The dynamical equation of the effective gluon mass

TL;DR

This paper derives an integral equation describing how the effective gluon mass varies with momentum in Landau gauge, ensuring gauge invariance through a nonperturbative vertex, and confirms its consistency with lattice data.

Contribution

It introduces a novel integral equation for the gluon mass's momentum dependence, based on a gauge-invariant framework involving a nonperturbative vertex, and compares results with lattice data.

Findings

The gluon mass is a non-monotonic function of momentum.

The derived mass equation aligns with lattice data for SU(2) and SU(3).

The approach enforces gauge invariance via a longitudinally coupled vertex.

Abstract

In this article we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding "one-loop dressed" Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rather stringent constraint on the derivative of the gluonic dressing function, which is comfortably satisfied by the large-volume lattice data for the gluon propagator, both for SU(2) and SU(3). The numerical treatment of the mass equation, under some simplifying assumptions, is presented for the aforementioned gauge groups, giving rise to a gluon mass that is a non-monotonic function of the momentum. Various theoretical improvements and possible future directions are briefly discussed.