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

TL;DR

This paper presents an exactly solvable model for sterile neutrino production via active-sterile mixing, revealing quantum Zeno suppression effects and providing insights into cosmological sterile neutrino generation.

Contribution

It derives the full quantum kinetic equations for sterile production across damping regimes, highlighting the impact of quantum Zeno suppression near MSW resonances.

Findings

Sterile production is suppressed in the strong damping regime due to quantum Zeno effects.

The model shows sterile production does not follow simple rate equations in certain regimes.

Resonant production is suppressed near MSW resonances, affecting cosmological neutrino models.

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 $\wtg = \Gamma_{aa}/2\Delta E$, 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. $\wtg \ll1,\wtg \gg 1$ describe the weak and strong damping limits respectively. For $\wtg\ll1$, $\Gamma_1 = \Gamma_{aa}\cos^2\tm ; \Gamma_{2}=\Gamma_{aa}\sin^2\tm$ where $\tm$ is the mixing angle in the medium and the sterile distribution function \emph{does not} obey a simple rate equation. For $\wtg \gg 1$, $\Gamma_1= \Gamma_{aa}$ and $\Gamma_2 = \Gamma_{aa} \sin^22\tm/4\wtg^2$, 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} $\sin\theta \lesssim \alpha_w$ with $\theta$ 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.