A finite-volume matrix Hamiltonian model for a Delta -> nucleon-pion system

TL;DR

This paper introduces a finite-volume matrix Hamiltonian model for analyzing Delta to nucleon-pion resonances in lattice QCD, providing a robust and generalizable method for extracting resonance parameters that aligns with effective field theory.

Contribution

The paper develops a transparent, exactly solvable matrix Hamiltonian model that can be extended to multi-channel problems and effectively determines resonance parameters from lattice QCD data.

Findings

The model accurately reproduces resonance parameters from pseudodata.

It is as robust as the Luescher method in finite-volume analysis.

Incorporating background interactions improves the resonance extraction.

Abstract

A matrix Hamiltonian model is developed to address the finite-volume effects appearing in studies of baryon resonances in lattice QCD. The Hamiltonian model includes interaction terms in a transparent way, and can be readily generalized to address multi-channel problems. The eigenvalue equation of the model is exactly solvable, and can be matched onto chiral effective field theory. The model is investigated in the case of Delta -> nucleon-pion scattering. A robust method for determining the resonance parameters from lattice QCD is developed. It involves constraining the free parameters of the model based on the lattice spectrum in question. The method is tested in the context of a set of pseudodata, and a picture of the model-dependence is obtained by examining a variety of regularization schemes in the model. A comparison is made with the Luescher method, and it is found that the matrix Hamiltonian method is equally robust. Both methods are tested in a more realistic scenario, where a background interaction corresponding to direct nucleon-pion scattering is incorporated into the pseudodata. The resulting extraction of the resonance parameters associated with the Delta baryon resonance provides evidence that an effective field theory style of approach yields a successful realization of finite-volume effects in the context of baryon resonances.