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

Understand

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.