Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM

Results are presented for the momentum-dependent two-loop contributions of to the masses and mixing effects in the Higgs sector of the MSSM. They are obtained in the Feynman-diagrammatic approach using a mixed on-shell/ renormalization that can directly be matched onto the higher-order corrections included in the code FeynHiggs. The new two-loop diagrams are evaluated with the program SecDec. The combination of the new momentum-dependent two-loop contribution with the existing one- and two-loop corrections in the on-shell/ scheme leads to an improved prediction of the light MSSM Higgs boson mass and a correspondingly reduced theoretical uncertainty. We find that the corresponding shifts in the lightest Higgs-boson mass are below in all scenarios considered, but they can extend up to the level of the current experimental uncertainty. The results are included in the code FeynHiggs.