The SUSY-QCD beta function to three loops

TL;DR

This paper computes the three-loop beta functions in SUSY-QCD using dimensional reduction, confirming their consistency with gauge invariance and supersymmetry, which is crucial for precise theoretical predictions.

Contribution

It provides the first three-loop calculations of renormalization constants and beta functions in softly broken SUSY-QCD, verifying their consistency with established gauge beta functions.

Findings

Beta functions match the known gauge beta function at three loops

Confirmed the consistency of DRED with SUSY and gauge invariance

Provided explicit three-loop renormalization constants for various fields

Abstract

A number of DR-bar renormalization constants in softly broken SUSY-QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and epsilon-scalars, and the renormalization constants for the quark and gluino mass as well as for all cubic vertices. The latter allow us to derive the corresponding beta functions through three loops, all of which we find to be identical to the expression for the gauge beta function obtained by Jack, Jones, and North [Jack:1996vg] (see also Ref. [Pickering:2001aq]). This explicitely demonstrates the consistency of DRED with SUSY and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories.