaryons due to a slightly enhanced ss̄ pair production from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.

Dileptons from the strongly-interacting Quark-Gluon Plasma within the Parton-Hadron-String-Dynamics (PHSD) approach

Dilepton production in In + In collisions at 158 A ⋅ GeV 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 m T spectra at intermediate masses is reproduced.

Parton–hadron–string dynamics: An off-shell transport approach for relativistic energies

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 (DQPM) for partons 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 q ¯ or qqq) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. The PHSD approach is applied to nucleus–nucleus 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. This finding implies that neither hadronic nor only partonic ‘models’ can be employed to extract physical conclusions in comparing model results with data. On the other hand – studying in detail Pb + Pb reactions from 40 to 158 A GeV – 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. Furthermore, we find a significant effect on the production of multi-strange antibaryons due to a slightly enhanced s s ¯ pair production in the partonic phase from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.

From Kadanoff-Baym dynamics to off-shell parton transport

The description of strongly interacting quantum fields is based on two-particle irreducible (2PI) approaches that allow for a consistent treatment of quantum systems out-of-equilibrium as well as in thermal equilibrium. As a theoretical test case the quantum time evolution of Φ4-field theory in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym-equations including the tadpole and sunset self energies. In particular we address the dynamics of the spectral (‘off-shell’) distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. A detailed comparison of the full quantum dynamics to approximate schemes like that of a standard kinetic (on-shell) Boltzmann equation is performed. We find that far off-shell 1↔3 processes are responsible for chemical equilibration, which is not included in the Boltzmann limit. Furthermore, we derive generalized transport equations for the same theory in a first order gradient expansion in phase space thus explicitly retaining the off-shell dynamics as inherent in the time-dependent spectral functions. The solutions of these equations compare very well with the exact solutions of the full Kadanoff-Baym equations with respect to the occupation numbers of the individual modes, the spectral evolution as well as the chemical equilibration process. Furthermore, the proper equilibrium off-shell distribution is reached for large times contrary to the quasiparticle Boltzmann limit. We additionally present a direct comparison of the solution of the generalized transport equations in the Kadanoff-Baym (KB) and Botermans-Malfliet (BM) form; both solutions are found to agree very well with each other. The off-shell transport equation in the BM scheme allows for an explicit solution within an extended dynamical quasiparticle Ansatz. This leads to generalized equations of motion for dynamical quasiparticles that exceed the classical Hamilton equations and allow for the description of dynamical spectral functions. The dynamical quasiparticle model (DQPM) is used to extract partonic spectral functions from lattice QCD in the temperature range 0.8≤T/Tc ≤10. By consideration of time-like and space-like sectors of ‘observables’ such as number densities, energy densities etc. mean-field potentials as well as effective interactions are extracted at different temperature T and quark chemical potentials μq. The latter determine the off-shell dynamics in the Parton-Hadron-String Dynamics (PHSD) transport approach. Illustrative examples for off-shell dynamics in the hadron and parton sector are presented for e+e- production from nucleus-nucleus collisions from SIS to RHIC energies. The generalized transport approach, furthermore, qualifies for the description of hadronization without leading to the problem of entropy reduction as in conventional coalescence models.

Parton dynamics and hadronization from the sQGP

The hadronization of an expanding partonic fireball is studied within the Parton-Hadron-String Dynamics (PHSD) approach which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. Apart from strong parton interactions the expansion and development of collective flow is found to be driven by strong gradients in the parton mean-fields. An analysis of the elliptic flow v 2 demonstrates a linear correlation with the spatial eccentricity ϵ as in the case of ideal hydrodynamics. The hadronization occurs by quark–antiquark fusion or 3 quark/3 antiquark recombination which is described by covariant transition rates. Since the dynamical quarks become very massive, the formed resonant ‘pre-hadronic’ color-dipole states ( q q ̄ or q q q ) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. This solves the entropy problem in hadronization in a natural way. Hadronic particle ratios turn out to be in line with those from a grand-canonical partition function at temperature T ≈ 170 MeV.

Parton transport and hadronization from the dynamical quasiparticle point of view

The hadronization of an expanding partonic fireball is studied within the parton-hadron-string-dynamics (PHSD) approach, which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. Apart from strong parton interactions, the expansion and development of collective flow is driven by strong gradients in the parton mean fields. An analysis of the elliptic flow ${v}_{2}$ demonstrates a linear correlation with the spatial eccentricity \ensuremath{\epsilon} as in ideal hydrodynamics. The hadronization occurs by quark-antiquark fusion or three-quark/three-antiquark recombination, which is described by covariant transition rates. Since the dynamical quarks become very massive, the formed resonant ``pre-hadronic'' color-dipole states ($q\overline{q}$ or $\mathrm{qqq}$) are of high invariant mass, too, and sequentially decay to the ground-state meson and baryon octets increasing the total entropy. This solves the entropy problem in hadronization in a natural way. The resulting particle ratios turn out to be in line with those from a grand-canonical partition function at temperature $T\ensuremath{\approx}170$ MeV rather independent from the initial temperature and indicate an approximate strangeness equilibration.

Dynamical quasiparticles properties and effective interactions in the sQGP

Dynamical quasiparticle properties are determined from lattice QCD along the line of the Peshier model for the running strong coupling constant in case of three light flavors. By separating time-like and space-like quantities in the number density and energy density the effective degrees of freedom in the gluon and quark sector may be specified from the time-like densities. The space-like parts of the energy densities are identified with interaction energy (or potential energy) densities. By using the time-like parton densities (or scalar densities) as independent degrees of freedom—instead of the temperature T and chemical potential μ q as Lagrange parameters—variations of the potential energy densities with respect to the time-like gluon and/or fermion densities lead to effective mean-fields for time-like gluons and quarks as well as to effective gluon–gluon, quark–gluon and quark–quark (quark–antiquark) interactions. The latter dynamical quantities are found to be approximately independent on the quark chemical potential μ q and thus well suited for an implementation in off-shell parton transport approaches. Results from the dynamical quasiparticle model (DQPM) in case of two dynamical light quark flavors are compared to lattice QCD calculations for the net quark density ρ q ( T , μ q ) as well as for the ‘back-to-back’ differential dilepton production rate by q – q ¯ annihilation. The DQPM is found to pass the independent tests.

QCD thermodynamics and confinement from a dynamical quasiparticle point of view

In this study it is demonstrated that a simple picture of the QCD gluon liquid emerges in the dynamical quasiparticle model that specifies the active degrees of freedom in the time-like sector and yields a potential energy density in the space-like sector. By using the time-like gluon density (or scalar gluon density) as an independent degree of freedom—instead of the temperature T as a Lagrange parameter—variations of the potential energy density lead to effective mean-fields for time-like gluons and an effective gluon–gluon interaction strength at low density. The latter yields a simple dynamical picture for the gluon fusion to color neutral glueballs when approaching the phase boundary from a temperature higher than T c and paves the way for an off-shell transport theoretical description of the parton dynamics.