Golden ratio neutrino mixing and A5A5 flavor symmetry

We provide a systematic and thorough exploration of lepton flavor models in which the solar mixing angle is related to the golden ratio. For scenarios in which the solar mixing angle is given by the inverse cotangent of the golden ratio, we demonstrate that A5A5 is the smallest non-Abelian finite group that contains all of the symmetries necessary to enforce this specific lepton mixing pattern. Within this context, we propose two lepton flavor models that yield this mixing pattern through the breaking of A5A5 at leading order to the Klein four subgroup in the neutrino sector. Both models have triplet embeddings of the lepton doublets as well as the charged lepton singlets. In the charged lepton sector, the residual symmetry is Z5Z5 in the first model, while in the second model, A5A5 is broken completely at leading order. For the second model, the reactor mixing angle vanishes at leading order and is of the order of the square of the Cabibbo angle at next-to-leading order, which is allowed by the global analysis of current lepton data.