Chromostatics of two-quark systems

We study an estimate for the mean-field potential between two heavy quarks ($\mathrm{qq}$) using Adler's chromostatics. To do so we work out the pseudocolor charge algebra for the $\mathrm{qq}$ system in $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ of color, which has not been correctly presented previously. Using the leading-logarithm, renormalization-group-improved Euclidean action for the gluon fields, we find that the mean-field potential depends crucially on the algebraic properties of the sources, and that while the quark-antiquark ($q\overline{q}$) system possesses an at-least-linear potential, as Adler showed, the $\mathrm{qq}$ system has infinite energy, and hence is decoupled from the physical spectrum. The physical states exhibit color screening.