Non-Abelian Debye screening: The color-averaged potential

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Abstract
The non-Abelian analogue of the Debye screening effect is investigated by means of perturbative calculations in high-temperature Yang-Mills theory. It is recalled that the gluon vacuum-polarization tensor, which is gauge dependent, does not directly yield the Debye screening mass beyond leading order. Instead, the correlation function of two Polyakov loops, representing the color-averaged potential energy of a static quark-antiquark pair, is examined as a possible means of defining a gauge-invariant Debye mass. Though apparently satisfactory to leading order, an examination of higher orders reveals two problems: (i) an unexpected breakdown of perturbation theory in the electrostatic sector and (ii) the emergence of the magnetostatic mass gap as the dominant decay mass of this correlation. These results might be the signal for a breakdown of gauge symmetry in the plasma phase and indicate the need for examining a gauge-invariant electrostatic correlation function that is free from color averaging.