A part-per-million measurement of the positive muon lifetime and a determination of the Fermi constant

The mean life of the positive muon has been measured to part-per-million precision using a time-structured beam, a ferromagnetic target, and a fast, multi-segmented and symmetric scintillator detection array. The result, based on data acquired in 2006, is $\tau_{\mu^+} = \unit[2196980.1 \pm 2.6 \pm 1.9]{ps},$ where the first uncertainty is statistical and the second is systematic. When combined with the measurement based on our 2007 dataset, the average is $\tau_{\mu^+}^{\rm avg} = \unit[2196980.3 \pm 2.8]{ps}$ and the derived value for the Fermi constant is $G_F = \unit[1.1663818 (8) \times 10^{-5}]{GeV^{-2}}$. This thesis describes the motivation for the measurement, the experimental technique, the data analysis, and the systematic uncertainties for the 2006 dataset