Production of a sterile species: quantum kinetics

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 ${\tau }_{dec}=2\mathrm{/}{\mathrm{\Gamma }}_{aa}$, 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: $\Gamma_1=\Gamma_{aa}\cos^2\tm ; \Gamma_2=\Gamma_{aa}\sin^2\tm$where$\Gamma_{aa}$ is the interaction rate of the active species in absence of mixing and $\text{tm}$ the mixing angle in the medium. These two time scales are widely different away from MSW 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 \emph{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.