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 g²T ln 1/g. n-gluon soft amplitudes are shown to be a sum of tree diagrams and obey tree-like Ward identities. These effective amplitudes are used to compute the one-soft-loop contribution to the gluon self-energy when the loop momentum is of order g²T ln 1/g. It allows one to identify a new collision term which, when inserted into the transport equation, takes into account collisions with gluon exchange ~g²T ln 1/g. The infrared behavior of the collision term exhibits a significant change.