Soft photons and hard thermal loops

We calculate within the Hard Thermal Loop expansion the production rate of soft photons and lepton pairs by a hot quark-gluon plasma at thermal equilibrium, up to the 2-loop order. Strong collinear divergences appear to mix the orders of the perturbative expansion so that the 2-loop order is in fact dominant compared to the 1-loop order. More precisely, angular integrals that would otherwise be of order 1 are found to behave as powers of $1\mathrm{/}g$ when the produced photon is massless, therefore breaking the standard HTL power counting rules.