Determination of the parameters of the Δ(1232) resonance from partial-wave analyses of elastic πN scattering

On the basis of data on the P33 amplitude from various partial-wave analyses of elastic πN scattering, the pole characteristics of the Δ(1232) resonance are determined within the resonance model. An approximate analytic formula that relates the residue to the background is obtained. Estimates confirm that the nonresonance part of the phase shift is small and differs significantly from the results of the calculations within the current algebra and the approach of effective Lagrangians. This contradiction is removed in a modified resonance-model version developed on the basis of taking into account the quadratic term in the expansion of the Jost function in a series at the pole point. It is shown that the coordinates of the pole and the phase shift of the residue change only slightly in relation to the results within the traditional model, but that the absolute value of the residue increases by about 20%