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 M _ { h } \lesssim 140 \mathrm { 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 \tau > 1 / H _ { 0 } freeze out of local thermal equilibrium , and conjecture that those with lifetimes \tau \ll 1 / H _ { 0 } may undergo cascade decay into lighter DM candidates and/or inject non-LTE neutrinos into the cosmic neutrino background .
A comparison is made between production through pion decays with the production of non-resonant production via active-sterile mixing .