Confinement, the gluon propagator and the interquark potential for heavy mesons

TL;DR

This paper investigates the limitations of finite gluon propagators in modeling confinement in heavy mesons and proposes a nonperturbative coupling mechanism to achieve linear confinement consistent with QCD.

Contribution

It introduces a novel mechanism based on a singular nonperturbative coupling constant that yields a finite gluon propagator and reproduces confinement effects.

Findings

Finite propagators do not produce confinement in quenched QCD.

A singular nonperturbative coupling can generate linear confinement.

The mechanism can be adapted for screened potentials in unquenched QCD.

Abstract

The interquark static potential for heavy mesons described by a massive One Gluon Exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.