Running of ${\alpha }_s$ and $m_b$ in the MSSM

Abstract

A consistent 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. The two-loop transition from the MS- to the DR-scheme is properly taken into account. In the second part of the paper, the bottom quark mass in the DR-scheme at the electroweak/SUSY scale is evaluated with four-loop accuracy. We find that the three-loop effects are comparable to the experimental uncertainty both for ${\alpha }_s$ and $m_b$.

Comments: 19 pages, 4 figures,references added