The Powers of Perturbation Theory : Loops and Gauge Invariance in Particle Physics

Sammanfattning: The Standard Model is the best particle physics theory we have, but there are still phenomena that it cannot explain. In this thesis I have worked on two different projects that connect to two of the biggest unsolved questions of the Standard Model.From observations of neutrino oscillations we know that at least one of the neutrinos has to be massive. But the neutrinos of the Standard Model are massless. The first paper in the thesis investigates a simple extension of the Standard Model that realizes a fifth force as a U(1) gauge group. In such models, extra care has to be taken to not introduce inconsistencies known as anomalies. It turns out that the simplest way to avoid these problems is to introduce three right-handed neutrinos. Such models can then incorporate neutrino masses in a convenient way. In the second paper we have investigated a twist on this model that does not have neutrino masses, but which makes other interesting models possible—such as a model with gauged lepton number.The observed asymmetry between matter and antimatter cannot be explained by the Standard Model. One of the more popular of the possible explanations is known as electroweak baryogenesis. In this scenario the asymmetry is determined during the electroweak phase transition in the early universe. The second project—spanning the three final papers of the thesis—has aimed to improve the approximation methods we use to calculate features of this phase transition. Such calculations are plagued by two big problems that seem to compete with each other. On the one hand, gauge invariant results seem to demand that a strict loop counting must be enforced. On the other hand, the loop approximation does not work well close to the phase transition. We argue that the solution is to use a different power counting, but still be strict about sticking to it.