Neutralino decays in the complex MSSM at one loop: A comparison of on-shell renormalization schemes

We evaluate two-body decay modes of neutralinos in the minimal supersymmetric Standard Model with complex parameters. Assuming heavy scalar quarks, we take into account all two-body decay channels involving charginos, neutralinos, (scalar) leptons, Higgs bosons and Standard Model gauge bosons. The evaluation of the decay widths is based on a full one-loop calculation including hard and soft QED radiation. Of particular phenomenological interest are decays involving the lightest supersymmetric particle (LSP), i.e., the lightest neutralino, or a neutral or charged Higgs boson. For the chargino/neutralino sector we employ two different renormalization schemes, which differ in the treatment of the complex phases. In the numerical analysis, we concentrate on the decay of the heaviest neutralino and show the results in the two different schemes. The higher-order corrections of the heaviest neutralino decay widths involving the LSP can easily reach a level of about 10-15%, while the corrections to the decays to Higgs bosons can be up to 20-30%, translating into corrections of similar size in the respective branching ratios. The difference between the two schemes, indicating the size of unknown two-loop corrections, is less than O(0.1%). These corrections are important for the correct interpretation of LSP and Higgs production at the LHC and at a future linear e super(+)e super(-) collider. The results will be implemented into the Fortran code FeynHiggs.