Abstract
An accidental U(1) Peccei-Quinn (PQ) symmetry automatically arises in a class of SO(10) unified theories upon gauging the SU(3)f flavour group. The PQ symmetry is protected by the ℤ4 × ℤ3 center of SO(10) × SU(3)f up to effective operators of canonical dimension six. However, high-scale contributions to the axion potential posing a PQ quality problem arise only at d = 9. In the pre-inflationary PQ breaking scenario the axion mass window is predicted to be ma ∈ [7 × 10−8, 10−3] eV, where the lower end is bounded by the seesaw scale and the upper end by iso-curvature fluctuations. A high-quality axion, that is immune to the PQ quality problem, is obtained for ma ≳ 2 0.02 eV. We finally offer a general perspective on the PQ quality problem in grand unified theories.
Highlights
Requirement of having the U(1)PQ to arise accidentally is a bare minimum that a sensible PQ theory in should structurally achieve
The main obstacle for such a program is the cancellation of the SU(3)3f gauge anomaly, which requires to extend the fermion content of SO(10). We show how this can be consistently done, and we extend the analysis of [15] in several respects: i) we point out that the same approach can be used beyond the renormalizable level, providing a way to tackle the PQ quality problem; ii) we identify the physical axion field and compute its low-energy couplings to SM matter fields
We realized that the charge assignment of [15] must be slightly modified, in order to avoid an alignment between two SO(10) Higgs representations which would otherwise lead to a Weinberg-Wilczek axion; iii) we address SU(3)f breaking dynamics
Summary
After having obtained the U(1)PQ to arise accidentally in the renormalizable Lagrangian, one should worry about possible sources of PQ breaking in the UV, which are often parametrized via effective operators suppressed by a cut-off scale ΛUV. In scenarios in which Einstein gravity is minimally coupled to the axion field, non-conservation of the PQ global charge arises from non-perturbative effects described by Euclidean wormholes Those are calculable in the semi-classical limit [29,30,31,32,33] and give a correction to the axion potential of the order of MP4le−Swh, where Swh ∼ MPl/fa is the wormhole action. The anomaly does not depend on the mass of the fermions running in the triangle loop, and it must be preserved through the various stages of symmetry breaking This feature will be useful for identifying the physical axion field and its low-energy couplings. The last, self-contained derivation is deferred to appendix A
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