The Structure of Renormalization in Gauge Theories at High Loop Level

Mason, Robert ORCID: 0000-0002-2024-0381 (2024) The Structure of Renormalization in Gauge Theories at High Loop Level. PhD thesis, University of Liverpool.

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Abstract

The investigation of the properties of perturbative Quantum Chromodynamics (pQCD) has typically been advanced in the first place in computationally simple schemes such as the modified minimal subtraction scheme. While we expect the underlying structure of pQCD to be renormalization group and gauge invariant, when taken to a finite order in perturbation theory, truncation will introduce differences above the current order in the small coupling constant. In this way, each scheme one renormalizes the theory in, or each gauge fixing term one uses, can only provide an incomplete viewpoint on the underlying dynamics. When multiple viewpoints are taken together, more information can be obtained. This thesis utilises a variety of schemes and gauge-fixing terms to investigate different aspects of pQCD, and further argues for the application of this approach to other problems. In particular, we investigate the use of scheme difference as a measure of theory uncertainty for estimates of formal parameters within a theory laboratory. For this we focus particularly on the R ratio and the Bjorken sum rule to the four loop level and on the symmetric momentum subtraction schemes. We also probe the structure of fixed points in the conformal window for a two coupling theory, where the gauge parameter acts as the second coupling. In addition to the canonical linear covariant gauges, we consider both the Curci-Ferrari and the Maximal Abelian gauges. We show there is a consistent infra-red stable fixed point across the different schemes and across these gauge-fixing terms. Additionally, we probe the Crewther relation for gauge-parameter dependent schemes. This examination suggests a modification is needed for the relation to be extended to these schemes. As a catalyst to investigating these problems we find the quark, gluon and ghost field anomalous dimensions as well as the quark mass anomalous dimension, for the minimal momentum subtraction scheme to the five loop level.

Item Type:	Thesis (PhD)
Additional Information:	Permanent email address robert.mason343@gmail.com
Divisions:	Faculty of Science and Engineering Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	21 Aug 2025 08:30
Last Modified:	21 Aug 2025 08:30
DOI:	10.17638/03190664
Supervisors:	Gracey, John
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3190664