Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Padé approximants

Abstract

In this letter, we discuss the determination of the $f_0(500)$ resonance by analytic continuation through Padé 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 Padé method as a simple and precise tool for extracting resonance poles from amplitudes.

8 pages, 7 figures. Updated the version to match the published one

References in corpus (8)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• A Rational Approach to Resonance Saturation in large-Nc QCD
• Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data
• A rational approximation to <VV-AA> and its O(p^6) low-energy constant
• Precise determination of resonance pole parameters through Padé approximants
• Some Remarks on the Pade Unitarization of Low-Energy Amplitudes
• Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave