Axion-neutrino Interplay in a Gauged Two-Higgs-doublet Model

We propose a gauged two-Higgs-doublet model (2HDM) featuring an anomalous PecceiQuinn symmetry, U(1)PQ. Dangerous tree-level flavour-changing neutral currents, common in 2HDMs, 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 problem 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 DFSZ-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 flavour-violating process of kaon decaying into pion plus axion, K → πa, is further suppressed by the U(1)X scale, providing a rather weak lower bound for the axion decay constant fa.