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

TL;DR

This paper proposes a temperature-dependent generalization of the Witten-Veneziano relation to explain eta' meson multiplicities observed in experiments at high temperatures, addressing limitations of the zero-temperature relation near chiral restoration.

Contribution

It introduces a model-independent, temperature-dependent modification of the Witten-Veneziano relation, aligning theoretical predictions with experimental data at finite temperatures.

Findings

The zero-temperature Witten-Veneziano relation cannot be directly extended to T close to T_Ch.

A new T-dependent quantity replaces the topological susceptibility in the relation.

Results are consistent with experimental eta' multiplicity data and are derived from a Dyson-Schwinger approach.

Abstract

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.