Title:

The anomalous magnetic moment of the muon and the QED coupling at the Z boson mass

In this thesis, we present our updated determinations for the leading order and higher order hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon (a_{\mu} {had,LOVP}, a_{\mu} {had,HOVP}), and for the hadronic contributions to the running of the QED coupling at the Zboson mass (\Delta\alpha_{had} {(5)}(M_Z 2)). At present the Standard Model (SM) predictions of the anomalous magnetic moment of the muon a_{\mu} {SM} is lower than the experimental measurement a_{\mu} {exp}$ by about 3 standard deviations. The precision of a_{\mu} {SM} is limited by hadronic contributions, of which a_{\mu} {had,LOVP} has the largest uncertainty. Therefore improving the accuracy and precision of a_{\mu} {had,LOVP} will help to clarify the origin of the discrepancy between theory and experiment. The running of the QED coupling at the Zboson mass \alpha(M_Z 2) is the least precise of the three parameters that is usually taken to define the electroweak sector of the SM. Its precision is limited by \Delta\alpha_{had} {(5)}(M_Z 2), and is a significant limiting factor for precision electroweak physics, e.g. the indirect determination of Higgs boson mass. We describe in detail our refined datadriven approach, which processes and combines a large number of e +e  hadronic annihilation data for use in our determinations. Error treatment is of course, also discussed in depth. We present a detailed breakdown of all the contributions to a_{\mu} {had,LOVP}, including the many new, more precise data used along with discussions on their impacts. We also perform an improved sum rule analysis for a specific energy region, which assists us in discriminating between two different choices of using data. Comparisons with previous analyses as well as with another group's recent determination are also made. For \Delta\alpha_{had} {(5)}(M_Z 2), we summarise the main results, discussing their effects as well as the comparison with other groups. More focus is given to a separate procedure used for preparing a set of new data that will improve the description of \alpha(q 2). We conclude the thesis by summing our a_{\mu} {had,LOVP}, a_{\mu} {had,HOVP} results with the latest predictions of contributions from the other sectors of the SM, leading to our own value for a_{\mu} {SM}. This is then discussed and compared to other recent determinations. Results for \Delta\alpha_{had} {(5)}(M_Z 2) and \alpha(M_Z 2) are also briefly reviewed. Finally, a summary of the whole thesis and future prospects in this area of study are given.
