Kinetics of the Chiral Phase Transition in a Quark–Meson \(σ \) Model

Using the two-particle irreducible (2PI) Φ-functional formalism for self-consistent approximations of a linear-σ model for quarks and mesons in and out of equilibrium, the build-up of fluctuations of net-baryon number during the time evolution of an expanding fireball is studied within a kinetic theory for the order parameter (σ field) and quark distribution functions. Initializing the system with purely Gaussian fluctuations a fourth-order cumulant is temporarily built up due to the evolution of the σ-field. This is counterbalanced, however, by the dissipative evolution due to collisions between quarks, anti-quarks, mesons, and the mean field, depending on the speed of the fireball expansion.