Golden Ratio Prediction for Solar Neutrino Mixing

TL;DR

This paper explores the connection between the solar neutrino mixing angle and the golden ratio, proposing a model based on dihedral symmetry to explain the observed angle and analyzing radiative corrections.

Contribution

It introduces a model using the dihedral group D_{10} to predict the solar neutrino mixing angle as related to the golden ratio, specifically cos theta_{12} = phi/2.

Findings

The model predicts the solar neutrino mixing angle as pi/5 (36 degrees).

Radiative corrections to the golden ratio predictions are estimated.

The symmetry group D_{10} naturally leads to the proposed angle.

Abstract

It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio phi. Two such proposals have been made, cot theta_{12} = phi and cos theta_{12} = phi/2. We compare these Ansatze and discuss a model leading to cos theta_{12} = phi/2 based on the dihedral group D_{10}. This symmetry is a natural candidate because the angle in the expression cos theta_{12} = phi/2 is simply pi/5, or 36 degrees. This is the exterior angle of a decagon and D_{10} is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions.