On the gluon plasmon self-energy at O(g)

The next-to-leading order contribution δβμν (ω,, q) to the polarization function of the hot gluon system is analysed at nonzero wave vectors q. Using Braaten-Pisarski resummation and general covariant gauges, δβμν is found to be gauge-fixing independent and transverse on the longitudinal mass-shell. The real part of the longitudinal component δβl is UV and IR stable (for real q). At imaginary q it is IR singular, and at the point ω = 0, q2 = −3m2 it coincides with the result of Rebhan for next-to-leading order Debye screening. When q approaches the lightcone, δβl diverges like 1ω2−q2, reflecting the breakdown of the Braaten-Pisarski decomposition scheme in this limit.