Understand
We investigate the possible size of two-loop radiative corrections to the Higgs trilinear coupling $\lambda_{hhh}$ in two types of models with extended Higgs sectors, namely in a Two-Higgs-Doublet Model (2HDM) and in the Inert Doublet Model (IDM).
- We calculate the leading contributions at two loops arising from the additional (heavy) scalars and the top quark of these theories in the effective-potential approximation.
- We include all necessary conversion shifts in order to obtain expressions both in the $\overline{\text{MS}}$ and on-shell renormalisation schemes, and in particular, we devise a consistent "on-shell" prescription for the soft-breaking mass of the 2HDM at the two-loop level.
- We illustrate our analytical results with numerical studies of simple aligned scenarios and show that the two-loop corrections to $\lambda_{hhh}$ remain smaller than their one-loop counterparts, with a typical size being 10-20% of the one-loop corrections, at least while perturbative unitarity conditions are fulfilled.