HNL see-saw: lower mixing limit and pseudodegenerate state

Heavy Neutral Leptons are popular hypothetical particles, first introduced as a way to explain neutrino oscillations, and since then extensively studied in relation to many other aspects of physics beyond the Standard Model. They also serve as viable targets for direct experimental searches, being effectively described only by HNL mass and mixing with each neutrino flavor. Motivated by this, we study the lower theoretical boundary for mixing with a specified flavor in two and three HNLs cases. We find the connection of this limit with the effective neutrino mass appearing in neutrinoless double beta decay (and similar expressions for mixing with muon and tau neutrino). In two HNLs case, there is a rather strict relation between mixing of different HNLs with the same neutrino flavor. We find that existing exclusion regions and their expected expansions in the near future are all described by a certain limit. We call that limit pseudodegenerate and find its relation to the symmetrical limit, already studied in the literature. We also study pseudodegenerate limit and conditions under which it is achieved in three HNLs case.