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Radiative corrections to the Yukawa coupling constants in two Higgs doublet models

We calculate one-loop corrected Yukawa coupling constants $hf\bar{f}$ for the standard model like Higgs boson $h$ in two Higgs doublet models. We focus on the models with the softly-broken $Z_2$ symmetry, which is imposed to avoid the flavor changing neutral current. Under the $Z_2$ symmetry, there are four types of Yukawa interactions. We find that one-loop contributions from extra Higgs bosons modify the $hf\bar{f}$ couplings to be maximally about $5\%$ under the constraint from perturbative unitarity and vacuum stability. Our results show that the pattern of tree-level deviations by the mixing effect in each type of Yukawa couplings from the SM predictions does not change even including radiative corrections. Moreover, when the gauge couplings $hVV$ ($V=W,Z$) are found to be slightly (with a percent level) differ from the SM predictions, the $hf\bar{f}$ couplings also deviate but more largely. Therefore, in such a case, not only can we determine the type of Yukawa couplings but also we can obtain information on the extra Higgs bosons by comparing the predictions with precisely measured $hf\bar{f}$ and $hVV$ couplings at future electron-positron colliders.