Axion phenomenology in the two Higgs doublet model with $U(1)_X$ gauge symmetry
In this work, we propose a Two-Higgs Doublet Model (2HDM) extension of the Standard Model (SM) with an additional $U(1)_X$ gauge symmetry, which forbids the flavor-changing neutral currents (FCNC) at tree level. We simultaneously address in such a model the strong-CP, dark matter, and neutrino mass problems. To do this, we need to implement an additional $U(1)_{PQ}$ symmetry and a Dirac seesaw mechanism. The neutrino 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. The axion in this model may explain the observed abundance of dark matter if $U(1)_{PQ}$ breaking scale is high enough. We notice that the $U(1)_X$ breaking scale suppresses the constraint on the axion decay constant, $f_a$, induced by the flavor violating process $K^+ \to \pi^+ a$. Lastly, we identify the preferred regions in the axion parameter space, taking into account the interplay of the energy scales leading to natural neutrino masses as well.