Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam

TL;DR

This paper demonstrates how an accidental Peccei-Quinn symmetry can emerge from discrete flavour symmetries within a Pati-Salam framework, linking flavour physics to the strong CP problem and predicting flavour-violating axion couplings.

Contribution

It introduces a model where a discrete A4 and Z3×Z5^2 symmetry produce an accidental PQ symmetry, protecting the axion solution and connecting flavour structure with the strong CP problem.

Findings

The model predicts specific flavour-violating axion couplings.

The PQ symmetry is protected from breaking operators.

Constraints on the axion scale from kaon decay limits.

Abstract

We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $ \mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $ CP $ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $ A_4 $ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of an accidental PQ symmetry arising from a discrete flavour symmetry constrains the form of the Yukawa matrices, providing a link between flavour and the strong $ CP $ problem. Our model predicts specific flavour-violating couplings of the flavourful axion and thus puts a strong limit on the axion scale from kaon decays.