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

Abstract

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 $\pi {\eta }^{\prime }$. 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 ${\eta }^{\prime }$ mesons. The inelasticities, the pole positions in the complex energy plane and their residues are calculated both for unphysical and physical meson masses.

arXiv comment34 pages, 14 figures, 2 tables. To match the published version in PRD

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