Lepton Mixing in $A_5$ Family Symmetry and Generalized CP

TL;DR

This paper explores lepton mixing patterns derived from $A_5$ symmetry and generalized CP, identifying five interesting patterns that fit experimental data and predicting CP phases, with a supersymmetric model supporting these findings.

Contribution

It introduces five new lepton mixing patterns from $A_5$ symmetry, linking them to experimental data and constructing a supersymmetric model that reproduces these patterns.

Findings

Five phenomenologically interesting mixing patterns identified.

Agreement with experimental data achieved for certain parameter values.

Supersymmetric model constructed to realize the mixing patterns.

Abstract

We study lepton mixing patterns which can be derived from the $A_5$ family symmetry and generalized CP. We find five phenomenologically interesting mixing patterns for which one column of the PMNS matrix is $(\sqrt{\frac{5+\sqrt{5}}{10}},\frac{1}{\sqrt{5+\sqrt{5}}},\frac{1}{\sqrt{5+\sqrt{5}}})^{T}$ (the first column of the golden ratio mixing), $(\sqrt{\frac{5-\sqrt{5}}{10}},\frac{1}{\sqrt{5-\sqrt{5}}},\frac{1}{\sqrt{5-\sqrt{5}}})^{T}$ (the second column of the golden ratio mixing), $(1,1,1)^{T}/\sqrt{3}$ or $(\sqrt{5}+1,-2,\sqrt{5}-1)^{T}/4$. The three lepton mixing angles are determined in terms of a single real parameter $\theta$, and agreement with experimental data can be achieved for certain values of $\theta$. The Dirac CP violating phase is predicted to be trivial or maximal while Majorana phases are trivial. We construct a supersymmetric model based on $A_5$ family symmetry and generalized CP. The lepton mixing is exactly the golden ratio pattern at leading order, and the mixing patterns of case III and case IV are reproduced after higher order corrections are considered.