Search for Higgs bosons of minimal supersymmetry: Impact of supersymmetric decay modes

We investigate the prospects for the detectability of the Higgs bosons of the minimal supersymmetric model (MSSM) at future colliders. First we delineate regions of MSSM parameter space where the various Higgs bosons may be observable at the CERN $e^{+}{e}^{-}$ collider LEP 200 or hadron supercolliders, assuming (as usual) that Higgs-boson decay modes to supersymmetric particles are not allowed. We find that, even with optimistic assumptions of detector capabilities, there exist regions of parameter space where none of the Higgs bosons are visible. Next, we show that there are substantial regions of parameter space where rates for Higgs-boson decays to supersymmetric particles are large, and even dominant. These decays reduce the rates for conventional Higgs-boson signatures, thus making conventional detection of Higgs bosons even more difficult. However, a number of new, promising modes for Higgs-boson detection have opened up. These include a "gold-plated" Higgs scalar or pseudoscalar decay to four leptons plus missing energy which may make possible a precise mass measurement of the lightest and second lightest neutralino. Furthermore, rare decays of the top quark into a $b$ quark plus three leptons may be visible, and signal charged-Higgs-boson decays to a chargino plus neutralino.