Accidental SO(10) axion from gauged flavour

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 ${\mathbb{Z}}_4\times {\mathbb{Z}}_3$ center of $\text{SO(10)}\times {\text{SU(3)}}_f$ 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 $m_a\in [7\times 10^{-8},10^{-3}]$ 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 $m_a\gtrsim 0.02$ eV. We finally offer a general perspective on the PQ quality problem in grand unified theories.

Comments: 26 pages, 2 figures; To appear in JHEP