  It is well known that generic two-Higgs-doublet models (2HDMs) suffer from
potentially large Higgs-mediated flavor-changing neutral current (FCNC)
problem, unless additional symmetries are imposed on the Higgs fields thereby
respecting the Natural Flavor Conservation Criterion (NFC) by Glashow and
Weinberg. A common way to respect the NFC is to impose Z_2 symmetry which is
softly broken by a dim-2 operator. Another new way is to introduce local U(1)_H
Higgs flavor symmetry that distinguishes one Higgs doublet from the other. In
this paper, we consider the Higgs phenomenology in Type-I 2HDMs with the U(1)_H
symmetry with the simplest U(1)_H assignments that the SM fermions are all
neutral under U(1)_H, and we make detailed comparison with the ordinary Type-I
2HDM. After imposing various constraints such as vacuum stability and
perturbativity as well as the electroweak precision observables and collider
search bounds on charged Higgs boson, we find that the allowed Higgs signal
strengths in our model are much broader than those in the ordinary Type-I 2HDM,
because of newly introduced U(1)_H-charged singlet scalar and U(1)_H gauge
boson. Still the ATLAS data on gg to h to gamma gamma cannot be accommodated.
Our model could be distinguished from the ordinary 2HDM with the Z_2 symmetry
in a certain parameter region and some channels. If the couplings of the new
boson turn out to be close to those in the SM, it would be essential to search
for extra U(1)_H gauge boson and/or one more neutral scalar boson to
distinguish two models.
