Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm

TL;DR

This paper introduces a universal, model-independent algorithm based on Padé approximants to accurately determine resonance poles and threshold energies in hadron physics from real spectral data, demonstrated on both models and experimental data.

Contribution

It presents a novel application of Padé approximants for extracting resonance poles and threshold energies directly from real spectral data in hadron physics.

Findings

Accurately extracted resonance poles for $ ho(770)$ and $f_0(500)$ mesons.

Method works well with both analytical models and experimental data.

Threshold predictions are feasible even with noisy data.

Abstract

We show how complex resonance poles and threshold energies for systems in hadron physics can be accurately obtained by using a method based on the Pad\'{e}-approximant which was recently developed for the calculation of resonance poles for atomic and molecular auto-ionization systems. The main advantage of this method is the ability to calculate the resonance poles and threshold energies from \emph{real} spectral data. In order to demonstrate the capabilities of this method we apply it here to an analytical model as well as to experimental data for the squared modulus of the vector pion form factor, the S0 partial wave amplitude for $\pi\pi$ scattering and the cross section ratio $R(s)$ for $e^+e^-$ collisions. The extracted values for the resonance poles of the $\rho(770)$ and the $f_0(500)$ or $\sigma$ meson are in very good agreement with the literature. When the data are noisy the prediction of decay thresholds proves to be less accurate but feasible.