A Precision Measurement of the Muon Decay Parameters $ρ$ and $δ$
The TWIST collaboration has performed new measurements of two of the parameters that describe muon decay: $ρ$, which governs the shape of the overall momentum spectrum, and $δ$, which governs the momentum dependence of the parity-violating decay asymmetry. This analysis gives the results $ρ=0.75014\pm 0.00017(\text{stat})\pm 0.00044(\text{syst})\pm 0.00011(η)$, where the last uncertainty arises from the correlation between $ρ$ and the decay parameter $η$, and $δ= 0.75067\pm 0.00030(\text{stat})\pm 0.00067(\text{syst})$. 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 $P_μ^πξ$ of $0.99524 < P_μ^πξ\leq ξ< 1.00091$ at 90% confidence are determined, where $P_μ^π$ is the polarization of the muon when it is created during pion decay, and $ξ$ 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.