Pad\'e Approximants and Resonance Poles

TL;DR

This paper introduces a systematic, model-independent method using Padé approximants and Montessus de Ballore theorem to accurately extract resonance pole positions and widths from scattering amplitudes.

Contribution

It presents a new, theoretically grounded procedure for resonance parameter extraction based on Padé theory and complex analysis, improving reliability and error estimation.

Findings

The method reliably unfolds the Second Riemann Sheet to locate resonance poles.

It provides a systematic, model-independent approach for resonance parameter extraction.

The approach ensures mathematically well-defined and error-controlled results.

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 a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the Second Riemann Sheet of an amplitude to search for 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.