Parametrization of PMNS matrix based on dodeca-symmetry

Abstract

The dodeca symmetry is designed to obtain the Cabibbo angle ${\theta }_C^{\mathrm{CKM}}$ approximately $15^{\mathrm{o}}$ and the (11) element of $\text{Vp}$ as $\cos 30^{\mathrm{o}}$, leading to ${\theta }_1^{\mathrm{PMNS}}+{\theta }_C^{\mathrm{CKM}}\simeq 45^{\mathrm{o}}$. This leading order dodeca symmetric $\text{Vp}$ is corrected by small parameters, especially as an expansion in terms of a small parameter $\beta$. Neglecting two Majorana phases, the expression of $\text{Vp}$ contains four parameters: a small $\beta$, and three $\text{Od}(1)$ parameters $A,B,$ and $\delta$. From the neutrino oscillation data, we present two parametrizations and estimate their $\beta$'s.

Comments: 7 pages