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

TL;DR

This study analyzes the $a_0(980)$ resonance using chiral effective field theory with a coupled-channel approach, fitting lattice and experimental data to understand scattering phase shifts and resonance properties.

Contribution

It provides a combined lattice and experimental analysis of the $a_0(980)$ resonance within chiral EFT, including phase shifts, inelasticities, and pole positions for physical and unphysical masses.

Findings

Successful description of lattice energy levels and experimental data

Different phase shifts obtained for physical meson masses

Calculated pole positions and residues in the complex energy plane

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 $\pi\eta'$. 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.