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 resummed 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.