Precision muon decay measurements and improved constraints on the weak interaction

The TWIST Collaboration has completed its measurement of the three muon decay parameters $\ensuremath{\rho}$, $\ensuremath{\delta}$, and ${P}_{\ensuremath{\mu}}\ensuremath{\xi}$. This paper describes our determination of $\ensuremath{\rho}$, which governs the shape of the overall momentum spectrum, and $\ensuremath{\delta}$, which controls the momentum dependence of the parity-violating decay asymmetry. The results are $\ensuremath{\rho}=0.749\text{ }77\ifmmode\pm\else\textpm\fi{}0.000\text{ }12(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.000\text{ }23(\mathrm{syst})$ and $\ensuremath{\delta}=0.750\text{ }49\ifmmode\pm\else\textpm\fi{}0.000\text{ }21(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.000\text{ }27(\mathrm{syst})$. These are consistent with the value of $3/4$ given for both parameters in the standard model, and each is over a factor of 10 more precise than the measurements published prior to TWIST. Our final results on $\ensuremath{\rho}$, $\ensuremath{\delta}$, and ${P}_{\ensuremath{\mu}}\ensuremath{\xi}$ have been incorporated into a new global analysis of all available muon decay data, resulting in improved model-independent constraints on the possible weak interactions of right-handed particles.