Rational Approximations in Quantum Chromodynamics

Abstract

We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Padé 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 Padé 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.

Comments: Ph.D. Thesis (Advisor: Santi Peris). 174 pages