From Extraction of Nucleon Resonances to LQCD

The intrinsic difficulties in extracting the hadron resonances from reaction data are illustrated by using several exactly soluble $ππ$ scattering models. The finite-volume Hamiltonian method is applied to predict spectra using two meson-exchange Hamiltonians of $πN$ reactions. Within a three-channel model with $πN$, $πΔ$ and $σN$ channels, we show the advantage of the finite-volume Hamiltonian method over the approach using the Lüscher formula to test Lattice QCD calculations aimed at predicting nucleon resonances. We discuss the necessary steps for using the ANL-Osaka eight-channel Hamiltonian to predict the spectra for testing the LQCD calculations for determining the excited nucleon states up to invariant mass $W= 2$ GeV.

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