Gauge invariant one-loop corrections to Higgs boson couplings in non-minimal Higgs models

We comprehensively evaluate renormalized Higgs boson couplings at one-loop level in non-minimal Higgs models such as the Higgs Singlet Model (HSM) and the four types of Two Higgs Doublet Models (THDMs) with a softly-broken $Z_2$ symmetry. The renormalization calculation is performed in the on-shell scheme improved by using the pinch technique to eliminate the gauge dependence in the renormalized couplings. We first review the pinch technique for scalar boson two-point functions in the Standard Model (SM), the HSM and the THDMs. We then discuss the difference in the results of the renormalized Higgs boson couplings between the improved on-shell scheme and the ordinal one with a gauge dependence appearing in mixing parameters of scalar bosons. Finally, we widely investigate how we can identify the HSM and the THDMs focusing on the pattern of deviations in the renormalized Higgs boson couplings from predictions in the SM.