A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos

TL;DR

This paper provides the first complete parametrization of the 9x9 flavor mixing matrix in inverse and linear seesaw models, detailing the mixing angles, CP phases, and deviations from unitarity in neutrino physics.

Contribution

It introduces the first full parametrization of the 9x9 flavor mixing matrix in inverse and linear seesaw scenarios, including explicit formulas and deviation analyses.

Findings

Derived exact inverse and linear seesaw formulas.

Presented a full parametrization with 36 angles and phases.

Analyzed deviations from unitarity in active neutrino mixing.

Abstract

The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases. The exact inverse and linear seesaw formulas are derived, respectively; and possible deviations of the $3\times 3$ active neutrino mixing matrix from its unitary limit are discussed by calculating the effective Jarlskog invariants and unitarity nonagons.