The Higgs mass in the CP violating MSSM, NMSSM, and beyond

We discuss the automatised calculation of the Higgs mass in renormalisable supersymmetric models with complex parameters at the two-loop level. Our setup is based on the public codes SARAH and SPheno, which can now compute the two-loop corrections to masses of all neutral scalars in such theories. The generic ansatz for these calculations and the handling of the ‘Goldstone Boson catastrophe’ is described. It is shown that we find perfect agreement with other existing two-loop calculations performed in the $\overline{\mathrm {DR}}$ scheme. We also use the functionality to derive results for the MSSM and NMSSM not available before: the Higgs mass in the constrained version of the complex MSSM and the impact of CP phases in the two-loop corrections beyond $O(\alpha _s \alpha _t)$ for the scale-invariant NMSSM are briefly analysed.