High Order Corrections to Fundamental Constants

Abstract

This thesis explores the determination of a few of the fundamental constants of the standard model by employing different methods than those historically used. Modern field theory techniques are applied to the calculation of the α ²(Zα)⁵ corrections to the Lamb shift leading to an increase in the precision of the current value. It is then shown how these same techniques can be used to compute the α( Zα)⁵ corrections to the bound electron g-factor. Next, the beyond the standard model decay of a muon into an electron and a particle called a Majoron is considered. This calculation provides the theory that underlies a new method of searching for the Majoron that does not require any modification of currently planned muon to electron conversion experiments. Finally, the two related decays of a b-quark decaying to a c-quark and leptons and a muon decaying to an electron and neutrinos are considered in a new kinematic configuration. This new approach provides the [special characters omitted] corrections to the semileptonic b-quark decay rate and is currently the only method that gives access to the [special characters omitted] corrections to the muon decay rate. All of these corrections are used in determining fundamental properties of the standard model as well as the ongoing search for new physics.