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

The production of a sterile species via active-sterile mixing in a thermal medium is studied in an exactly solvable model. The exact time evolution of the sterile distribution function is determined by the dispersion relations and damping rates Γ1,2 for the quasiparticle modes. These depend on γ=Γₐₐ/2ΔE, with Γₐₐ the interaction rate of the active species in absence of mixing and ΔE the oscillation frequency in the medium without damping. γ1, γ1 describe the weak and strong damping limits, respectively. For γ1, Γ₁=Γₐₐcos²θₘ; Γ₂=Γₐₐsin²θₘ where θₘ is the mixing angle in the medium and the sterile distribution function does not obey a simple rate equation. For γ1, Γ₁=Γₐₐ and Γ₂=Γₐₐsin²2θₘ/4γ², is the sterile production rate. In this regime sterile production is suppressed and the oscillation frequency vanishes at an Mikheyev-Smirnov-Wolfenstein (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 only available near an MSW resonance if sin2θαw with θ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary γ 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.