Renormalization Group and Pade Applications to Quantum Field Theory: Perturbative and Non-perturbative Regions

Pade approximants (PA) have been widely applied in practically all areas of physics. This work focuses on developing PA as tools for both perturbative and non-perturbative Quantum Field Theory (QFT). In perturbative QFT, a systematic estimation of higher (unknown) loop terms via asymptotic Pade approximation procedure (APAP) is established and enhanced by application to renormalization-group-(RG-)invariant quantities. This methodology is applied to hadronic Higgs decay rates (both within the Standard Model and its MSSM extension), Higgs-sector cross-sections, inclusive semileptonic decays, QCD (Quantum Chromodynamics) correlation functions and the QCD static potential. APAP is also applied directly to RG functions in massive phi-4 theory. In non-perturbative QFT Pade summation methods are employed to probe the large coupling regions of QCD. In analysing all the possible Pade-approximants to truncated Beta-function for QCD, the singularity structure corresponding to the all-orders Beta-function is analyzed. Noting the consistent ordering of poles and roots for such approximants, these are found free of defective (pole) behaviour and physical conclusions are then drawn.