Testable Inverse Seesaw Motivated from a High Quality QCD Axion

Abstract

The QCD axion remains one of the most compelling solutions to the strong CP problem. Meanwhile, the type-I seesaw mechanism offers an elegant explanation for the lightness of the observed neutrino masses; however, its extremely heavy Majorana states place it far beyond experimental reach. Low-scale alternatives such as the inverse seesaw improve testability but typically lack a strong theoretical motivation. In this paper we bridge this gap by showing that gauging the discrete symmetry $\mathbb Z_4 \times \mathbb Z_3$-motivated by the internal structure of the Standard Model-naturally yields a QCD axion with a high-quality Peccei-Quinn symmetry solving the strong CP problem, while simultaneously enforcing the field content and hierarchy required for a natural inverse seesaw. The resulting model is highly predictive and has the potential to be fully tested by future experiments. Beyond addressing the strong CP problem and the origin of neutrino masses, our scenario also contains a viable dark-matter candidate and offers potential mechanisms for generating the baryon asymmetry of the Universe.