Symmetries as a guide to regularization ambiguities: Standard and Beyond Standard Model examples

Abstract

This thesis is about regularization of ultraviolet divergences appearing in the perturbative expansion of quantum field theories (QFTs). We present a general view of the ambiguities that may arise in the regularization program and develop a systematic approach to extract them from a general Feynman amplitude. We show that they are intimately related with the breaking of the symmetries of the underlying quantum field theory. We also show they are related to the violation of momentum routing invariance (MRI) of Feynman diagrams, allowing us to regard MRI as a symmetry to be preserved in the perturbative expansion of QFTs. We apply our formalism to a variety of theories and examples such as: the Higgs decay to two photons, the photon-photon scattering, and N=1 supersymmetric electrodynamics. In all cases we verify that regularization ambiguities can be consistently extracted being related to the breaking of the symmetries of the underlying QFT. We also study the role played by quadratic divergences on a variety of examples showing its connection (or not) to the ambiguities aforementioned.of an equality to one.