Schwinger mechanism in QCD

TL;DR

This paper investigates the nonperturbative formation of bound states in QCD that enable the Schwinger mechanism, leading to a gauge-invariant generation of a gluon mass through solving a Bethe-Salpeter equation.

Contribution

It derives and numerically solves an approximate Bethe-Salpeter equation for bound states responsible for gluon mass generation in QCD, providing evidence for their formation.

Findings

Non-trivial solutions to the Bethe-Salpeter equation were found.

The results support the dynamical formation of bound states in QCD.

This work advances understanding of gluon mass generation mechanisms.

Abstract

The generation of a momentum-dependent gluon mass proceeds through a sophisticated implementation, at the level of the Schwinger-Dyson equation for the gluon propagator, of the Schwinger mechanism, whose central dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. In addition to triggering the aforementioned mechanism, these excitations introduce poles in the various off-shell Green's functions of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators, acting effectively as composite Nambu-Goldstone bosons. In this work we focus on the dynamics leading to the actual formation of such bound states. Specifically, we derive and solve numerically an approximate version of the homogeneous Bethe-Salpeter equation governing the wave function of this special bound state. It is found that this integral equation admits physically meaningful non-trivial solutions, indicating that the QCD dynamics produce one of the crucial ingredients required for the gauge-invariant generation of a gluon mass.