  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.
