Pion production in nonequilibrium chiral perturbation theory

Abstract

We apply the formalism of chiral perturbation theory out of thermal equilibrium to describe explosive production of pions via the parametric resonance mechanism. To lowest order the Lagrangian is that of the nonlinear sigma model where the pion decay constant becomes a time-dependent function. This model allows for a consistent nonequilibrium formulation within the framework of the closed time path method, where one-loop effects can be systematically accounted for and renormalized. We work in the narrow resonance regime where there is only one resonant band. The pion distribution function is peaked around the resonant band where the number of pions grow exponentially in time. The present approach is limited to remain below the back-reaction time, although it accounts for nearly all the pion production during the typical plasma lifetime. Our results agree with the analysis performed in the $O(4)$ model. The space and time components ${f}_{\ensuremath{\pi}}^{s,t}(t)$ are also analyzed. To one loop ${f}_{\ensuremath{\pi}}^{s}\ensuremath{\ne}{f}_{\ensuremath{\pi}}^{t}$ unlike the equilibrium case and their final central values are lower than the initial ones. This effect can be interpreted in terms of a reheating of the plasma.