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 MSSM and in the SM are derived to the one-loop level and compared in the M_A⁰MZ limit. The computation has been done in a general R_ξ gauge and the on-shell renormalization scheme is chosen. By a comparison of the renormalized lightest Higgs-boson h⁰ vertex functions with respect to the corresponding SM ones, we find that the differences between the predictions of both models are summarized in the lightest Higgs-boson mass correction ΔM_h⁰. Consequently, the radiative corrections are absorbed in the Higgs-boson mass, and the trilinear and quartic h⁰ self-couplings acquire the same structure as the couplings of the SM Higgs boson. Therefore, decoupling of the heavy MSSM Higgs bosons occurs and the MSSM h⁰ self-interactions converge to the SM ones in the M_A⁰MZ limit.