Hard thermal loops near the light-cone

In hot gauge theories, perturbation theory at the scale of the Debye screening mass requires the resummation of the so-called hard thermal loops, which corresponds to using an effective action obtained by integrating out the modes with momentum of order of the temperature. As is well-known, quantities which are sensitive to the nonperturbative magnetic screening mass still remain incalculable in this re-summed perturbation theory. A different breakdown of the latter occurs whenever external momenta are light-like, because the hard thermal loops themselves develop collinear singularities. However, taking into account asymptotic thermal masses for the hard modes regulates the hard thermal loops without spoiling their gauge invariance. (author)