Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Pad\'e approximants

TL;DR

This paper enhances the Padé approximant method for extracting the $f_0(500)$ resonance pole from $\pi\pi$ scattering data by incorporating threshold behavior, leading to more accurate pole determinations.

Contribution

It introduces a refined approach that enforces correct threshold behavior in Padé approximants, improving resonance pole extraction accuracy.

Findings

Improved pole position determinations for the $f_0(500)$ resonance.

Demonstrated the effectiveness of threshold behavior in Padé approximants.

Validated the method's precision for resonance analysis.

Abstract

In this letter, we discuss the determination of the $f_0(500)$ resonance by analytic continuation through Pad\'e approximants of the $\pi\pi$-scattering amplitude from the physical region to the pole in the complex energy plane. Using as input a class of admissible parametrizations of the scalar-isoscalar $\pi\pi$ partial wave and imposing now the correct threshold behavior of the partial amplitude, we improve on the determinations of pole positions obtained in Ref. [1], thus empowering the Pad\'e method as a simple and precise tool for extracting resonance poles from amplitudes.