Massive neutrinos and invisible axion minimally connected

We survey a few minimal scalar extensions of the standard electroweak model that provide a simple setup for massive neutrinos in connection with an invisible axion. The presence of a chiral $U(1)$ à la Peccei-Quinn drives the pattern of Majorana neutrino masses while providing a dynamical solution to the strong $CP$ problem and an axion as a dark matter candidate. We paradigmatically apply such a renormalizable framework to type-II seesaw and to two viable models for neutrino oscillations where the neutrino masses arise at one and two loops, respectively. We comment on the naturalness of the effective setups as well as on their implications for vacuum stability and electroweak baryogenesis.

Figure 1

Sample diagrams leading to the $\mathrm{\Delta }L=2$ Weinberg operator at the tree level (a), one loop (b), and two loops (c) in the type-II seesaw, Zee, and Zee-Babu models, respectively.

Figure 2

The tree-level “hug” diagram responsible for the Majorana neutrino mass in the PQ-extended type-II seesaw model.

Figure 3

Sample one-loop diagram responsible for the Majorana neutrino mass in the PQ-extended Babu-Julio model. Because of the family dependence of the PQ charges, both Higgs doublets couple to the first leptonic family.

Figure 4

Two-loop diagram responsible for the neutrino Majorana mass in the PQ-extended Zee-Babu model.

Figure 5

Naturalness bounds on the mass of the exotic scalar multiplets present in the different PQ-extended neutrino mass models, as a function of the ultraviolet cutoff, see Eq. (58).