J. M. M. Hall, A. C. -P. Hsu, D. B. Leinweber, A. W. Thomas, R. D. Young
The connection between the asymptotic states of the S-matrix and the energy spectrum in a finite volume is investigated in the context of a Delta-Nucleon-pion interaction model that can be solved exactly. In particular, Luescher's method, which proposes a definite relationship between the elastic scattering phase shift and the finite-volume energy levels, is shown to exhibit a deviation from the correct resonance position that behaves approximately like 1/L in the range of volumes of interest. A new method is proposed, whereby the energy levels from a lattice calculation are used to determine the parameters of the model. The phase shift may then be evaluated using an infinite-volume t-matrix. The model-dependence of the method is investigated. At box sizes that are currently considered quite large, model-dependent effects are estimated to be an order of magnitude smaller than the deviations associated with Luescher's method. The extraction of the resonance position is also shown to be relatively independent of L.
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http://arxiv.org/abs/1207.3562
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