Measuring the Trilinear Couplings of MSSM Neutral Higgs Bosons at High-Energy $e^+ e^-$ Colliders

We present a detailed analysis of multiple production of the lightest CP-even Higgs boson (h) of the Minimal Supersymmetric Standard Model (MSSM) at high-energy e^+ e^- colliders. We consider the production of the heavier CP-even Higgs boson (H) via Higgs-strahlung e^+e^- \to ZH, in association with the CP-odd Higgs boson (A) in e^+e^- \to AH, or via the fusion mechanism e^+e^- resulting in a pair of lighter Higgs bosons (h) in the final state. These processes can enable one to measure the trilinear Higgs couplings \lambda_{Hhh} and \lambda_{hhh}, which can be used to theoretically reconstruct the Higgs potential. We delineate the regions of the MSSM parameter space in which these trilinear Higgs couplings could be measured at a future e^+ e^- collider. In our calculations, we include in detail the radiative corrections to the Higgs sector of the MSSM, especially the mixing in the squark sector.