Study for a model-independent pole determination of overlapping resonances

Abstract

We apply a model-independent reconstruction method to experimental data in order to identify complex poles of overlapping resonances. The algorithm is based on the Schlessinger Point Method where data points are interpolated using a continued-fraction expression. Statistical uncertainties of the experimental data are propagated with resampling. In order to demonstrate the feasibility of this method, we apply it to the $S$-wave $J/\psi \to \gamma {\pi }^0{\pi }^0$ decay. We benchmark the method on known analytic models, which allows us to estimate the deviation from the true value. We then perform the pole extraction from BESIII data, and identify the $f_0(1500)$, $f_0(1710)$, and $f_0(2020)$ scalar states. Our results are in reasonable agreement with recent results, which suggests the proposed method as a promising model-independent alternative for the determination of resonance poles that is solely based on available experimental data.

Comments: v1: 9 pages, 4 figures; v2: 12 pages, 7 figures. Major revision: added more details about the SPM and noise-filtering algorithms and a thorough analysis of the independence of the resonance locations from the number of input points. Conclusions unchanged