Precise determination of resonance pole parameters through Pad\'e approximants

TL;DR

This paper introduces a precise, model-independent method using Padé approximants to extract resonance pole parameters from scattering data, providing improved accuracy and systematic uncertainty analysis for meson resonances.

Contribution

The paper presents a novel application of Padé approximants for model-independent determination of resonance poles from phase-shift data, with detailed uncertainty analysis.

Findings

Accurate pole positions for $f_0(500)$, $ ho(770)$, and $f_2(1270)$ resonances.

High-precision determination of resonance couplings to two pions.

Systematic comparison with previous resonance parameter determinations.

Abstract

In this work, we present a precise and model--independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Pad\'e approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-- and twice-- subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the $f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $\rho(770)$ at $\sqrt{s}=(761.4\pm 1.2)-i(71.8 \pm 1.0)$ MeV, and the pole of the $f_2(1270)$, located at $\sqrt{s}=(1267.3\pm 1.7)-i(95.0\pm 2.3)$ MeV. The couplings of the resonances to two pions are also determined with high precision, obtaining respectively, $3.8\pm 0.4$ GeV, $5.92\pm 0.15$ and $4.41\pm 0.23$ GeV$^{-1}$. Special attention is dedicated to the systematic treatment of the theoretical and statistical uncertainties, together with their comparison with previous determinations.