Study for a model-independent pole determination of overlapping resonances

TL;DR

This paper introduces a model-independent method using the Schlessinger Point Method to identify complex poles of overlapping resonances directly from experimental data, demonstrated on meson decay data and benchmarked against known models.

Contribution

The paper presents a novel, model-independent approach for extracting resonance poles from experimental data, avoiding reliance on specific theoretical models.

Findings

Successfully identified scalar states $f_0(1500)$, $f_0(1710)$, and $f_0(2020)$ from BESIII data.

Validated the method against analytic models, estimating deviations from true values.

Showed the method's consistency with recent results, indicating its reliability.

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.