Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM

Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, M-h, at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to M-h (Borowka et al., Eur Phys J C 74(8): 2994, 2014; Degrassi et al., Eur Phys J C 75(2): 61, 2015), using a hybrid on-shell-(DR) over bar scheme, with apparently different results. We show that the differences can be traced back to a different renormalization of the top-quark mass, and that the claim in Ref. Degrassi et al. (Eur Phys J C 75(2): 61, 2015) of an inconsistency in Ref. Borowka et al. (Eur Phys J C 74(8): 2994, 2014) is incorrect. We furthermore compare consistently the results for M-h obtained with the top-quark mass renormalized on-shell and (DR) over bar. The latter calculation has been added to the FeynHiggs package and can be used to estimate missing higher-order corrections beyond the two-loop level.