Sterile neutrinos produced near the electroweak scale: Mixing angles, MSW resonances, and production rates

Abstract

We study the production of sterile neutrinos in the region $T\ensuremath{\sim}{M}_{W}$ in an extension beyond the standard model with the seesaw mass matrix originating in Yukawa couplings to Higgs-like scalars with masses and vev's of the order of the electroweak scale. Sterile neutrinos are produced by the decay of scalars and standard model vector bosons. We obtain the index of refraction, dispersion relations, mixing angles in the medium and production rates including those for right-handed sterile neutrinos, from the standard model and beyond the standard model self-energies. For $1\ensuremath{\lesssim}{M}_{W}/T\ensuremath{\lesssim}3$ we find narrow MSW resonances with $k\ensuremath{\lesssim}T$ for both left- and right-handed neutrinos even in absence of a lepton asymmetry in the (active) neutrino sector, as well as very low energy ($k/T\ensuremath{\ll}|\ensuremath{\xi}|$) narrow MSW resonances in the presence of a lepton asymmetry consistent with the bounds from Wilkinson Microwave Anisotropy Probe and Big Bang Nucleosynthesis. For small vacuum mixing angle, consistent with observational bounds, the absorptive part of the self-energies lead to a strong damping regime very near the resonances resulting in the exact degeneracy of the propagating modes with a concomitant breakdown of adiabaticity. We argue that cosmological expansion sweeps through the resonances, resonant and nonresonant sterile neutrino production results in a highly nonthermal distribution function enhanced at small momentum $k<T$, with potentially important consequences for their free-streaming length and transfer function at small scales.