Low-lying baryon resonances from lattice QCD

TL;DR

This paper demonstrates how lattice QCD can be used to compute baryon resonance properties by analyzing finite-volume spectra and scattering matrices, with results on the $ ext{Delta}$ and $ ext{Lambda}(1405)$ resonances.

Contribution

It introduces a non-perturbative lattice QCD approach to extract baryon resonance energies and scattering information, including a novel analysis of the $ ext{Lambda}(1405)$ resonance structure.

Findings

Successful extraction of the $ ext{Delta}$ resonance energy.

Identification of a two-pole structure near the $ ext{Lambda}(1405)$.

Discussion of potential application to the Roper resonance.

Abstract

Calculating the properties of baryon resonances from quantum chromodynamics requires evaluating the temporal correlations between hadronic operators using integrations over field configurations weighted by a phase associated with the action. By formulating quantum chromodynamics on a space-time lattice in imaginary time, such integrations can be carried out non-perturbatively using a Markov-chain Monte Carlo method with importance sampling. The energies of stationary states in the finite volume of the lattice can be extracted from the temporal correlations. A quantization condition involving the scattering $K$-matrix and a complicated ``box matrix'' also yields a finite-volume energy spectrum. By appropriately parametrizing the scattering $K$-matrix, the best-fit values of the $K$-matrix parameters are those that produce a finite-volume spectrum which most closely matches that obtained from the Monte Carlo computations. Results for the $\Delta$ resonance are presented, and a study of scattering for energies near the $\Lambda(1405)$ resonance is outlined, showing a two pole structure. The prospects for applying this methodology to the Roper resonance are discussed.