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Rational Approximations in Quantum Chromodynamics
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We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic functions (inspired by the Large-Nc limit in QCD) where we explore the Minimal Hadronic Approximation through the extraction of Low-Energy Constants and Condensate parameters of a two-point Green's function; and the second one related with meromorphic functions of Stieltjes-type where we present a critical analysis to a unitarization process applied to the Linear Sigma Model and also and application of the Pad\'e Theory to the vacuum polarization function of a heavy quark. We also show the ability of these approximations when working with experimental data. Along these line, we make special emphasis on the reliability of that theory to control on systematic errors.
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Analytically Consistent Reconstruction of Finite Data Using Pad\'e Sequences
Tracking how spurious pole-zero pairs move across Padé approximation orders lets an iterative algorithm flag inconsistent data points and reconstruct the underlying function while preserving genuine analytic structures.
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