Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing

TL;DR

This paper explores using icosahedral symmetry (A5) as a family symmetry in the lepton sector, proposing a model where the solar neutrino mixing angle is related to the golden ratio, with specific predictions for mixing angles.

Contribution

It introduces a new model using icosahedral symmetry to relate neutrino mixing angles to the golden ratio, including explicit mathematical tools for model-building.

Findings

Solar angle related to the golden ratio

Atmospheric angle is maximal

Reactor angle vanishes at leading order

Abstract

We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.