Abstract
The kinetics of the chiral phase transition is studied within a linear quark-meson-σ model, using a Monte-Carlo approach to semiclassical particle-field dynamics. The meson fields are described on the mean-field level and quarks and antiquarks as ensembles of test particles. Collisions between quarks and antiquarks as well as the annihilation to σ mesons and the decay of σ mesons is treated, using the corresponding transition-matrix elements from the underlying quantum field theory, obeying strictly the rule of detailed balance and energy-momentum conservation. The approach allows to study fluctuations without making ad hoc assumptions concerning the statistical nature of the random process as necessary in Langevin-Fokker-Planck frameworks.
Highlights
One of the motivations for the study of ultrarelativistic heavy-ion collisions is to gain a detailed understanding of the phase diagram of strongly interacting matter [1]
At the largest energies as achieved at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) a hot and dense fireball is formed which can be described to a surprising accuracy as a nearly perfect fluid of strongly coupled quarks and gluons (QGP) undergoing a transition to a hot hadron-resonance gas
How to effectively model the phase transition (e.g., with the Nambu-Jona-Lasinio (NJL) or the σ model with extensions taking into account gluonic degrees of freedom implementing Polyakov loops) arises and, which of the features of the phase structure predicted for such models applying thermal quantum field theory like fluctuations of conserved charges survive for a rapidly expanding and cooling fireball as created in heavy-ion collisions
Summary
One of the motivations for the study of ultrarelativistic heavy-ion collisions is to gain a detailed understanding of the phase diagram of strongly interacting matter [1]. 3. Semiclassical particle-field dynamics The challenge in applying the above model to an off-equilibrium dynamical simulation of a system of particles (here quarks and antiquarks) and mean fields (representing the mesons) is that in order to reproduce the equilibrium-phase structure as depicted in 1 as the stationary limit, one has to ensure that both kinetic and chemical equilibration is possible through the introduction of the appropriate elastic collision terms for qq and qq scattering as well as quarknumber changing processes such as qq ↔ σ. At the same time the principle of detailed balance is fulfilled, using the coarse-graining approach to locally map the field-energy-momentum distribution to a local-equilibrium Maxwell-Juttner distribution to reinterpret the mean field as a meson phase-space distribution and using the leading-order transition rates (cross sections) of the underlying QFT linear σ model fulfilling the detailedf(E) Fourier amplitudes
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