Padé Approximants and Resonance Poles

Abstract

Based on the mathematically well defined Padé 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.

12 pages, 17 figures

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• On the scalar $\pi K$ form factor beyond the elastic region
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Vector form factor of the pion in chiral effective field theory
• Study for a model-independent pole determination of overlapping resonances
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
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• Extracting the resonance parameters from experimental data on scattering of charged particles
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants
• Dispersive determination of resonances from $\pi \pi$ scattering data
• Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Padé approximants
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