Distillation and position-space sampling for local multiquark interpolators

TL;DR

This paper introduces a position-space sampling method within lattice QCD distillation to efficiently handle local multiquark interpolators, demonstrating its effectiveness for mesons and tetraquarks, and exploring its impact on the $T_{cc}(3875)^+$ state.

Contribution

The paper presents a novel position-space sampling technique that reduces computational costs for local multiquark operators in lattice QCD distillation.

Findings

Method works well for meson operators.

Method is effective for local tetraquark operators.

Small energy shift observed for $T_{cc}(3875)^+$ when including tetraquark operators.

Abstract

Distillation in lattice QCD is a smearing method that uses the lowest eigenvectors of the spatial Laplacian to construct a subspace in which the Dirac operator can be fully inverted. However, local multiquark interpolators are expensive in this framework because the cost of the contractions scales with a high power of the number of Laplacian eigenvectors. To address this, a position-space sampling method within distillation is presented that avoids this cost scaling. Our simulations show that this method works well for meson operators, but also for local tetraquark operators. In a preliminary study, we investigate the relevance of the latter for the ground state energy of the $T_{cc}(3875)^+$ tetraquark. There we find a downward shift in the lowest level when local tetraquark operators are added to a basis of bilocal scattering operators in the variational method. However, this shift is small compared to the error of the energy.