Decoding Two-Particle States in QCD with Spatial Wavefunctions

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 ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ system, the optimized operators resolve distinct eigenstates separated by only $\sim 5$ MeV near the threshold $2m_{{\mathrm{\Omega }}_{ccc}}\simeq 9700$ MeV. This exceptional resolving power opens new possibilities for studies of a wide range of hadronic systems in QCD.