Production of Supersymmetric Higgs Bosons at LEP x LHC

Within the Minimal Supersymmetric Standard Model (MSSM), we study the production of the neutral scalar and pseudoscalar as well as the charged Higgs bosons together with fermions or sfermions in deep inelastic $ep$ scattering at $\sqrt{s}=1.6$ TeV. We focus on the parameter space where a Higgs particle is likely to be invisible at LEP2 and LHC. Although we choose gaugino/higgsino mixing scenarios that maximize the corresponding production rates we find only for the production of the scalar Higgs bosons in the non-supersymmetric channels non-negligible cross sections of the order of $10^2$ fb.