The decayh0→A0A0in the minimal supersymmetric model

The decay $h^0\to A^0{A}^0$ (where $h^0$ and $A^0$ are the lightest $\mathrm{CP}$-even and $\mathrm{CP}$-odd Higgs bosons of a two-Higgs-doublet model) is kinematically forbidden at the tree level in the minimal supersymmetric model. However, if radiative corrections are included, the mass of $h^0$ can be larger than twice the mass of $A^0$ over part of the supersymmetric parameter space. Moreover, in this parameter regime, $h^0$ must be lighter than the $Z$. We compute the radiatively corrected width for $h^0\to A^0{A}^0$ to leading-logarithmic accuracy, and verify that this decay can be the dominant $h^0$ decay mode. Thus, in searches for $e^{+}{e}^{-}\to h^0{A}^0$ at the CERN $e^{+}{e}^{-}$ colliders LEP and LEP II, one must search for events with $A^0{A}^0{A}^0$ final states in order to set unambiguous limits for the $A^0$ mass.