Eigenvector-eigenvalue identities and an application to flavor physics

TL;DR

This paper extends eigenvector-eigenvalue identities to include mixing parameters, revealing intricate connections and permutation symmetries, with applications to flavor physics.

Contribution

It introduces generalized identities involving mixing parameters and highlights the role of permutation symmetry in understanding these relations.

Findings

Derived simple relations between eigenvalues and mixing parameters.

Identified permutation symmetry as a key principle in the identities.

Provided insights applicable to flavor physics models.

Abstract

The eigenvector-eigenvalue identities are expanded to include general mixing parameters. Some simple relations are obtained and they reveal an intricate texture of connections between the eigenvalues and the mixing parameters. Permutation symmetry ($S_{3}\times S_{3}$) plays an indispensable role in our analysis. It is the guiding principle for the understanding of our results -- all of them are tensor equations under permutation.