Axion phenomenology in Two-Higgs Doublet Model with extra gauge symmetry $U(1)_X$
In this work, we propose a Two-Higgs Doublet Model (2HDM) extension of the Standard Model (SM). The flavor-changing neutral currents (FCNC) are forbidden by an extra gauge symmetry, $U(1)_X$. This model offers simultaneous solutions to the problems of strong CP and dark matter with the addition of an anomalous global symmetry, $U(1)_{PQ}$, and of the neutrino masses with a Dirac seesaw mechanism realization. The neutrinos masses are suppressed by the ratio of the breaking scales of the two extra symmetries of the model, leading to the characterization of the breaking scale of $U(1)_X$ as intermediate. Signals may be within experimental reach in the next generations of colliders. The gauge boson associated with $U(1)_X$ does not mix the SM $Z$ boson. There are hints this is a general feature in extended scalar sector models. This model's axion may explain the observed abundance of dark matter if $U(1)_{PQ}$ breaking scale is high enough. Preferred regions in the axion parameter space are identified. Lastly, we notice that the constraint on the axion decay constant, $f_a$, by the flavor violating process $K^+ \to \pi^+ a$ is suppressed by the $U(1)_X$ breaking scale.