Breakdown of the hard thermal loop expansion for quasi-real photons production

We discuss the bremsstrahlung production of soft real and virtual photons in a quark-gluon plasma at thermal equilibrium beyond the Hard Thermal Loop (HTL) resummation. The physics is controlled by the ratio $Q^{2}/q_{0}^{2}$ of the virtuality to the energy. When $Q^{2}/q_{0}^{2} ? g^{2}$ where g is the strong coupling constant, the emission rate is enhanced by a factor 1/g² over the HTL results due to light-cone singularities and the bremsstrahlung is induced by scattering of the quark via both transverse and longitudinal soft gluon exchanges. When $Q^{2}/q_{0}^{2}$ increases, the enhancement factor is given by $q_{0}^{2}/Q^{2}$. When this ratio is near unity, the bremsstrahlung contribution is of the same order as the rate predicted by the HTL resummation. In that case, the bremsstrahlung is induced by both soft and hard gluon exchanges.