Fermion Mass Hierarchies and Flavour Mixing from a Minimal Discrete Symmetry

TL;DR

This paper presents a minimal model using S3 x Z3 symmetry to explain fermion mass hierarchies and mixing angles, successfully reproducing observed neutrino and quark sector features with predictive power.

Contribution

It introduces a simple, symmetry-based framework that naturally accounts for fermion mass hierarchies and mixing angles, including neutrino oscillation parameters.

Findings

Predicts b23=b4+O(bb_c^2) and b13=O(bb_c^2) for neutrino mixing angles.

Automatically reproduces charged lepton mass hierarchy from symmetry breaking.

Extends to quark sector with natural mass spectrum and mixing angles, except for a small enhancement needed for the first two generations.

Abstract

We construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is broken down to a \nu_\mu-\nu_\tau parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing \theta_{13}. In the charged lepton sector the \nu_\mu-\nu_\tau parity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2), \lambda_c denoting the Cabibbo angle. A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.