Hunting resonance poles with Rational Approximants

TL;DR

This paper introduces a mathematically rigorous, model-independent method based on Padé theory and Montessus de Ballore's theorem to accurately extract resonance pole positions from scattering amplitudes.

Contribution

It presents a new, systematic approach for resonance pole extraction using rational approximants, ensuring theoretical safety and error control.

Findings

Successfully unfolds the Second Riemann sheet to locate resonance poles.

Provides a model-independent and systematic procedure.

Offers a reliable way to predict resonance parameters with error estimates.

Abstract

Based on the mathematically well defined Pad\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed. In particular, thanks to the Montessus de Ballore's theorem we are able to unfold the Second Riemann sheet of an amplitude to search the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. This letter partially covers the material presented by the author at the 15th International QCD Conference: QCD 10 (25th anniversary), Montpellier, France, 28 Jun - 3 Jul 2010 and at the Quark Confinement and the Hadron Spectrum IX, 30 August - 3 September 2010, Madrid, Spain.