Production of a sterile species: Quantum kinetics

Abstract

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is ${\ensuremath{\tau}}_{\mathrm{dec}}=2/{\ensuremath{\Gamma}}_{aa}$, but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: ${\ensuremath{\Gamma}}_{1}={\ensuremath{\Gamma}}_{aa}{cos}^{2}{\ensuremath{\theta}}_{m}$; ${\ensuremath{\Gamma}}_{2}={\ensuremath{\Gamma}}_{aa}{sin}^{2}{\ensuremath{\theta}}_{m}$ where ${\ensuremath{\Gamma}}_{aa}$ is the interaction rate of the active species in the absence of mixing and ${\ensuremath{\theta}}_{m}$ the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the ``polarization vector'' and show their equivalence to those obtained from the quantum master equation and effective action.