Updated study of the $\eta$-${\eta }^{\prime }$ mixing and the thermal properties of light pseudoscalar mesons at low temperatures

Abstract

Within the framework of the $U(3)$ chiral perturbation theory, we revisit the masses, decay constants and the mixing parameters of the light pseudoscalar mesons $\pi ,K,\eta$ and ${\eta }^{\prime }$. The low energy constants up to next-to-next-to-leading order are determined by including the light-quark mass dependences of the various quantities from different lattice QCD simulations and relevant phenomenological inputs. Then we study the finite-temperature behaviors of the masses of the light pseudoscalar mesons. The thermal behaviors of the $\eta$-${\eta }^{\prime }$ mixing angles in singlet-octet and quark-flavor bases are also explored. While the masses of the $\pi ,K$, and $\eta$ are increased when increasing the temperatures, the mass of the ${\eta }^{\prime }$ turns out to be slightly decreased in the low-temperature region.

Comments: 19 pages, 10 figures. To match the published version in PRD