Consistent on shell renormalisation of electroweakinos in the complex MSSM: LHC and LC predictions

We extend the formalism developed in Ref. [20] for the renormalisation of the chargino-neutralino sector to the most general case of the MSSM with complex parameters. We show that products of imaginary parts arising from MSSM parameters and from absorptive parts of loop integrals can already contribute to predictions for physical observables at the one-loop level, and demonstrate that the consistent treatment of such contributions gives rise to non-trivial structure, either in the field renormalisation constants or the corrections associated with the external legs of the considered diagrams. We furthermore point out that the phases of the parameters in the chargino-neutralino sector do not need to be renormalised at the one-loop level, and demonstrate that the appropriate choice for the mass parameters used as input for the on-shell conditions depends both on the process and the region of MSSM parameter space under consideration. As an application, we compute the complete one-loop results in the MSSM with complex parameters for the process h(a) to chi(i)+chi(j)- (Higgs-propagator corrections have been incorporated up to the two-loop level), which may be of interest for SUSY Higgs searches at the LHC, and for chargino pair-production at an e+e- Linear Collider, e+e- to chi(i)+chi(j)-. We investigate the dependence of the theoretical predictions on the phases of the MSSM parameters, analysing in particular the numerical relevance of the absorptive parts of loop integrals.