Ambiguities in the zero momentum limit of the thermal π^oγγ triangle diagram

Modifications of the $\pi^o\to 2\gamma$ decay amplitude by thermal effects have already been considered by several authors, leading to quite different results. I consider in this paper the triangle diagram connecting a neutral pion to two photons in a constituent quark model, within the real-time formulation of thermal field theory and study the zero external momentum limit of this diagram. It appears that this limit is not unique and depends strongly on the kinematical configuration of the external particles. This non-uniqueness is shown to explain the contradiction between existing results. I end with some considerations suggesting that this decay amplitude may be significantly modified by the resummation of hard thermal loops, due to infrared singularities.