Self-interactions of the lightest minimal supersymmetric standard model Higgs boson in the large pseudoscalar-mass limit

We investigate the decoupling properties of the Higgs-sector-induced one-loop corrections in the lightest Higgs-boson self-couplings, in the framework of the minimal supersymmetric standard model (MSSM). The renormalized n-point vertex functions with external Higgs particles in the $\mathrm{MSSM}$ and in the $\mathrm{SM}$ are derived to the one-loop level and compared in the $M_{A^0}\gg M_Z$ limit. The computation has been done in a general $R_{\xi }$ gauge and the on-shell renormalization scheme is chosen. By a comparison of the renormalized lightest Higgs-boson $h^0$ vertex functions with respect to the corresponding $\mathrm{SM}$ ones, we find that the differences between the predictions of both models are summarized in the lightest Higgs-boson mass correction $\Delta M_{h^0}.$ Consequently, the radiative corrections are absorbed in the Higgs-boson mass, and the trilinear and quartic $h^0$ self-couplings acquire the same structure as the couplings of the $\mathrm{SM}$ Higgs boson. Therefore, decoupling of the heavy $\mathrm{MSSM}$ Higgs bosons occurs and the MSSM $h^0$ self-interactions converge to the $\mathrm{SM}$ ones in the $M_{A^0}\gg M_Z$ limit.