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}$)\pm 0.00011(\eta)$,wherethelastuncertaintyarisesfromthecorrelationbetween$\rho$andthedecayparameter$\eta$,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 $0.99524 < P_\mu^\pi\xi \leq \xi < 1.00091$at90$P_\mu^\pi$ 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.