Precise predictions for ha→hbhc decays in the complex MSSM

Complete one-loop results for the decay widths of neutral Higgs bosons (ha) into lighter neutral Higgs bosons (hb,hc) are 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. 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 h2→h1h1 have the highest search sensitivity, and the existence of an unexcluded region with Mh1≈45GeV is confirmed.