We examine the phase shifts and inelasticities associated with the $N^*(1440)$ Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. All three hypotheses are able to describe the scattering data well. In the third hypothesis the Roper resonance couples the low-lying bare basis-state component associated with the ground state nucleon with the virtual meson-baryon contributions. Here the non-trivial superpositions of the meson-baryon scattering states are complemented by bare basis-state components explaining their observation in contemporary lattice QCD calculations. The merit of this scenario lies in its ability to not only describe the observed nucleon energy levels in large-volume lattice QCD simulations but also explain why other low-lying states have been missed in todays lattice QCD results for the nucleon spectrum.
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