Parametrization of PMNS matrix based on dodeca-symmetry

TL;DR

This paper proposes a parametrization of the PMNS matrix based on dodeca-symmetry, connecting it to the Cabibbo angle and neutrino mixing angles, with corrections modeled by small parameters.

Contribution

It introduces a novel dodeca-symmetry-based parametrization of the PMNS matrix, incorporating small parameters and providing two estimations from neutrino oscillation data.

Findings

The parametrization relates neutrino mixing angles to dodeca-symmetry.

Two specific parametrizations are derived and their small parameter values estimated.

The approach simplifies the understanding of neutrino mixing in terms of symmetry.

Abstract

The dodeca symmetry is designed to obtain the Cabibbo angle $\theta_C^{\rm CKM}$ approximately $15^{\rm o}$ and the (11) element of $\Vp$ as $\cos 30^{\rm o}$, leading to $\theta_1^{\rm PMNS}+\theta_C^{\rm CKM}\simeq 45^{\rm o}$. This leading order dodeca symmetric $\Vp$ is corrected by small parameters, especially as an expansion in terms of a small parameter $\beta$. Neglecting two Majorana phases, the expression of $\Vp$ contains four parameters: a small $\beta$, and three $\Od(1)$ parameters $A,B,$ and $\delta$. From the neutrino oscillation data, we present two parametrizations and estimate their $\beta$'s.