Two Higgs doublet models with local U(1)_H gauge symmetry and dark matter

We propose to implement the softly broken Z_2 symmetry in the usual two Higgs doublet model (2HDM) to spontaneously broken local U(1)_H gauge symmetry, and show that the resulting phenomenology can be very rich and is distinctly different from the usual 2HDMs. Likewise, the exact Z_2 symmetry in ordinary inert doublet model (IDM) could be a remnant of spontaneously broken local U(1)_H symmetry stabilizing dark matter (DM). In this case, new channels for DM pair annihilation into U(1)_H gauge boson(s) open up, allowing the DM mass below \lesssim 40 GeV, unlike the usual IDM.