Abstract
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, ${Z}^{\ensuremath{'}}$, 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, ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}a$, is further suppressed by the $U(1{)}_{X}$ scale, providing a rather weak lower bound for the axion decay constant ${f}_{a}$.
Highlights
The origin of small neutrino masses and the nature of dark matter (DM) are two of the most pressing issues with no answers within the Standard Model (SM) of particle physics
We propose a model in which the issues of neutrino masses, dark matter and strong CP problem are addressed simultaneously
Different constructions of 2HDMs with a Uð1ÞX symmetry have already been proposed to explain the suppression of flavor-changing neutral currents (FCNCs) [36], along with the implementation of WIMP [37] and axion [38] dark matter candidates, seesaw mechanism for the neutrino masses [39,40,41] and other phenomenological issues [42]
Summary
The origin of small neutrino masses and the nature of dark matter (DM) are two of the most pressing issues with no answers within the Standard Model (SM) of particle physics. Masses per se and other intrinsically related properties, such as neutrino mass ordering and absolute scale, CP phase and whether neutrinos are their own antiparticles [9] Another major drawback of the SM is the absence of a suitable candidate to account for the observed dark matter relic abundance [10], whose evidence arises from many sources [11]: from studies of galaxy rotation curves to cosmic microwave background data. Different constructions of 2HDMs with a Uð1ÞX symmetry have already been proposed to explain the suppression of FCNCs [36], along with the implementation of WIMP [37] and axion [38] dark matter candidates, seesaw mechanism for the neutrino masses [39,40,41] and other phenomenological issues [42].
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