# Finite Family Groups for Fermionic and Leptoquark Mixing Patterns

## TL;DR

This paper uses a model-independent approach to identify non-Abelian discrete flavor symmetries that can predict fermion mixing matrices and leptoquark coupling patterns, aiding future flavor model development.

## Contribution

It introduces a bottom-up, model-independent algorithm to find predictive non-Abelian flavor groups relevant for fermion mixing and leptoquark phenomenology.

## Key findings

- Identifies numerous non-Abelian flavor groups compatible with observed mixing matrices.
- Provides a framework for exploring leptoquark couplings without detailed model assumptions.
- Suggests potential explanations for lepton non-universality hints in B-meson decays.

## Abstract

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns derived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these `simplified models' can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $\mathcal{R}_{K^{(\star)}}$. Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $\mathcal{R}_{K^{(\star)}}$ measurements withstand further experimental scrutiny.