High-Precision Predictions for the MSSM Higgs Sector at $O(\alpha_{b} \alpha_{s})$

We evaluate O(alpha_b alpha_s) corrections in the Higgs boson sector of the CP-conserving MSSM, generalising the known result in the literature to arbitrary values of tan beta. A detailed analysis of the renormalisation in the bottom/scalar bottom sector is performed. Concerning the lightest MSSM Higgs boson mass, we find relatively small corrections for positive mu, while for mu < 0 the genuine two-loop O(alpha_b alpha_s) corrections can amount up to 3 GeV. Different renormalisation schemes are applied and numerically compared. It is demonstrated that some care has to be taken in choosing an appropriate renormalisation prescription in order to avoid artificially large corrections. The residual dependence on the renormalisation scale is investigated, and the remaining theoretical uncertainties from unknown higher-order corrections in this sector are discussed for different regions of the MSSM parameter space.