Gluon plasma frequency - the next-to-leading order term

The longitudinal-electric oscillations of the hot gluon system are studied beyond the well known leading order term at high temperature T and small coupling g. The coefficient #eta# in #omega#"2 = m"2(1 + #eta#g#sq root#N) is calculated, where #omega# triple bond #omega#(#vector#q = 0) is the long-wavelength limit of the frequency spectrum, N the number or colours and m"2 = g"2NT"2/9. In the course of this, for the real part of the gluon self-energy, the Braaten-Pisarski resummation programme is found to work well in all details. The coeffcient #eta# is explicitly seen to be gauge independent within the class of covariant gauges. Infrared singularities cancel as well as collinear singularities in the two-loop diagrams with both inner momenta hard. However, as it turns out, none of these two-loop contributions reaches the relative order O(g) under study. The minus sign in our numerical result #eta# = -.53 is in accord with the intuitive picture that the studied mode might soften with increasing coupling (lower temperature) until a phase transition is reached at zero-frequency. The minus sign thus exhibits the 'glue' effect for the first time in a dynamical quantity of hot QCD. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(93-080) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman