Axion-neutrino interplay in a gauged two-Higgs-doublet model

We propose a gauged two-Higgs-doublet model featuring an anomalous Peccei-Quinn symmetry, U(1) PQ. Dangerous tree-level flavor-changing neutral currents, common in two-Higgs-doublet models, are forbidden by the extra gauge symmetry, U(1)X. In our construction, the solutions to the important issues of neutrino masses, dark matter, and the strong CP problems are interrelated. Neutrino masses are generated via a Dirac seesaw mechanism and are suppressed by the ratio of the U(1)X and the U(1)PQ breaking scales. Naturally small neutrino masses suggest that the breaking of U(1)X occurs at a relatively low scale, which may lead to observable signals in near-future experiments. Interestingly, spontaneous symmetry breaking does not lead to mixing between the U(1)X gauge boson, Z′, and the standard Z. For the expected large values of the U(1)PQ scale, the associated axion becomes "invisible," with Dine-Fischler-Srednicki-Zhitnitsky-like couplings, and may account for the observed abundance of cold dark matter. Moreover, a viable parameter space region, which falls within the expected sensitivities of forthcoming axion searches, is identified. We also observe that the flavor-violating process of kaon decaying into pion plus axion, K+ → π+ a, is further suppressed by the U(1)X scale, providing a rather weak lower bound for the axion decay constant fa.