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

Xiao-Wei Gu, Chun-Gui Duan, Zhi-Hui Guo

Published 2018-03-20Version 1

Within the framework of $U(3)$ chiral perturbation theory, we revisit the masses, decay constants and the mixing parameters of the light pseudoscalar mesons $\pi, K, \eta$ and $\eta'$. 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 $\eta$-$\eta'$ 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 $\eta'$ mass turns out to be slightly decreased in the low-temperature region.