On the Gluon Plasmon Self-Energy at O(g)

Abstract

The next-to-leading order contribution \d\P\omn (\o ,\vc q ) to the polarization function of the hot gluon system is analysed at non-zero wave vectors \vc q \,. Using Braaten-Pisarski resummation and general covariant gauges, \d\P\omn is found to be gauge-fixing independent and transverse on the longitudinal mass-shell. The real part of the longitudinal component \d\P_\ell is UV and IR stable (for real $q$). At imaginary $q$ it is IR singular, and at the point \o=0, $q^2=-3m^2$ it coincides with the result of Rebhan for next-to-leading order Debye screening. When $q$ approaches the lightcone, \d\P_\ell diverges like 1 / \wu {\o^2 - q^2} , reflecting the breakdown of the Braaten-Pisarski decomposition scheme in this limit.Comment: 14 pages, LaTe