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

Abstract

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

Comments: 14 pages, LaTeX