Ultrasoft amplitudes in hot QCD

By using the Boltzmann equation describing the relaxation of colour excitat ions in the QCD plasma, we obtain effective amplitudes for the ultrasoft co lour fields carrying momenta of order g(2)T. These amplitudes are of the sa me order in g as the hard thermal loops (HTL), which they generalize by inc luding the effects of the collisions among the hard particles. The ultrasof t amplitudes share many of the remarkable properties of the HTL's: they are gauge invariant, obey simple Ward identities, and, in the static limit, re duce to the usual Debye mass for the electric fields. However, unlike the H TL's, which correspond effectively to one-loop diagrams, the ultrasoft ampl itudes resum an infinite number of diagrams of the hare perturbation theory . By solving the linearized Boltzmann equation, we obtain a formula for the colour conductivity which accounts for the contributions of the hard and s oft modes beyond the leading logarithmic approximation. (C) 2000 Elsevier S cience B.V. All rights reserved.