Production of a sterile species: quantum kinetics

TL;DR

This paper develops a quantum-field-theoretic treatment of active-sterile neutrino production in a thermal medium by analyzing a two-flavor scalar model coupled to a bath. It derives a complete set of quantum kinetic equations via two independent methods: a non-equilibrium effective action and a quantum master equation, revealing two distinct damping scales $\Gamma_1=\Gamma_{aa}\cos^2\theta_m$ and $\Gamma_2=\Gamma_{aa}\sin^2\theta_m$, and a decoherence time $\tau_{dec}=2/\Gamma_{aa}$. A generalized transition probability in the medium, $P_{a\rightarrow s}$, is obtained that depends on these scales and on the oscillation frequency difference, while off-diagonal coherences decay and the equilibrium state becomes diagonal in the propagating-mode basis. The work also connects the effective action and master-equation formalisms to the standard polarization-vector formulation, clarifying the limitations of simple rate equations and highlighting the central role of the medium’s quasiparticle poles in sterile neutrino production and kinetics.

Abstract

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 $τ_{dec} = 2/Γ_{aa}$, 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: $Γ_1=Γ_{aa}\cos^2\tm ; Γ_2=Γ_{aa}\sin^2\tm$ where $Γ_{aa}$ is the interaction rate of the active species in absence of mixing and $\tm$ 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.

Figures (2)

• Figure 1: One loop self-energy for the active species at order $G$, corresponding to the matter potential $V_{aa}=G \langle \chi^2 \rangle$.
• Figure 2: One loop self-energy for the active species to order $G^2$. The cut discontinuity across the $W-\chi$ lines yields the imaginary part $\mathrm{Im}\widetilde{\Sigma}_{aa}(k;\omega)$.