Probing the L2I,2J = S11 resonances in the πN scattering via the K-matrix and independent pole approach

Abstract

We reconstruct the two nucleon resonances in the S₁₁ partial-wave using the K-matrix parametrization. We obtained a total of four poles of the scattering amplitude located in different unphysical Riemann sheets. Each pole is linked to the peak structures seen in the S₁₁ partial-wave. This analysis is facilitated using the independent uniformized S-matrix pole method where the effect of the individual pole can be analyzed. It turned out that the peak at the ηN threshold and the line shape between the two thresholds are influenced by the fourth sheet pole. This is in contrast to the common identification that the second Riemann sheet pole always has the strongest effect on the energy region between the two thresholds. On the other hand, the peak well above the ηN threshold is produced mainly by a pole in the fourth sheet.