The formal seesaw mechanism of Majorana neutrinos with unbroken gauge symmetry

TL;DR

This paper reformulates the canonical seesaw mechanism for Majorana neutrinos under unbroken gauge symmetry, deriving an exact formula and clarifying the relationship between different neutrino states and parameters.

Contribution

It introduces a formal approach to the seesaw mechanism with unbroken gauge symmetry and establishes explicit relations between original and derived parameters.

Findings

Derived an exact seesaw formula for Majorana neutrinos.

Clarified the mismatch between heavy neutrino states in different frameworks.

Provided an Euler-like parametrization of the flavor mixing matrix.

Abstract

We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We elucidate the reason why there is a mismatch between the mass eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis and those associated with the seesaw framework, and establish the exact and explicit relations between the "original" and "derivational" seesaw parameters by using an Euler-like parametrization of the $6\times 6$ active-sterile flavor mixing matrix.