Majoron as the QCD axion in a radiative seesaw model

The smallness of neutrino mass, the strong $CP$ problem, and the existence of dark matter are explained in an economical way. The neutrino mass is generated by the colored version of a radiative seesaw mechanism by using color adjoint mediators. The Majorana mass term of the adjoint fermion, which carries lepton number $U(1{)}_{\mathbb{L}}$, is induced by its spontaneous breaking, resulting in a Majoron which doubles as the quantum chromodynamics axion, thereby solving the strong $CP$ problem. The breaking of $U(1{)}_{\mathbb{L}}$ sets simultaneously the seesaw scale for neutrino mass and the Peccei-Quinn breaking scale. This axion is a good candidate for dark matter as usually assumed.

Figure 1

One-loop diagram for neutrino mass generation.