Momentum Dependent Two-Loop Corrections to the Neutral Higgs Boson Masses in the MSSM

The momentum dependent two-loop contributions of the order $\mathcal{O}$($\alpha_s \alpha_t$) to the masses in the Higgs-boson sector of the MSSM are computed. Adopting the Feynman-diagrammatic approach and using a mixed on-shell/$\overline{DR}$ renormalization scheme, the new corrections can directly be matched onto the higher-order corrections included in the code FeynHiggs. Two-loop diagrams involving several mass scales are evaluated with the program SecDec. The combination of the new momentum dependent two-loop contribution with the existing one- and two-loop corrections leads to an improved prediction of the light MSSM Higgs-boson mass with reduced theoretical uncertainty. The resulting shifts in the lightest Higgs-boson mass $M_h$ can extend up to the level of the current experimental uncertainty of about 500 MeV in the scenario considered in these proceedings.