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

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 $θ_{13}$ as input, our model predicts a solar mixing angle $θ_{12}$ in very good agreement with experiment; it also predicts a correlation between the atmospheric mixing angle $θ_{23}$ and the $CP$-violating Dirac phase $δ$.

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