Importance of closed quark loops for lattice QCD studies of tetraquarks

TL;DR

This paper emphasizes the importance of including closed quark loop diagrams in lattice QCD calculations for tetraquarks, demonstrating their critical role in accurately identifying the $a_0(980)$ meson.

Contribution

It introduces efficient techniques for computing correlation matrices with closed quark loops and shows their essential contribution to physical results in tetraquark studies.

Findings

Closed quark loops significantly affect correlation matrix results.

Evidence suggests an additional state near $K+ ar K$ and $\\eta + \\pi$ thresholds.

Indications of the $a_0(980)$ meson as a tetraquark candidate.

Abstract

To investigate the light scalar tetraquark candidate $a_0(980)$ (quantum numbers $J^P =0^+$), a correlation matrix including a variety of two- and four-quark interpolating operators has to be computed. We discuss efficient techniques to compute the elements of this correlation matrix, in particular diagrams with closed quark loops. Furthermore, we present evidence that such diagrams are not negligible given our precision, and their contribution is essential to obtain physically meaningful results. In particular, we find indications of the existence of an "additional" state around the two-particle thresholds of $K+ \bar K$ and $\eta +\pi$, which could correspond to the $a_0(980)$ meson.