Updated study of the $��$-$��'$ mixing and the thermal properties of light pseudoscalar mesons at low temperatures

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 $��, K, ��$ and $��'$. 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 $��$-$��'$ mixing angles in singlet-octet and quark-flavor bases are also explored. While the masses of the $��, K$, and $��$ are increased when increasing the temperatures, the mass of the $��'$ turns out to be slightly decreased in the low-temperature region.
19 pages, 10 figures. To match the published version in PRD