Sterile neutrinos produced near the EW scale I: mixing angles, MSW
  resonances and production rates
  We study the production of sterile neutrinos in the region $T\sim M_W$ in an
extension beyond the standard model with the see-saw 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 $1 \lesssim M_W/T \lesssim 3$ we find narrow MSW
resonances with $k \lesssim T$ 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 ($k/T \ll |\xi|$) narrow MSW resonances in the presence of a lepton
asymmetry consistent with the bounds from WMAP and BBN. 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 \emph{exact} degeneracy of the propagating modes with a
concomitant breakdown of adiabaticity. We argue that cosmological expansion
sweeps through the resonances, \emph{resonant and non-resonant} sterile
neutrino production results in a highly \emph{non-thermal} distribution
function enhanced at small momentum $k < T$, with potentially important
consequences for their free streaming length and transfer function at small
scales.
