A Nearest-neighbor Expansion of Lepton Flavor Mixing in Powers of the $\mu$-$\tau$ Permutation Symmetry Breaking Effect

TL;DR

This paper proposes a method to describe lepton flavor mixing using a nearest-neighbor expansion of a unitary matrix, emphasizing the role of $$-$$ permutation symmetry breaking and its implications for CP violation and unitarity in matter.

Contribution

It introduces a novel expansion approach for lepton mixing matrices based on symmetry breaking effects, enhancing understanding of CP violation.

Findings

Effective description of lepton mixing patterns

Insights into leptonic CP violation in matter

Application of symmetry breaking expansion

Abstract

We point out that the observed pattern of lepton flavor mixing can be well described by a proper nearest-neighbor expansion of a constant $3\times 3$ unitary matrix in powers of a small parameter characterizing the fine effect of $\mu$-$\tau$ permutation symmetry breaking. We take an example of this kind for illustration, and provide complete discussions on the usefulness in the study of leptonic CP violation and unitarity triangles in matter.