Testable Inverse Seesaw Motivated from a High Quality QCD Axion

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.

💡 Research Summary

The paper presents a unified framework that simultaneously addresses the strong CP problem, the origin of neutrino masses, dark matter, and the baryon asymmetry by exploiting discrete gauge symmetries already hinted at by the Standard Model (SM) fermion structure. The authors start from the observation that the SM admits two anomaly‑free discrete symmetries, a (\mathbb Z_4) under which all chiral fermions carry charge +1 and a (\mathbb Z_3) reflecting the three‑generation family structure. By gauging the product (\mathbb Z_4\times\mathbb Z_3) and introducing three right‑handed neutrinos (\bar N_i) (to cancel the (\mathbb Z_4) Dai‑Freed anomaly) together with three singlet Majorana fermions (\chi_i) (to cancel the (\mathbb Z_3) anomaly), the model automatically generates a global Peccei‑Quinn (PQ) symmetry.

A complex scalar (\Phi), charged under the discrete symmetries, plays the role of the PQ field. When (\Phi) acquires a vacuum expectation value (\langle\Phi\rangle\equiv F_a), the PQ symmetry is spontaneously broken, giving rise to the QCD axion (a). Because the discrete gauge symmetries cannot be violated by quantum gravity, the lowest‑dimension Planck‑suppressed operator that breaks PQ is (\Phi^{12}/M_{\rm Pl}^8). This high dimensionality ensures that for (F_a\lesssim 2\times10^{12}) GeV the axion potential remains dominated by QCD effects, solving the “axion quality problem” without any fine‑tuning. At the same time, the misalignment mechanism yields the correct dark‑matter abundance for (F_a\gtrsim10^{11}) GeV, fixing the axion mass to the range (3\times10^{-5})–(5\times10^{-4}) eV, well within the reach of upcoming haloscope searches.

The same discrete symmetries dictate the neutrino sector. The Lagrangian contains the following non‑renormalizable operators (suppressed by powers of the reduced Planck mass (M_{\rm Pl})):

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