scale as it has massless neutrinos and no viable candidate for dark matter. Hence the vacuum stability analysis must be carried out within [[Standard Model ]{}]{}extensions which can address these issues. We now move on to consider simple seesaw extensions of [[Standard Model ]{}]{}accounting for neutrino masses (and/or dark matter) and show that, the Higgs vacuum stability in these simple and realistic scenarios can be completely dominated by new couplings. Thus for our purposes it suffices to discuss electroweak vacuum stability at two loops, without going into fine details about input parameters [^3].

High-scale Type-I Seesaw mechanism {#sec:seesaw}
==================================

We begin with [[Standard Model ]{}]{}extensions accounting for naturally small neutrino masses, and in latter sections we consider schemes which also include viable dark matter candidates. It is well known that, in the [[Standard Model ]{}]{}neutrinos are massless, while the observation of neutrino oscillations has conclusively proven that at least two of the three “active” neutrinos are massive [@Kajita:2016cak; @McDonald:2016ixn].

In the most general “type-I seesaw” mechanism, proposed in [@Schechter:1980gr], neutrino masses arise from the exchange of an arbitrary number of singlet “right-handed neutrinos”, $\nu_{R_i}$, $i = 1,2,\cdots n$, added to the [[Standard Model ]{}]{}for this purpose. Since these right-handed neutrinos 