\eta' Multiplicity and the Witten-Veneziano relation at finite temperature

We discuss and propose the minimal generalization of the Witten-Veneziano relation to finite temperatures, prompted by STAR and PHENIX experimental results on the multiplicity of eta' mesons. After explaining why these results show that the zero-temperature Witten-Veneziano relation cannot be straightforwardly extended to temperatures T too close to the chiral restoration temperature T_Ch and beyond, we find the quantity which should replace, at T>0, the Yang-Mills topological susceptibility appearing in the T=0 Witten-Veneziano relation, in order to avoid the conflict with experiment at T>0. This is illustrated through concrete T-dependences of pseudoscalar meson masses in a chirally well-behaved, Dyson-Schwinger approach, but our results and conclusions are of a more general nature and, essentially, model-independent.