On mass generation in Landau-gauge Yang-Mills theory

TL;DR

This paper investigates the origin of the mass gap in Landau-gauge Yang-Mills theory by solving Dyson-Schwinger equations, exploring the role of longitudinal poles and gauge invariance, and proposing mechanisms to reconcile different solutions.

Contribution

It provides a detailed analysis of the mass gap generation mechanism in Landau-gauge Yang-Mills theory using coupled Dyson-Schwinger equations and discusses conditions for gauge invariance preservation.

Findings

Mass gap linked to longitudinal projection of gluon self-energy.

Massless pole found in ghost-gluon vertex for scaling solution.

Proposed mechanism to reconcile scaling and decoupling solutions.

Abstract

A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborate the findings of earlier works, namely that the mass gap generation is tied to the longitudinal projection of the gluon self-energy, which acts as an effective mass term in the equations. Because an explicit mass term is in conflict with gauge invariance, this leaves two possible scenarios: If it is viewed as an artifact, only the scaling solution survives; if it is dynamical, gauge invariance can only be preserved if there are longitudinal massless poles in either of the vertices. We find that there is indeed a massless pole in the ghost-gluon vertex, however in our approximation with the assumption of complete infrared dominance of the ghost this pole is only present for the scaling solution. We also put forward a possible mechanism that may reconcile the scaling solution, with an infrared dominance of the ghost, with the decoupling solutions based on longitudinal poles in the three-gluon vertex as seen in the PT-BFM scheme.