Accidental Peccei–Quinn symmetry from discrete flavour symmetry and Pati–Salam.

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 Z 3 × 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. [ABSTRACT FROM AUTHOR]