From Kadanoff-Baym dynamics to off-shell parton transport

Abstract

Abstract. The description of strongly interacting quantum fields is based on twoparticle 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 Φ 4 -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 nucleusnucleus 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.

Charge-dependent directed flow in asymmetric nuclear collisions

“…In the PHSD the initial kinetic energy is converted in hard nucleon-nucleon collisions to string like configurations via PYTHIA 6.4 and these 'strings' decay to partonic quasiparticles with spectral functions in line with the dynamical quasiparticle model (DQPM, see [30]) if the energy density is above critical (≈ 0.5 GeV/fm 3 ). The initial conversion of energy happens during roughly 0.15 fm/c at the top RHIC energy when the nuclei pass though each other.…”

Impact of the initial size of spatial fluctuations on the collective flow in Pb–Pb collisions at $\sqrt{{{s}_{{\rm NN}}}}$ = 2.76 TeV

“…Once the proper (complex) selfenergies of the degrees of freedom are known, the time evolution of the system is fully governed by off-shell transport equations (as described in Refs. [47,48]). This approach allows for a simple and transparent interpretation of lattice QCD results for thermodynamic quantities as well as correlators and leads to effective strongly interacting partonic quasiparticles with broad spectral functions.…”

“…For a review on off-shell transport theory we refer the reader to Ref. [48]; model results and their comparison with experimental observables for heavy-ion collisions from the lower super-proton-synchrotron (SPS) to relativistic-heavy-ion-collider (RHIC) energies can be found in Refs. [21,49,50,51] including electromagnetic probes such as e + e − or µ + µ − pairs [52,53] or real photons [54].…”

Dilepton production in proton-proton and Pb+Pb collisions atsNN=2.76TeV

“…For details about the DQPM model and the off-shell transport, we refer the reader to the review in Ref. [17].…”