Production of a sterile species via active-sterile mixing: an exactly solvable model

Abstract

The production of a sterile species via active-sterile mixing in a thermal medium is studied in an exactly solvable model. The \emph{exact} time evolution of the sterile distribution function is determined by the dispersion relations and damping rates $Γ_{1,2}$ for the quasiparticle modes. These depend on $\wtg = Γ_{aa}/2ΔE$, with $Γ_{aa}$ the interaction rate of the active species in absence of mixing and $ΔE$ the oscillation frequency in the medium without damping. $\wtg \ll1,\wtg \gg 1$ describe the weak and strong damping limits respectively. For $\wtg\ll1$, $Γ_1 = Γ_{aa}\cos^2\tm ; Γ_{2}=Γ_{aa}\sin^2\tm$ where $\tm$ is the mixing angle in the medium and the sterile distribution function \emph{does not} obey a simple rate equation. For $\wtg \gg 1$, $Γ_1= Γ_{aa}$ and $Γ_2 = Γ_{aa} \sin^22\tm/4\wtg^2$, is the sterile production rate. In this regime sterile production is suppressed and the oscillation frequency \emph{vanishes} at an MSW resonance, with a breakdown of adiabaticity. These are consequences of quantum Zeno suppression. For active neutrinos with standard model interactions the strong damping limit is \emph{only} available near an MSW resonance \emph{if} $\sinθ\lesssim α_w$ with $θ$ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary $\wtg$ are obtained from the quantum master equation. Cosmological resonant sterile neutrino production is quantum Zeno suppressed relieving potential uncertainties associated with the QCD phase transition.