Decoding Two-Particle States in QCD with Spatial Wavefunctions

TL;DR

This paper introduces a new method for constructing optimized two-particle operators in lattice QCD by incorporating spatial wavefunctions and a novel noise-based quark smearing technique, enabling precise resolution of near-threshold states.

Contribution

It presents a systematic approach to build operators with strong coupling to two-particle states and a new smearing method for efficient lattice QCD computations, improving state resolution.

Findings

Successfully resolved eigenstates separated by ~5 MeV near threshold

Demonstrated the effectiveness of the new operators in the $oldsymbol{ ext{Ω}_{ccc} ext{Ω}_{ccc}}$ system

Enhanced the ability to study hadronic systems with close-lying energy levels

Abstract

A systematic way to constructing optimized interpolating operators strongly coupled to QCD two-particle states is developed, which is achieved by incorporating inter-hadron spatial wavefunctions. To efficiently implement these operators in lattice QCD, a novel quark smearing technique utilizing noise vectors is proposed. Applied to the $\Omega_{ccc}\Omega_{ccc}$ system, the optimized operators resolve distinct eigenstates separated by only $\sim 5$ MeV near the threshold $2m_{\Omega_{ccc}} \simeq 9700$ MeV. This exceptional resolving power opens new possibilities for studies of a wide range of hadronic systems in QCD.