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We survey a few minimal scalar extensions of the standard electroweak modelthat provide a simple setup for massive neutrinos in connection with aninvisible axion. The presence of a chiral $U(1)$ \`a la Peccei-Quinn drives thepattern of Majorana neutrino masses while providing a dynamical solution to thestrong CP problem and an axion as a dark matter candidate. We paradigmaticallyapply such a renormalizable framework to type-II seesaw and to two viablemodels for neutrino oscillations where the neutrino masses arise at one and twoloops, respectively. We comment on the naturalness of the effective setups aswell as on their implications for vacuum stability and electroweakbaryogenesis.

Massive neutrinos and invisible axion minimally connected