The Five-loop Beta Function for a General Gauge Group

T Luthe,A Maier,Y Schröder,P Marquard

doi:10.5506/aphyspolb.48.2331

Abstract

We present results for the gluon field anomalous dimension in perturbative QCD and derive the corresponding Beta function at five-loop order. All given results are valid for a general gauge group.

Highlights

We present results for the gluon field anomalous dimension in perturbative Quantum Chromodynamics (QCD) and derive the corresponding Beta function at five-loop order
In modern high-energy physics experiments, in order to closely scrutinize our established particle physics models such as the Standard Model (SM), it is important to push the precision of theoretical predictions that follow from these models to the highest possible level
We present our results for the gluon field anomalous dimension obtained in [18], which together with the results obtained in [17] allows for the extraction of the Beta function [18]

Summary

Introduction

In modern high-energy physics experiments, in order to closely scrutinize (and eventually go beyond) our established particle physics models such as the Standard Model (SM), it is important to push the precision of theoretical predictions that follow from these models to the highest possible level. Perhaps the second most important representative of this set is the (gauge-invariant) renormalization constant for the quark mass, needed for a precise evolution of measured low-energy quark masses to current and future high-energy collider experiments It has been known at two [20] and three loops [21, 22] for a long time already; at four loops, complete results for SU(N ) and QED as well as general Lie groups are available [23, 24]; at five loops, mass renormalization is known for SU(3) as well as general Lie groups [16, 25, 26]. We present our results for the five-loop gluon field anomalous dimension (in the Feynman gauge), from which we extract the (gauge-invariant) Beta function.

Renormalization constants and anomalous dimensions

Results

Conclusions