Nucleon resonance structure in the finite volume of lattice QCD

Understand

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 pole positions 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.