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 ${\Gamma }_{1,2}$ for the quasiparticle modes. These depend on $\text{wtg}={\Gamma }_{aa}/2\Delta E$, with ${\Gamma }_{aa}$ the interaction rate of the active species in absence of mixing and $\Delta E$ the oscillation frequency in the medium without damping. $\text{wtg}\ll 1,\text{wtg}\gg 1$ describe the weak and strong damping limits respectively. For $\text{wtg}\ll 1$, ${\Gamma }_1={\Gamma }_{aa}{\cos }^2\text{tm};{\Gamma }_2={\Gamma }_{aa}{\sin }^2\text{tm}$ where $\text{tm}$ is the mixing angle in the medium and the sterile distribution function \emph{does not} obey a simple rate equation. For $\text{wtg}\gg 1$, ${\Gamma }_1={\Gamma }_{aa}$ and ${\Gamma }_2={\Gamma }_{aa}{\sin }^{2}2\text{tm}/4{\text{wtg}}^2$, 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} $\sin \theta \lesssim {\alpha }_w$ with $\theta$ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary $\text{wtg}$ 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.

Comments: To appear in Phys. Rev. D