Rephasing Invariants of Quark and Lepton Mixing Matrices

TL;DR

This paper systematically studies rephasing invariants of quark and lepton mixing matrices within the standard model and seesaw mechanism, classifying invariants, exploring their relations, and analyzing phase restrictions due to Majorana mass matrix symmetries.

Contribution

It introduces a comprehensive classification of rephasing invariants and analyzes their relations and constraints in models with Majorana neutrinos.

Findings

Classified basic rephasing invariants for quark and lepton mixing matrices.

Identified relations and independence conditions among invariants.

Discussed phase restrictions imposed by Majorana mass matrix symmetries.

Abstract

Rephasing invariants of quark and lepton mixing matrices are obtained in the standard model extended by the seesaw mechanism, and in its low-energy effective theory with the dimension-five Majorana mass operator. We classify the basic invariants, discuss non-trivial relations between them, and determine the independent invariants which characterize all the information in the mixing matrices in a basis-independent way. We also discuss the restrictions on the allowed ranges for the mixing phases, and on the rephasing invariants, which follow from a discrete invariance of the Majorana mass matrix.