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Higher order corrections to Higgs boson decays in the MSSM with complex parameters

We discuss Higgs boson decays in the CP-violating MSSM, and examine their phenomenological impact using cross section limits from the LEP Higgs searches. This includes a discussion of the full 1-loop results for the partial decay widths of neutral Higgs bosons into lighter neutral Higgs bosons (h_a -> h_b h_c) and of neutral Higgs bosons into fermions (h_a -> f fbar). In calculating the genuine vertex corrections, we take into account the full spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. These genuine vertex corrections are supplemented with Higgs propagator corrections incorporating the full one-loop and the dominant two-loop contributions, and we illustrate a method of consistently treating diagrams involving mixing with Goldstone and Z bosons. In particular, the genuine vertex corrections to the process h_a -> h_b h_c are found to be very large and, where this process is kinematically allowed, can have a significant effect on the regions of the CPX benchmark scenario which can be excluded by the results of the Higgs searches at LEP. However, there remains an unexcluded region of CPX parameter space at a lightest neutral Higgs boson mass of ~45 GeV. In the analysis, we pay particular attention to the conversion between parameters defined in different renormalisation schemes and are therefore able to make a comparison to the results found using renormalisation group improved/effective potential calculations.