Baryon resonances and hadronic interactions in a finite volume

TL;DR

This paper introduces a new matrix Hamiltonian approach to relate finite-volume lattice QCD energy levels to scattering phase shifts, improving resonance parameter extraction and comparison with experimental data.

Contribution

A novel exactly solvable matrix Hamiltonian model is developed to connect finite-volume energy spectra with scattering phase shifts, applicable to multi-channel hadronic interactions.

Findings

The method accurately extracts resonance positions from pseudodata.

Results are stable across different volumes and regularization schemes.

Comparison shows favorable performance against Luescher's method.

Abstract

In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy spectrum of the finite-volume lattice with the asymptotic behaviour of the S-matrix. A new technique for comparing energy eigenvalues with scattering phase shifts is introduced, which involves the construction of an exactly solvable matrix Hamiltonian model. The model framework is applied to the case of $\Delta\rightarrow N\pi$ decay, but is easily generalized to include multi-channel scattering. Extracting resonance parameters involves matching the energy spectrum of the model to that of a lattice QCD calculation. The resulting fit parameters are then used to generate phase shifts. Using a sample set of pseudodata, it is found that the extraction of the resonance position is stable with respect to volume for a variety of regularization schemes, and compares favorably with the well-known Luescher method. The model-dependence of the result is briefly investigated.