Nucleon resonance structure in the finite volume of lattice QCD

Abstract

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