Abstract
The intrinsic difficulties in extracting the hadron resonances from reaction data are illustrated by using several exactly soluble $\pi\pi$ scattering models. The finite-volume Hamiltonian method is applied to predict spectra using two meson-exchange Hamiltonians of $\pi N$ reactions. Within a three-channel model with $\pi N$, $\pi\Delta$ and $\sigma N$ channels, we show the advantage of the finite-volume Hamiltonian method over the approach using the L\"uscher 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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