A Measurement of the Michel Parameters ρ and ƞ in Leptonic Tau Decays

This thesis describes a precise measurement of the Michel parameters ρ and ƞ using the leptonic tau decays recorded by the CLEO II detector. These measurements can be used to provide limits on the non-(V - A) contributions to the Lorentz structure of the charged weak interactions in tau decays. The electronic decay of the tau lepton, τ → evv, is used to measure the spectral shape Michel parameter: ρε = 0.732 ± 0.014 ± 0.009, where the first error is statistical and the second systematic. This measurement is extracted from the electron energy spectrum; the energy spectrum is insensitive to the low energy spectral shape Michel parameter ƞε, and thus insensitive to the presence of scalar couplings. The muonic decay mode of the tau lepton, τ → µvv, is used to measure both the spectral shape Michel parameters: ρµ = 0.747 ± 0.048 ± 0.044 and ƞµ = 0.010 ± 0.149 ± 0.171 simultaneously. Once again, the first errors are statistical and the second systematic. The two parameters are strongly correlated; the correlation coefficient Cρƞ is 0.949. Assuming lepton universality of the vector-like couplings, the two leptonic decay modes are simultaneously analyzed to improve the measurement of the ƞ parameter. Since the electron mode is insensitive to the ƞ parameter, we can measure ρ very precisely using the electron mode. This measurement can now be used to constrain the ρ measurement in the muon analysis, and thus obtain: ρεµ = 0.735 ± 0.013 ± 0.008 and ƞεµ = -0.015 ± 0.061 ± 0.062, where the first errors a.re statistical and the second systematic. The correlation coefficient is now reduced to 0.615. These measurements are all more precise than previous measuren1ents; some are more precise than previous world average measurements. No indications for any deviations from the Minimal Standard Model have been found. This measurement of the ƞ parameter provides a lower limit on the charged Higgs mass in the Minimal Supersymmetric Standard Model: mH± > (0.97 x tan β) GeV at the 90% confidence level. This limit is not very interesting unless tan β is very large.