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

In this work we show how by using a Padé type analytical continuation scheme, based on the Schlessinger point method, it is possible to find higher production thresholds in hadron physical problems. Recently, an extension of this numerical approach to the complex energy plane enabled the calculations of auto-ionization decay resonance poles in atomic and molecular systems. Here we use this so-called Resonances via Padé (RVP) method, to show its convergence beyond the singular point in hadron physical problems. In order to demonstrate the capabilities of the RVP method, two illustrations for the ability to identify singularities and branch points are given. In addition, two applications for hadron physical problems are given. In the first one, we identify the decay thresholds from a numerically calculated spectral function. In the second one, we use experimental data. First, we calculate the resonance pole of the f0(500) or σ meson using the S0 partial wave amplitude for ππ scattering in very good agreement with the literature. Second, we use data on the cross section ratio R(s) for e+e− collisions and discuss the prediction of decay thresholds which proves to be difficult if the data is noisy.