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 $\overline{\mathrm{MS}}$ to the $\overline{\mathrm{DR}}$ scheme is properly taken into account. We find that the three-loop effects are comparable to the experimental uncertainty for ${\alpha }_s$.

Submitted for the SUSY07 proceedings, 4 pages, 2 figures