New renormalization scheme in extended Higgs sectors for Higgs precision measurements

We discuss a new renormalization scheme for mixing angles in extended Higgs sectors for the coming era of the Higgs precise measurements at future lepton colliders. We focus on the two Higgs doublet models (2HDMs) with a softly-broken $Z_2$ symmetry as a simple and important example, in which two mixing angles $\alpha$ and $\beta$ appear in the Higgs sector. In this new scheme, the counterterms for two mixing angles $\delta \alpha$ and $\delta \beta$ are determined by requiring that deviations in the decay rates of $h\to Z{Z}^{\ast }\to Z{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $h\to \tau \tau$ from the corresponding predictions in the standard model at NLO are given by the square of the scaling factor at tree level. We show how this scheme works in the 2HDMs, and demonstrate how the other decay rates (e.g., $h\to W{W}^{\ast }$, $h\to b\bar{b}$, etc.) are predicted at NLO.