Optimized Two-Baryon Operators in Lattice QCD

TL;DR

This paper develops optimized two-baryon operators using the HAL QCD method, enabling stable extraction of energy spectra and potentials in lattice QCD, which improves the study of hadron-hadron interactions.

Contribution

It introduces a new set of optimized operators that effectively isolate eigenstates of two baryons, enhancing the accuracy of energy and potential measurements in lattice QCD.

Findings

Optimized operators yield stable effective energies for ground and excited states.

Agreement between eigenenergies and HAL QCD potential within statistical errors.

Reliable extraction of potentials regardless of correlation dominance.

Abstract

A set of optimized interpolating operators which are dominantly coupled to each eigenstate of two baryons on the lattice is constructed by the HAL QCD method. To test its validity, we consider heavy dibaryons $\Omega_{3Q}\Omega_{3Q}$ ($Q=s,c$) calculated by (2+1)-flavor lattice QCD simulations with nearly physical pion mass. The optimized two-baryon operators are shown to provide effective energies of the ground and excited states separately stable as a function of the Euclidean time. Also they agree to the eigenenergies in a finite lattice box obtained from the leading-order HAL QCD potential $V({\boldsymbol{r}})$ within statistical errors. The overlapping factors between the optimized sink operators and the state created by the wall-type source operator indicate that $V( \boldsymbol{r})$ can be reliably extracted, no matter whether the spacetime correlation of two baryons is dominated by the ground state or the excited state. It is suggested that the optimized set of operators is useful for variational studies of hadron-hadron interactions.