Nonperturbative four-gluon vertex in soft kinematics

TL;DR

This paper investigates the nonperturbative behavior of the four-gluon vertex in specific kinematics using Schwinger-Dyson equations and lattice simulations, revealing infrared suppression and consistent effective charge results.

Contribution

It introduces a combined nonperturbative analysis of the four-gluon vertex using Schwinger-Dyson equations and lattice data, confirming the planar degeneracy hypothesis.

Findings

Significant infrared suppression of the form factor.

Excellent agreement between Schwinger-Dyson and lattice results.

Consistent effective charge calculations across methods.

Abstract

We present a nonperturbative study of the form factor associated with the projection of the full four-gluon vertex on its classical tensor, for a set of kinematics with one vanishing and three arbitrary external momenta. The treatment is based on the Schwinger-Dyson equation governing this vertex, and a large-volume lattice simulation, involving ten thousand gauge field configurations. The key hypothesis employed in both approaches is the ``planar degeneracy'', which classifies diverse configurations by means of a single variable, thus enabling their meaningful ``averaging''. The results of both approaches show notable agreement, revealing a considerable suppression of the averaged form factor in the infrared. The deviations from the exact planar degeneracy are discussed in detail, and a supplementary variable is used to achieve a more accurate description. The effective charge defined through this special form factor is computed within both approaches, and the results obtained are in excellent agreement.