Running of alpha(s) and m(b) in the MSSM
A consistent evolution of the strong coupling constant ${\ensuremath{\alpha}}_{s}$ from ${M}_{Z}$ to the grand unified theory (GUT) scale is presented, involving three-loop running and two-loop decoupling. The two-loop transition from the $\overline{\mathrm{MS}}$- to the $\overline{\mathrm{DR}}$-scheme is properly taken into account. In the second part of the paper, the bottom quark mass in the $\overline{\mathrm{DR}}$-scheme at the electroweak/supersymmetry (SUSY) scale is evaluated with four-loop accuracy. We find that the three-loop effects are comparable to the experimental uncertainty both for ${\ensuremath{\alpha}}_{s}$ and ${m}_{b}$.