Towards softer scales in hot QCD - art. no. 045017

An effective theory fur the soft held modes in hot QCD has been obtained re cently by integrating out the field modes of moments of order T and gT. The mean hard particle distribution obeys a transport equation with a collisio n term. The scale that comes out for the soft field is g(2)T In 1/g. n-gluo n 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-so ft-loop contribution to the gluon self-energy when the loop momentum is of order g(2)T ln 1/g. It allows one to identify a new collision term which, w hen inserted into the transport equation, takes into account collisions wit h gluon exchange similar tog(2)T In 1/g. The infrared behavior of the colli sion term exhibits a significant change.