Minimal Seesaw extension for Neutrino Mass and Mixing, Leptogenesis and Dark Matter: FIMPzillas through the Right-Handed Neutrino Portal

We propose a minimal seesaw extension to simultaneously account for realistic neutrino mass and mixing, the baryon asymmetry of the Universe via leptogenesis and a viable dark matter relic density, in which two right-handed neutrinos are coupled to a dark Dirac fermion and complex scalar field, both charged under a global $U(1)_D$ symmetry. As a concrete example, we consider the Littlest Seesaw model which describes neutrino mass and mixing and accounts for leptogenesis, thereby fixing the neutrino Yukawa couplings and right-handed neutrino masses. By considering the freeze-in production mechanism of dark matter, we explore the parameter space of right-handed neutrino portal couplings and dark particle masses which give the correct dark matter relic abundance, focussing on the case of a superheavy Dirac fermion dark matter particle, with a mass around $10^{10}$ GeV. Such a FIMPzilla can provide a successful explanation of the dark matter relic abundance, with its production reliant on neutrino Yukawa couplings over much of the parameter space, depending on the assumed dark particle masses, and the reheat temperature.