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

Details $η$ and $η'$ mesons in the Dyson-Schwinger approach at finite temperature $η$ and $η'$ mesons in the Dyson-Schwinger approach at finite temperature

2007-08-09

arxiv.org/abs/0708.1260v1

Phys.Rev.D76:096009,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 15 figures

Scientific paper

10.1103/PhysRevD.76.096009

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.

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