Low-lying baryon resonances from lattice QCD

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.