Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry

TL;DR

This paper explores lepton flavor models based on $A_5$ symmetry that naturally produce a solar mixing angle related to the golden ratio, proposing two models with specific symmetry breaking patterns and analyzing their phenomenological implications.

Contribution

It identifies $A_5$ as the minimal group capable of enforcing golden ratio related lepton mixing and constructs two explicit models demonstrating this mechanism.

Findings

Two models achieve the golden ratio solar mixing angle.

The second model predicts a small reactor angle consistent with data.

Residual symmetries in the models influence the mixing patterns.

Abstract

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 $A_5$ 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 $A_5$ 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 $Z_5$ in the first model, while in the second model, $A_5$ 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.