Resolution of the multichannel anomaly in the extraction of S-matrix resonance-pole parameters

Within the framework of a mathematically well-defined coupled-channel T-matrix model we have improved the existing multichannel pole-extraction procedure based on the numerical analytic continuation of the channel propagator, and for the first time we present the full set of pole parameters for already published amplitudes. Standard single-channel pole-extraction method (speed plot) was then applied to those amplitudes and resulting sets of T-matrix poles were inspected. The anomaly has been established that in some partial waves the pole values extracted using the standard single-channel methods differ not only from the values obtained using the analytic continuation method, but also change from one reaction to another. Inspired by this peculiarity, we have developed a new single-channel pole-extraction method based solely on the assumption of the partial wave analyticity. Since the speed plot turns out to be the lowest order term of the proposed method, the anomaly is understood and resolved.

Figure 1

A very simplified example: one resonance and one channel opening.

Figure 2

The illustration of the regularization method in the case of $N(1535)$ ${\mathrm{S}}_{11}$ resonance.