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

TL;DR

This paper revisits the properties and mixing of light pseudoscalar mesons using $U(3)$ chiral perturbation theory, analyzing their masses, decay constants, and thermal behaviors with updated lattice QCD data.

Contribution

It provides a refined analysis of meson properties and their temperature dependence, incorporating next-to-next-to-leading order constants from recent lattice QCD simulations.

Findings

Masses of $\

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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 $\eta'$. 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 mass of the $\eta'$ turns out to be slightly decreased in the low-temperature region.