Gluon mass scale through nonlinearities and vertex interplay

TL;DR

This paper introduces a new method for analyzing the gluon gap equation that accounts for its nonlinear structure, enabling a unique determination of the gluon mass scale consistent with lattice data.

Contribution

It develops a systematic iterative approach to approximate the gluon kinetic term and renormalization, improving upon previous linearized treatments for more accurate gluon mass predictions.

Findings

Achieves positive, monotonically decreasing gluon masses.

Matches lattice simulation data for gluon propagators.

Reveals the impact of vertex interplay on gluon mass behavior.

Abstract

We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial {\it Ans\"atze}, which are subsequently improved by means of a systematic iterative procedure. The multiplicative renormalization of the central equation is carried out following an approximate method, which is extensively employed in the studies of the standard quark gap equation. This approach amounts to the effective substitution of the vertex renormalization constants by kinematically simplified form factors of the three- and four-gluon vertices. The resulting numerical interplay, exemplified by the infrared suppression of the three-gluon vertex and the mild enhancement of the four-gluon vertex, is instrumental for obtaining positive-definite and monotonically decreasing running gluon masses. The resulting gluon propagators, put together from the gluon masses and kinetic terms obtained with this method, match rather accurately the data obtained from large-volume lattice simulations.