Tetraquarks, hadronic molecules, meson-meson scattering and disconnected contributions in lattice QCD

TL;DR

This paper emphasizes the importance of including disconnected contractions in lattice QCD calculations for accurately studying tetraquarks, hadronic molecules, and meson scattering, demonstrating that neglecting them leads to missing key scalar meson information.

Contribution

It reveals that disconnected contributions are crucial and often dominant in lattice QCD studies of certain hadronic states, challenging the common practice of neglecting them.

Findings

Disconnected contributions are leading order when both connected and disconnected contractions exist.

Neglecting disconnected parts results in loss of information about scalar mesons.

Including disconnected contractions is essential for accurate lattice QCD results on tetraquarks and related states.

Abstract

There are generally two types of Wick contractions in lattice QCD calculations of a correlation function --- connected and disconnected ones. The disconnected contribution is difficult to calculate and noisy, thus it is often neglected. In the context of studying tetraquarks, hadronic molecules and meson-meson scattering, we show that whenever there are both connected and singly disconnected contractions, the singly disconnected part gives the leading order contribution, and thus should never be neglected. As an explicit example, we show that information about the scalar mesons sigma, f0(980), a0(980) and kappa will be lost when neglecting the disconnected contributions.