HNL see-saw: lower mixing limit and pseudodegenerate state

TL;DR

This paper investigates the theoretical lower bounds on heavy neutral lepton mixing, introduces the pseudodegenerate limit, and explores its implications for neutrino physics and experimental searches.

Contribution

It establishes the lower mixing limits for HNLs, introduces the pseudodegenerate limit, and analyzes their relations in two and three HNL scenarios.

Findings

Identified the lower boundary for HNL mixing with specific flavors.

Connected the pseudodegenerate limit to experimental exclusion regions.

Derived conditions for pseudodegenerate states in three HNLs.

Abstract

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.