Massless bound-state excitations and the Schwinger mechanism in QCD

TL;DR

This paper investigates how massless bound-state excitations contribute to the Schwinger mechanism, leading to an effective gluon mass in QCD, by analyzing the three-gluon vertex, Bethe-Salpeter equation, and their implications.

Contribution

It provides a detailed analytical and numerical study showing the formation of massless bound states in QCD and their role in generating a dynamical gluon mass.

Findings

Non-trivial solutions to the Bethe-Salpeter equation support bound-state formation.

Relations between bound-states and gluon mass are derived from Slavnov-Taylor identities.

The momentum dependence of the gluon mass is determined from the bound-state dynamics.

Abstract

The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic building blocks of these bound-states and the gluon mass are then obtained from the Slavnov-Taylor identities and the Schwinger-Dyson equation governing the gluon propagator. The homogeneous Bethe-Salpeter equation determining the wave-function of the aforementioned bound state is then derived, under certain simplifying assumptions. It is then shown, through a detailed analytical and numerical study, that this equation admits non-trivial solutions, indicating that the QCD dynamics support indeed the formation of such massless bound states. These solutions are subsequently used, in conjunction with the aforementioned relations, to determine the momentum-dependence of the dynamical gluon mass. Finally, further possibilities and open questions are briefly discussed.