The effective gluon mass and its dynamical equation

TL;DR

This paper derives a nonperturbative equation governing the momentum evolution of the gluon mass in quantum chromodynamics, demonstrating that the mass is positive, decreasing, and consistent with theoretical expectations.

Contribution

It provides the first full derivation and numerical solution of the gluon mass evolution equation within the PT-BFM formalism, incorporating non-perturbative vertices and preserving gauge identities.

Findings

Gluon mass is positive and decreases monotonically with momentum.

The derived equation is solved numerically across all physical momenta.

Results align with theoretical and phenomenological expectations.

Abstract

We present the general derivation of the full nonperturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The gluon mass originates from the inclusion of longitudinally coupled vertices containing massless poles of non-perturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The equation is obtained within the PT-BFM formalism, where the corresponding Schwinger-Dyson equation involves a reduced number of fully dressed diagrams. The resulting homogeneous integral equation is solved numerically for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses, in agreement with a variety of less formal considerations.