A Ghost Story: Ghosts and Gluons in the IR regime of QCD

TL;DR

This paper investigates the deep infrared behavior of gluon and ghost propagators in QCD, combining analytical and numerical methods, and finds that the decoupling solution aligns with lattice QCD results.

Contribution

It introduces a combined analytical and numerical approach to study IR QCD Green functions and supports the decoupling solution as the physically relevant one.

Findings

Decoupling solution is favored by lattice QCD.

Derived a numerical method for solving GPDSE with lattice inputs.

Proved the bare ghost dressing function diverges at infinite cut-off.

Abstract

We discuss the different methods to obtain reliable informations about the deep infra-red behaviour of the gluon and ghost Green functions in QCD. We argue that a clever combination of analytical inputs and numerical ones is necessary. We illustrate this statement about the distinction between two classes of solutions of the ghost propagator Dyson-Schwinger equation (GPDSE). We conclude that the solution II ("decoupling") with a finite renormalised ghost dressing function at zero momentum is strongly favored by lattice QCD, We derive a method to solve numerically the GPDSE using lattice inputs concerning the gluon propagator. We derive an analytical small momentum expansion of the Ghost dressing function. We prove from the large cut-off behaviour of the ghost propagator renormalisation constant, $\widetilde Z_3$, that the bare ghost dressing function is infinite at the infinite cut-off limit.