Nucleon resonance structure in the finite volume of lattice QCD

An approach for relating the nucleon resonances extracted from pi N reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of pi N reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance can be related to the probability P-N* (E) of finding the bare state, N*, in the pi N scattering states in infinite volume. We further demonstrate that the probability P-N*(V)(E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P-N*(E) as the volume increases. Our findings suggest that the comparison of P-N*(E) and P-N*(V)(E) can be used to examine whether the nucleon resonances extracted from the pi N reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P-N*(V)(E) directly from lattice QCD. The practical differences between our approach and the approach using the Luscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.