Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry

TL;DR

This paper explores how finite discrete flavor symmetries can predict quark and lepton mixing patterns, identifying specific groups that closely match experimental data and proposing measures to evaluate their predictivity.

Contribution

It extends previous analyses by including Dirac neutrinos and introduces a measure to compare the predictivity of various flavor groups.

Findings

Identified groups predicting realistic mixing angles for neutrinos and quarks.

Found that the group (Z_18 × Z_6) ⋊ S_3 is most predictive among studied groups.

Proposed a measure to evaluate the predictivity of flavor symmetry groups.

Abstract

Assuming the Majorana nature of neutrinos, we recently performed a scan of leptonic mixing patterns derived from finite discrete groups of order less than 1536. Here we show that the 3 groups identified there as giving predictions close to experiment, also contain another class of abelian subgroups that predict an interesting leading order quark mixing pattern where only the Cabibbo angle is generated at leading order. We further broaden our study by assuming that neutrinos are Dirac particles and find 4 groups of order up to 200 that can predict acceptable quark and leptonic mixing angles. Since large flavor groups allow for a multitude of leading order mixing patterns, we define a measure that is suitable to compare the predictivity of a given flavor group taking this fact into account. We give the result of this measure for a wide range of discrete flavor groups and identify the group (Z_18 \times Z_6) \rtimes S_3 as being most predictive in the sense of this measure. We further discuss alternative measures and their implications.