Chiral study of the $a_0(980)$ resonance and $\pi\eta$ scattering phase shifts in light of a recent lattice simulation

We investigate the $a_0(980)$ resonance within chiral effective field theory through a three-coupled-channel analysis, namely $\pi\eta$, $K\bar{K}$ and $\pi\eta'$. A global fit to recent lattice finite-volume energy levels from $\pi\eta$ scattering and relevant experimental data on a $\pi\eta$ event distribution and the $\gamma\gamma\to\pi\eta$ cross section is performed. Both the leading and next-to-leading-order analyses lead to similar and successful descriptions of the finite-volume energy levels and the experimental data. However, these two different analyses yield different $\pi\eta$ scattering phase shifts for the physical masses for the $\pi, K, \eta$ and $\eta'$ mesons. The inelasticities, the pole positions in the complex energy plane and their residues are calculated both for unphysical and physical meson masses.