A perturbative framework to probe infrared sensitivity in non-Abelian gauge theories

TL;DR

This paper introduces a perturbative framework using a Higgs mechanism to study infrared sensitivity in non-Abelian gauge theories, aiming to better understand non-perturbative effects in QCD processes.

Contribution

It develops a novel approach by promoting the gluon mass to a parameter in a gauge theory with spontaneous symmetry breaking, enabling infrared sensitivity analysis at two-loop order.

Findings

Computed $ ext{O}(m_g)$ corrections to heavy quark mass relations

Established a two-loop framework for infrared sensitivity analysis

Proposed a new laboratory for collider observable studies

Abstract

Understanding the infrared sensitivity of perturbative predictions in QCD is important for assessing the magnitude of possible non-perturbative power corrections to processes with large momentum transfer. In renormalon models, this sensitivity can be related to computable dependences of perturbative quantities on a small gluon mass. However, this procedure cannot be applied to collider processes with gluons at the Born level. To address this problem, we promote the gluon mass to a parameter of a consistent non-Abelian quantum field theory where the gauge symmetry is spontaneously broken through the Higgs mechanism. Working in the limit in which the gluon mass $m_\mathrm{g}$ is the smallest dimensionful parameter, we compute through two loops the $\mathcal{O}(m_\mathrm{g})$ contributions to the relation between the pole and $\overline{\rm MS}$ masses of a heavy quark and to the relation between corresponding field counterterms. We expect that the proposed framework will provide a useful laboratory for probing linear infrared sensitivity of collider observables in QCD.