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

TL;DR

This paper calculates the evolution of the strong coupling constant in the MSSM using three-loop accuracy, showing that higher-order effects are significant compared to experimental uncertainties.

Contribution

It provides a detailed three-loop level analysis of $eta$-functions and decoupling effects in the MSSM, improving precision in coupling constant evolution.

Findings

Three-loop effects are comparable to experimental uncertainties.

Proper two-loop scheme transition is incorporated.

Enhanced precision in $eta$-function calculations.

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 $\alpha_s$.