Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex

TL;DR

This paper investigates the coupled equations governing gluon mass generation in pure Yang-Mills theories, emphasizing the role of the three-gluon vertex and achieving a self-consistent solution aligned with lattice data.

Contribution

It introduces a joint treatment of the gluon propagator and bound-state formation equations, highlighting the importance of the three-gluon vertex's suppression for consistent solutions.

Findings

Converges to a single gauge coupling value close to lattice results.

Demonstrates the critical role of the three-gluon vertex suppression.

Provides a self-consistent framework for gluon mass generation.

Abstract

We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behaviour of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfillment depends crucially on the details of the three-gluon vertex, which contributes to both of them, but with different weight. In particular, the characteristic suppression of this vertex at intermediate and low energies enables the convergence of the iteration procedure to a single gauge coupling, whose value is reasonably close to that extracted from related lattice simulations.