A Precision Measurement of the Muon Decay Parameters $\rho$ and $\delta$

The TWIST collaboration has performed new measurements of two of the parameters that describe muon decay: $\rho$, which governs the shape of the overall momentum spectrum, and $\delta$, which governs the momentum dependence of the parity-violating decay asymmetry. This analysis gives the results $\rho=0.75014\pm 0.00017(\text{stat})\pm 0.00044(\text{syst})\pm 0.00011(\eta)$, where the last uncertainty arises from the correlation between $\rho$ and the decay parameter $\eta$, and $\delta = 0.75067\pm 0.00030(\text{stat})\pm 0.00067(\text{syst})$. These are consistent with the value of 3/4 given for both parameters in the Standard Model of particle physics, and are a factor of two more precise than the measurements previously published by TWIST. A new global analysis of all available muon decay data incorporating these results is presented. Improved lower and upper limits on the decay parameter $P_\mu^\pi\xi$ of $0.99524 < P_\mu^\pi\xi \leq \xi < 1.00091$ at 90% confidence are determined, where $P_\mu^\pi$ is the polarization of the muon when it is created during pion decay, and $\xi$ governs the muon decay asymmetry. These results set new model-independent constraints on the possible weak interactions of right-handed particles. Specific implications for left-right symmetric models are discussed.