Running of $\alpha_s$ in the MSSM with three-loop accuracy

Abstract

The evolution of the strong coupling constant $\alpha_s$ from $M_Z$ to the GUT scale is presented, involving three-loop running and two-loop decoupling. Accordingly, the two-loop transition from the $\bar{\rm MS}$ to the $\bar{\rm DR}$ scheme is properly taken into account. We find that the three-loop effects are comparable to the experimental uncertainty for $\alpha_s$.