Implication of rephasing invariant parameters on texture specific mass matrices

TL;DR

This paper investigates how rephasing invariant parameters relate to texture-specific mass matrices in quark and lepton sectors, analyzing their implications for CP violation and calculating predicted ranges of these invariants.

Contribution

It provides a detailed analysis of CP-odd invariants for texture two zero mass matrices, offering new insights into their phase structures and CP violation implications.

Findings

Calculated ranges of Jarlskog invariant for seven texture cases

Established relationships between CP invariants and mass matrix textures

Implications for CP violation in leptonic and quark sectors

Abstract

In the quark sector, Jarlskog rephasing invariant parameter $J_{CP}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to the magnitude of the imaginary part of $J_{CP}$ . With the observation of non-zero and large "reactor mixing angle", it is widely believed that CP might be violated in the leptonic sector. In this context, we have examined in detail the relationship of CP odd invariants for texture specific mass matrices. In particular, we have calculated the predicted ranges of Jarlskog rephasing invariant parameter and other weak basis invariants for all the seven viable cases for texture two zero mass matrices.