Lattice QCD investigation of the structure of the $a_0(980)$ meson

TL;DR

This study uses lattice QCD to explore the internal quark structure of the $a_0(980)$ meson, revealing it as a superposition of quark-antiquark and tetraquark components, with significant effects from closed quark loops.

Contribution

It introduces a comprehensive lattice QCD analysis including all relevant diagrams and employs a novel statistical method, AMIAS, to identify the meson's structure.

Findings

Identification of an additional energy level near $K + ar{K}$ and $ ext{η} + ext{π}$ thresholds.

Evidence that the $a_0(980)$ couples to both $ar{q} q$ and tetraquark interpolating fields.

Closed quark loop diagrams significantly influence the results.

Abstract

We investigate the quark content of the scalar meson $a_0(980)$ using lattice QCD. To this end we consider correlation functions of six different two- and four-quark interpolating fields. We evaluate all diagrams, including diagrams, where quarks propagate within a timeslice, e.g. with closed quark loops. We demonstrate that diagrams containing such closed quark loops have a drastic effect on the final results and, thus, may not be neglected. Our analysis shows that in addition to the expected spectrum of two-meson scattering states there is an additional energy level around the two-particle thresholds of $K + \bar{K}$ and $\eta + \pi$. This additional state, which is a candidate for the $a_0(980)$ meson, couples to a quark-antiquark as well as to a diquark-antidiquark interpolating field, indicating that it is a superposition of an ordinary $\bar{q} q$ and a tetraquark structure. The analysis is performed using AMIAS, a novel statistical method based on the sampling of all possible spectral decompositions of the considered correlation functions, as well as solving standard generalized eigenvalue problems.