Higgs mass prediction in the MSSM at three-loop level in a pure $\overline{\text{DR}}$ context

The impact of the three-loop effects of order $\alpha_t\alpha_s^2$ on the mass of the light CP-even Higgs boson in the MSSM is studied in a pure $\overline{\text{DR}}$ context. For this purpose, we implement the results of Kant et al. into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the SUSY scale $M_S$. Himalaya can be linked also to other two-loop $\overline{\text{DR}}$ codes, thus allowing for the elevation of these codes to the three-loop level.