Schwinger displacement of the quark-gluon vertex

TL;DR

This paper investigates how the Schwinger mechanism causes a displacement in the quark-gluon vertex's Ward identity in QCD with two light quarks, supported by lattice data and integral equation analysis.

Contribution

It demonstrates the presence of Schwinger mechanism-induced displacements in the quark-gluon vertex and connects theoretical predictions with lattice data in real-world QCD.

Findings

Displacement in the Ward identity of the quark-gluon vertex observed.

Massless poles in the vertex are characterized by coupled integral equations.

Lattice data deviations align with theoretical expectations of the residue.

Abstract

The action of the Schwinger mechanism in pure Yang-Mills theories endows gluons with an effective mass, and, at the same time, induces a measurable displacement to the Ward identity satisfied by the three-gluon vertex. In the present work we turn to Quantum Chromodynamics with two light quark flavors, and explore the appearance of this characteristic displacement at the level of the quark-gluon vertex. When the Schwinger mechanism is activated, this vertex acquires massless poles, whose momentum-dependent residues are determined by a set of coupled integral equations. The main effect of these residues is to displace the Ward identity obeyed by the pole-free part of the vertex, causing modifications to its form factors, and especially the one associated with the tree-level tensor. The comparison between the available lattice data for this form factor and the Ward identity prediction reveals a marked deviation, which is completely compatible with the theoretical expectation for the attendant residue. This analysis corroborates further the self-consistency of this mass-generating scenario in the general context of real-world strong interactions.