Non-Abelian Debye screening. II. The singlet potential

The problems encountered in an earlier attempt to compute the non-Abelian Debye screening mass are rectified by considering the correlation of the eigenvalues of the untraced Polyakov loop. This gauge-invariant function is free from color averaging and is shown to yield the singlet potential of a static quark-antiquark pair at finite temperature. A perturbative computation requires that the electrostatic potential $A_4$ be endowed with a gauge-symmetry-breaking vacuum expectation value, the occurrence of which would explain the breakdown of perturbation theory encountered in the earlier calculation. While the symmetry breakdown cannot reliably be seen perturbatively, its effects on perturbative calculations can be assessed. It is found that most perturbative results, even the supposedly well-established low-order ones, would be affected. This would take the study of the quark-gluon plasma well out of the reach of perturbation theory and make nonperturbative techniques indispensable even at very high temperatures.