[Show abstract][Hide abstract] 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 multichannel 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 Δ→Nπ 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 Lüscher 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 Nπ↔Nπ scattering is incorporated into the pseudodata. The resulting extraction of the resonance parameters associated with the Δ 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.
[Show abstract][Hide abstract] 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.