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

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The next-to-leading order contribution δβ μν ( 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, δβ μν is found to be gauge-fixing independent and transverse on the longitudinal mass-shell. The real part of the longitudinal component δβ l is UV and IR stable (for real q). At imaginary q it is IR singular, and at the point ω = 0, q 2 = −3 m 2 it coincides with the result of Rebhan for next-to-leading order Debye screening. When q approaches the lightcone, δβ l diverges like 1 ω 2−q 2 , reflecting the breakdown of the Braaten-Pisarski decomposition scheme in this limit.