$\eta$ and $\eta'$ mesons in the Dyson-Schwinger approach at finite temperature

TL;DR

This paper investigates how the properties of $ ext{η}$ and $ ext{η'}$ mesons change with temperature using the Dyson-Schwinger approach, revealing a significant mass increase of $ ext{η'}$ near the chiral transition, impacting heavy-ion collision phenomenology.

Contribution

The study extends the Dyson-Schwinger framework to finite temperature and the strange sector, providing new insights into the temperature dependence of pseudoscalar mesons and the axial anomaly effects.

Findings

$ ext{η'}$ mass increases near the chiral transition temperature.

The Witten-Veneziano relation's extension to finite temperature may be unreliable.

Potential suppression of $ ext{η'}$ production in heavy-ion collisions.

Abstract

We study the temperature dependence of the pseudoscalar meson properties in a relativistic bound-state approach exhibiting the chiral behavior mandated by QCD. Concretely, we adopt the Dyson-Schwinger approach with a rank-2 separable model interaction. After extending the model to the strange sector and fixing its parameters at zero temperature, T=0, we study the T-dependence of the masses and decay constants of all ground-state mesons in the pseudoscalar nonet. Of chief interest are $\eta$ and $\eta^\prime$. The influence of the QCD axial anomaly on them is successfully obtained through the Witten-Veneziano relation at T=0. The same approach is then extended to T>0, using lattice QCD results for the topological susceptibility. The most conspicuous finding is an increase of the $\eta^\prime$ mass around the chiral restoration temperature $T_{\rm Ch}$, which would suggest a suppression of $\eta^\prime$ production in relativistic heavy-ion collisions. The increase of the $\eta^\prime$ mass may also indicate that the extension of the Witten-Veneziano relation to finite temperatures becomes unreliable around and above $T_{\rm Ch}$. Possibilities of an improved treatment are discussed.