Wavefunction-based operator optimization for two-hadron systems in lattice QCD

TL;DR

This paper introduces a systematic method for constructing optimized two-hadron operators in lattice QCD using wavefunctions and a novel quark smearing technique, improving state identification and analysis of scattering effects.

Contribution

It develops a new operator optimization approach incorporating inter-hadron wavefunctions and a $Z_3$ noise-based smearing technique, enhancing lattice QCD studies of two-hadron systems.

Findings

Successful identification of $ ext{Ω}_{ccc} ext{Ω}_{ccc}$ states with narrow energy gaps

Effective suppression of scattering state contamination in correlation functions

Potential for broad application to various two-hadron systems

Abstract

A systematic way to constructing optimized interpolating operators for two-hadron systems is developed by incorporating inter-hadron spatial wavefunctions. The wavefunctions can be obtained from an iterative process with an appropriate initial guess. To implement these operators, a novel quark smearing technique utilizing $Z_3$ noise vectors is proposed, which allows for effectively incorporating inter-hadron spatial wavefunctions at the source without using all-to-all quark propagators. Proof-of-principle application to the $\Omega_{ccc}\Omega_{ccc}$ system using physical-point lattice configurations with a large size $La\simeq8.1$~fm shows that optimized operators enables clear identification of states around $2m_{\Omega_{ccc}}\simeq 9700$ MeV with the energy gap as narrow as $\sim 5$ MeV. A comparison on correlation functions, effective energies, and HAL QCD potentials between unoptimized operators and optimized operators is given, with a special emphasis on the effects from nearby elastic scattering states. Potential applicability of the optimized operator to various two-hadron systems and its relation to the variational method are also discussed.