Implications of Higgs boson search data on the two-Higgs doublet models with a softly broken $Z_2$ symmetry

Based on current data of the Higgs boson search at the Large Hadron Collider, we constrain the parameter space of the two-Higgs doublet models where a softly broken $Z_2$ symmetry is employed to avoid flavor-changing neutral currents at tree level. There are four types of Yukawa interactions under the $Z_2$ charge assignments of the standard model fermions. We find that the model with type-II Yukawa interactions can better explain the experimental data among all. In this scenario, the couplings of the light CP-even Higgs boson $h$ with weak gauge bosons are almost standard model-like or only slightly different in a small range of $\tan \beta$. In particular, we scrutinize a well-constrained region previously ignored by other analyses and study the phenomenology of the extra Higgs bosons at the Large Hadron Collider.