Thermal properties and evolution of the $U_A(1)$ factor for 2+1 flavors

Abstract

Thermal evolution of the axial anomaly is investigated in the system of the linear sigma model for $2+1$ flavors. We explore the functional form of the effective potential and the coefficient of the `t Hooft determinant term. It is found that the latter develops a non-trivial structure as a function of the chiral condensate and grows everywhere with respect to the temperature. This shows that mesonic fluctuations strengthen the axial anomaly at finite temperature and it does not get vanished at the critical point. The phenomenon has been found to have significance in the thermal properties of the mesonic spectra, especially concerning the $\eta -{\eta }^{\prime }$ system.

9 pages, 6 figures, typos corrected, matches published version

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• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model
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• Hubble selection of the weak scale from QCD quantum critical point
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• Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
• Susceptibilities of rotating quark matter in Fourier-Bessel basis
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature