Analytical Quantum Field methods in Particle Physics

In this thesis we deal with different aspects of quantum field theory, particularly in non-perturbative but also perturbative regimes, applied to the intellectual construction that is the Standard Model for Particle Physics (SM), but also its extension via effective theories. We have developed the following practical contributions in different subfields of Particle Physics: qualitatively assessing why the SM has those specific symmetries, explaining the $^3P_0$ mechanism of meson decay from fundamental Quantum Chromodynamics (QCD) calculations, experimentally distinguishing Effective Theories of the Electroweak sector beyond the SM in accelerators, extrapolating LHC data (low energies) to possible resonant regions of new physics (high energies) with controlled uncertainties and studying precision calculations of QCD (high energies) in coordinate space.