The Golden Ratio Prediction for the Solar Angle from a Natural Model with A5 Flavour Symmetry

TL;DR

This paper presents a theoretical model using A5 flavor symmetry that predicts the solar neutrino mixing angle based on the Golden Ratio, aligning with observed neutrino mixing patterns.

Contribution

The model uniquely derives the solar mixing angle as the inverse of the Golden Ratio using a specific flavor symmetry framework, with stability against higher-order corrections.

Findings

Predicts maximal atmospheric mixing angle

Achieves vanishing reactor angle

Derives tan θ12 = 1/φ, where φ is the Golden Ratio

Abstract

We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan {\theta}_12 = 1/{\phi} where {\phi} is the Golden Ratio. The model is based on the flavour symmetry A5 \times Z5 \times Z3, spontaneously broken by a set of flavon fields. By minimizing the scalar potential of the theory up to the next-to-leading order in the symmetry breaking parameter, we demonstrate that this mixing pattern is naturally achieved in a finite portion of the parameter space, through the vacuum alignment of the flavon fields. The leading order approximation is stable against higher-order corrections. We also compare our construction to other models based on discrete symmetry groups.