The Higgs sector of the complex minimal supersymmetric standard model

Complete one-loop results for the decay widths of neutral Higgs bosons ( h(_a)) into lighter neutral Higgs bosons ( h(_b), h(_c). ) arc presented for the MSSM with complex parameters. The results are obtained in the Feynman-diagrammatic approach, taking into account the full dependence on the spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. The genuine triple-Higgs vertex contributions are supplemented with two-loop propagator-type corrections, yielding the currently most precise prediction for this class of processes. The genuine vertex corrections turn out to be very important, yielding a large increase of the decay width compared to a prediction based on the tree-level vertex. One-loop propagator-type mixing between neutral Higgs bosons and Goldstone and Z bosons is also consistently taken into account. Complete one-loop results for the decay of a neutral Higgs boson into fermions are also presented, which include the full dependence on complex phases. The new results are used to analyse the impact of the experimental limits from the LEP Higgs searches on the parameter space with a very light MSSM Higgs boson. It is found that a significant part of the parameter space of the CPX benchmark scenario exists where channels involving the decay h(_2)→ h(_1) h(_1) have the highest search sensitivity, and the existence of an unexcluded region with M(_h1) ~ 45 GeV is confirmed. The public code Higgs Bounds is also presented, which can be used in conjunction with models with an arbitrary number of neutral Higgs bosons to determine whether parameter points have been excluded at the 95% CL by the LEP and Tevatron Higgs searches