Abstract
We investigate the influence of chiral symmetry which varies along the space-time evolution of a system, by considering the chiral phase transition in a nonequilibrium expanding quark-antiquark system. The chiral symmetry is described by the mean field order parameter, whose value is the solution of a self-consistent equation, and affects the space-time evolution of the system through the force term in the Vlasov equation. The Vlasov equation and the gap equation are solved concurrently and continuously for a longitudinal boost-invariant and transversely rotation-invariant system. This numerical framework enables us to carefully investigate how the phase transition and collision affect the evolution of the system. It is observed that the chiral phase transition gives rise to a kink in the flow velocity, which is caused by the force term in the Vlasov equation. The kink is enhanced by larger susceptibility and tends to be smoothed out by nonequilibrium effects. The spatial phase boundary appears as a ``wall'' for the quarks, as the quarks with low momentum are bounced back, while those with high momentum go through the wall but are slowed down.
Highlights
One of the major motivations in the study of finitetemperature quantum chromodynamics (QCD) is to shed light on the phase structure of the strong interaction in matter
Model calculations based on the Nambu–Jona-Lasinio (NJL) model, the quark meson model, and various beyond mean field frameworks have all predicted that the chiral phase transition at finite density is a first-order phase transition [5,6,7,8]
The force term is considered in the test particle method [18,19,22,23,24], its effect has not been carefully examined, and we find it plays an important role in the evolution of the system around the phase transition
Summary
One of the major motivations in the study of finitetemperature quantum chromodynamics (QCD) is to shed light on the phase structure of the strong interaction in matter. Through a systematic measurement over a range of beam energies, the beam energy scan (BES) program makes It possible to search for the CEP in the QCD phase diagram [9,10,11]. [18,19], the authors investigate the chiral phase transition in a free-streaming quark-antiquark system by solving the Vlasov equation through the test. [21] the nonequilibrium and collision effects on the deconfinement phase transition are investigated by solving the Vlasov equation assuming Bjorken symmetry. In order to study the chiral phase transition in the nonequilibrium state, we investigate an expanding quark-anitquark gas system by solving the coupled Vlasov equation as well as the gap equation. V, we summarize this work and give a brief outlook
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