On quark-lepton mixing and the leptonic CP violation

TL;DR

This paper explores a model linking quark and lepton mixing matrices through specific product forms, incorporating corrections to well-known mixing patterns to fit experimental data on leptonic mixing and CP violation.

Contribution

It proposes a novel approach where the PMNS matrix is expressed as a product involving the CKM matrix and a see-saw derived matrix, with modifications to classical mixing patterns to match observations.

Findings

Modified BM, TBM, and GR patterns fit leptonic mixing data

The model accommodates observed CP phase and mass differences

Provides a framework connecting quark and lepton sectors

Abstract

In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark and lepton sector is a difficult task, unless one introduces ad-hoc relations among the matrices that diagonalize such different kinds of fermions. In this paper, we discuss in detail the possibility that the PMNS matrix is given by the product U_{PMNS}=V^\ast_{CKM} T^\ast where T comes from the diagonalization of a see-saw like mass matrix that can be of a Bimaximal (BM), Tri-Bimaximal (TBM) and Golden Ratio (GR) form, and identify the leading corrections to such patterns that allow a good fit to the leptonic mixing matrix as well as to the CP phase. We also show that the modified versions of BM, TBM and GR can easily accommodate the solar and atmospheric mass differences