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

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.