Heavy SUSY Higgs Bosons at $e^+e^-$ Linear Colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future $e^+ e^-$ colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass $m_0$, gaugino mass $m_{1/2}$ and trilinear coupling $A$, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low $\tb$ solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high $\tb$ case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into $b$ and $\tau$ pairs. The main production mechanisms for the heavy Higgs particles are the associated $AH$ production and $H^+H^-$ pair production with cross sections of the order of a few fb.