Towards softer scales in hot QCD

An effective theory for the soft field modes in hot QCD has been obtained recently by integrating out the field modes of momenta of order T and gT . The mean hard particle distribution obeys a transport equation with a collision term. The scale that comes out for the soft field is gT ln 1/g . Explicit solutions have been written for the linearized mean field distribution and for the polarization tensor. The n-gluon soft amplitudes are shown to be similar to the hard thermal loop ones as they are effectively one-loop diagrams. We constrain the three-gluon soft vertex to obey Ward identities. Then we compute the one-loop contribution to the gluon self-energy when the loop momentum is of order gT ln 1/g with effective vertices and propagators. It allows to identify a new collision term which should be included in the transport equation in order to integrate out the momenta of order gT ln 1/g and to be able to reach an effective theory for the soft field modes with momenta gT . ∗Preprint INLN 2000/14