Running of $\alpha_s$ and $m_b$ in the MSSM

TL;DR

This paper presents a precise analysis of the running of the strong coupling constant and bottom quark mass within the MSSM, incorporating high-order loop calculations to match experimental accuracy.

Contribution

It provides a comprehensive three-loop evolution of $oldsymbol{oldsymbol{oldsymbol{oldsymbol{ ext{alpha}}}_s}}$ and a four-loop evaluation of $oldsymbol{oldsymbol{oldsymbol{oldsymbol{m_b}}}}$ at relevant scales, including scheme transitions.

Findings

Three-loop effects are comparable to experimental uncertainties.

Consistent evolution of $oldsymbol{oldsymbol{oldsymbol{oldsymbol{ ext{alpha}}}_s}}$ from $M_Z$ to GUT scale.

Precise bottom quark mass evaluation at electroweak/SUSY scale.

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 $m_b$.