Exploring smoking-gun signals of the Schwinger mechanism in QCD

TL;DR

This paper investigates the Schwinger mechanism in QCD, identifying signals that suggest gluons acquire an effective mass through bound-state poles, with results validated by lattice simulations and Bethe-Salpeter equations.

Contribution

It provides a detailed derivation of the non-Abelian Ward identity related to the Schwinger mechanism and introduces a novel smoking-gun signal for gluon mass generation.

Findings

Excellent agreement between Bethe-Salpeter and Ward identity methods

Statistical significance of the Schwinger mechanism signal is three standard deviations

Validation of the Schwinger mechanism's role in gluon mass generation

Abstract

In QCD, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be three standard deviations.