The case for mixed dark matter from sterile neutrinos

Abstract

Sterile neutrinos are SU(2) singlets that mix with active neutrinos via a mass matrix, its diagonalization leads to mass eigenstates that couple via standard model vertices. We study the cosmological production of heavy neutrinos via standard model charged and neutral current vertices under a minimal set of assumptions: i) the mass basis contains a hierarchy of heavy neutrinos, ii) these have very small mixing angles with the active (flavor) neutrinos, iii) standard model particles, including light (active-like) neutrinos are in thermal equilibrium. If kinematically allowed, the same weak interaction processes that produce active-like neutrinos also produce the heavier species. We introduce the quantum kinetic equations that describe their production, freeze out and decay and discuss the various processes that lead to their production in a wide range of temperatures assessing their feasibility as dark matter candidates. The final distribution function at freeze-out is a mixture of the result of the various production processes. We identify processes in which finite temperature collective excitations may lead to the production of the heavy species. As a specific example, we consider the production of heavy neutrinos in the mass range Mh ≲ 140 MeV from pion decay shortly after the QCD crossover including finite temperature corrections to the pion form factors and mass. We consider the different decay channels that allow for the production of heavy neutrinos showing that their frozen distribution functions exhibit effects from ``kinematic entanglement'' and argue for their viability as mixed dark matter candidates. We discuss abundance, phase space density and stability constraints and argue that heavy neutrinos with lifetime τ> 1/H0 freeze out of local thermal equilibrium, and conjecture that those with lifetimes τ ≪ 1/H0 may undergo cascade decay into lighter DM candidates and/or inject non-LTE neutrinos into the cosmic neutrino background. We provide a comparison with non-resonant production via active-sterile mixing.