Higgs-to-Higgs boson decays in a 2HDM at next-to-leading order

The detailed investigation of the Higgs sector at present and future colliders necessitates from the theory side as precise predictions as possible, including higher order corrections. An important ingredient for the computation of higher order corrections is the renormalization of the model parameters and fields. In this paper we complete the renormalization of the 2-Higgs-Doublet Model (2HDM) Higgs sector launched in a previous contribution with the investigation of the renormalization of the mixing angles $\alpha$ and $\beta$. Here, we treat the renormalization of the mass parameter $m_{12}^2$ that softly breaks the $\mathbb{Z}_2$ symmetry of the 2HDM Higgs sector. We investigate the impact of two different renormalization schemes on the sample Higgs-to-Higgs decay $H\to hh$. This decay also allows us to analyze the renormalization of the mixing angles and to confirm the properties extracted before in other Higgs decays. In conclusion we find that a gauge-independent, process-independent and numerically stable renormalization of the 2HDM Higgs sector is given by the application of the tadpole-pinched scheme for the mixing angles $\alpha$ and $\beta$ and by the use of the $\overline{MS}$ scheme for $m_{12}^2$.