# η and η′ mesons in the Dyson-Schwinger approach at finite temperature

Horvatić, Davor and Klabučar, Dubravko and Radzhabov, A. E. (2007) η and η′ mesons in the Dyson-Schwinger approach at finite temperature. Physical Review D, 76 (9). pp. 96009-14. ISSN 1550-7998

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Language: English

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.