Golden ratio lepton mixing and nonzero reactor angle with $A_5$

Abstract

We furnish a supersymmetric extension of the Standard Model with a flavour discrete symmetry $A_5$ under which the lepton fields transform as an irreducible triplet. Additional (`flavon') superfields are used to break $A_5$ into a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ subgroup in the charged-lepton sector and another ${\mathbb{Z}}_2$ subgroup in the neutrino sector. The first column of the resulting lepton mixing matrix is predicted and has entries which are related to the golden ratio. Using the observed ${\theta }_{13}$ as input, our model predicts a solar mixing angle ${\theta }_{12}$ in very good agreement with experiment; it also predicts a correlation between the atmospheric mixing angle ${\theta }_{23}$ and the $CP$-violating Dirac phase $\delta$.

Comments: 17 pages, 3 figures. v2: references added. v3: accepted by J. Phys. G