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

Duarte Fontes, Dennis Horstmann, Kirill Melnikov, Davide Maria Tagliabue

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.

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

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 is the smallest dimensionful parameter, we compute through two loops the contributions to the relation between the pole and 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.
Paper Structure (13 sections, 59 equations, 4 figures)

This paper contains 13 sections, 59 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The model
  3. The Lagrangian of the model and its particle content
  4. Renormalization
  5. Calculation
  6. Preliminaries
  7. Master integrals
  8. Relation between the pole and the $\overline{\rm MS}$ top-quark masses
  9. Relation between the top-quark field counterterms in the on-shell subtraction and $\overline{\rm MS}$ schemes
  10. Conclusions
  11. Feynman rules
  12. On-shell scheme conditions for 2-loop fermion mass and field counterterms
  13. Expressions for the two-loop counterterms

Figures (4)

  • Figure 1: Two-loop Feynman diagrams for the top-quark self-energy.
  • Figure 2: Feynman diagrams for the top-quark self-energy with one-loop counterterm insertions.
  • Figure 3: One-loop vacuum polarization.
  • Figure 4: Details of the subsets of diagrams appearing in the vacuum polarization, cf. Figure \ref{['fig:VP-global']}.