Measurement of the Eta Parameter in Muon Decay.

The e^{+} momentum spectrum arising from the unpolarized decay mu ^{+}to e^{+}nu _{e}| {nu}_ {mu} has been measured using stopped muons with an axial-focusing, magnetic spectrometer. A comparison of the data to the calculated spectrum between 6.15 MeV/c and 52.83 MeV/c, concentrating on the lower and middle parts of this range, gave a direct value for the eta parameter. The best-fit value, with rho fixed to 3/4, was found to be eta = -0.080 +/- 0.088 (statistical) +/- 0.056 (systematic), which represents a factor of two improvement in error over previous direct determinations. The low-energy part of the spectrum is vulnerable to contamination due to Bhabha scattering and bremsstrahlung of decay e^{+} in the muon-stop counter or other parts of the spectrometer; the systematic error is dominated by uncertainties in the corrections for this. Major sources of error are discussed, which include the calibration of the muon stopping depth in the target; uncertainties in the Bhabha scattering and bremsstrahlung cross sections; approximations in the Monte Carlo simulation of the spectrometer and uncertainties in counter calibrations. Corrections for spectrometer effects were primarily made with an improved version of the scEGS4/ scPRESTA condensed -history Monte Carlo code. Techniques for variance reduction and interpolation were used extensively to reduce computation time. The accuracy of this code and the physics it contains are discussed for the energies relevant to muon decay experiments. Some of the physics effects which could, in principle, cause deviations of the unpolarized spectrum from that predicted by the V-A hypothesis are reviewed in this thesis. First and higher-order radiative corrections to the unpolarized spectrum are also studied.