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.
Highlights
Spontaneous breaking of chiral symmetry and the UAð1Þ anomaly are two characteristic features of QCD in vacuum
In order not to muddle the discussions with the model-dependent thermal pion decay constant, we focus on the situation by expressing all the physical quantities in terms of F and refrain from the discussions with the expressions given in terms of the renormalized Fπ
In this work we update the determinations of the low energy constants of the Uð3Þ chiral perturbation theory up to next-to-next-to-leading order, by including phenomenological inputs and various independent lattice simulation data on the η-η0 mixing, the kaon masses, the pion and kaon decay constants
Summary
Spontaneous breaking of chiral symmetry and the UAð1Þ anomaly are two characteristic features of QCD in vacuum The former gives the octet of the pseudo-Nambu-Goldstone bosons (pNGBs), i.e., π, K, η, while the latter provides an explanation to the large mass of the η0. The masses of the light flavor pseudoscalar mesons π, K, η and η0 will be definitely affected by the restoration of the UAð1Þ and chiral symmetries. New lattice results, including the pion-mass dependences of the mixing angles and decay constants in the quark-flavor basis, are considered, comparing with the study in Ref. The relevant chiral Lagrangians and the NNLO calculations of the masses, decay constants and mixing parameters of the pNGBs π, K, η and η0 are briefly discussed in Sec. II, where we determine the χPT LECs by taking into account the various lattice simulation results and phenomenological inputs.
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