  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.
