Yang-Mills Gauss law and the heavy quark binding energy in the presence of a dimension-2 gluon condensate

TL;DR

This paper investigates the heavy quark-antiquark binding energy in Yang-Mills theory, explicitly solving the constraint equations and relating the results to a dimension-2 gluon condensate, providing a new analytical approach to confinement.

Contribution

It introduces a first-order path integral formalism to explicitly solve the Yang-Mills constraint and links the quark binding energy to a dimension-2 gluon condensate.

Findings

Derived an asymptotic series solution for the constraint equation.

Predicted the QCD string tension in terms of the gluon condensate.

Connected the results to Operator Product Expansion (OPE) analyses.

Abstract

We study the binding energy of a heavy quark-antiquark ($q\bar{q}$) pair using the first-order path integral formalism. This makes the Yang-Mills constraint equation explicit, and highlights that it is valid without relying on a semiclassical approximation. A generalized gauge-covariant Coulomb gauge is chosen to allow for a decomposition of the chromoelectric field into a gauge-covariant generalization of transverse and longitudinal parts. This decomposition makes it clear that the $q\bar{q}$ binding energy is determined solely by the solution to the constraint equation. Assuming that the low-energy physics is dominated by the existence of a dimension-2 gluon condensate, we develop an asymptotic series solution to the constraint equation and thus to the $q\bar{q}$ binding energy. We predict a QCD string tension in terms of the condensate strength and quadratic Casimir eigenvalues, and relate our result to results coming from OPE analyses.