CP-odd Weak Basis Invariants for Neutrino Mass Matrices with a Texture Zero and a Vanishing Minor

TL;DR

This paper develops CP-odd weak basis invariants for specific neutrino mass matrices with texture zeros and vanishing minors, providing conditions for CP invariance and exploring implications for CP violation types.

Contribution

It introduces a comprehensive set of CP-odd invariants for these neutrino textures and establishes criteria for CP invariance, advancing understanding of CP violation in neutrino physics.

Findings

Derived necessary and sufficient conditions for CP invariance.

Analyzed relationships between different CP-odd invariants.

Explored implications for Dirac and Majorana CP violation.

Abstract

We construct the $CP$-odd weak basis invariants in the flavor basis for all the phenomenologically viable neutrino mass matrices with a texture zero and a vanishing minor and, also, find the necessary and sufficient conditions for $CP$ invariance . We examine the interrelationships between different $CP$-odd weak basis invariants for these texture structures and investigate their implications for Dirac- and Majorana-type $CP$ violation.