Nucleon resonance structure in the finite volume of lattice QCD

TL;DR

This paper develops a method to connect nucleon resonance data from reaction experiments with lattice QCD calculations using a finite-volume Hamiltonian approach, enabling consistency checks between experimental and lattice results.

Contribution

It introduces a novel framework relating resonance pole positions to the probability of bare states in finite and infinite volumes, bridging experimental data and lattice QCD.

Findings

Resonance pole positions relate to the probability of bare states in scattering.

Finite-volume probabilities approach infinite-volume probabilities as volume increases.

The method offers a way to compare experimental resonance data with lattice QCD results.

Abstract

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. 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 L\"uscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.