From Extraction of Nucleon Resonances to LQCD

TL;DR

This paper compares methods for extracting nucleon resonance spectra, highlighting the advantages of the finite-volume Hamiltonian approach over traditional Lüscher formula techniques in predicting excited nucleon states from lattice QCD data.

Contribution

It demonstrates the effectiveness of the finite-volume Hamiltonian method in predicting nucleon resonance spectra and discusses its application to complex multi-channel models for testing lattice QCD results.

Findings

Finite-volume Hamiltonian method outperforms Lüscher formula in certain resonance predictions.

Application to three-channel models shows improved spectral predictions.

Framework for testing lattice QCD calculations up to 2 GeV excitation energy.

Abstract

The intrinsic difficulties in extracting the hadron resonances from reaction data are illustrated by using several exactly soluble $\pi\pi$ scattering models. The finite-volume Hamiltonian method is applied to predict spectra using two meson-exchange Hamiltonians of $\pi N$ reactions. Within a three-channel model with $\pi N$, $\pi\Delta$ and $\sigma N$ channels, we show the advantage of the finite-volume Hamiltonian method over the approach using the L\"uscher formula to test Lattice QCD calculations aimed at predicting nucleon resonances. We discuss the necessary steps for using the ANL-Osaka eight-channel Hamiltonian to predict the spectra for testing the LQCD calculations for determining the excited nucleon states up to invariant mass $W= 2 $ GeV.