Axion Protection from Flavor

TL;DR

This paper demonstrates that protecting the QCD axion from explicit PQ violation requires flavor symmetries to suppress low-dimension operators, proposing a mechanism to keep PQ symmetry intact up to dimension 12 using flavor symmetries.

Contribution

It introduces a novel 'axion flavor protection' mechanism that leverages flavor symmetries to prevent low-dimension PQ-violating operators, ensuring the axion solves the strong CP problem.

Findings

Explicit PQ violation is linked to Yukawa matrix determinants.

Suppression of operators up to dimension 12 is achievable with flavor symmetries.

The mechanism is compatible with radiative fermion mass generation and grand unification.

Abstract

The QCD axion fails to solve the strong CP problem unless all explicit PQ violating, Planck-suppressed, dimension n<10 operators are forbidden or have exponentially small coefficients. We show that all theories with a QCD axion contain an irreducible source of explicit PQ violation which is proportional to the determinant of the Yukawa interaction matrix of colored fermions. Generically, this contribution is of low operator dimension and will drastically destabilize the axion potential, so its suppression is a necessary condition for solving the strong CP problem. We propose a mechanism whereby the PQ symmetry is kept exact up to n=12 with the help of the very same flavor symmetries which generate the hierarchical quark masses and mixings of the SM. This "axion flavor protection" is straightforwardly realized in theories which employ radiative fermion mass generation and grand unification. A universal feature of this construction is that the heavy quark Yukawa couplings are generated at the PQ breaking scale.