Precision muon decay measurements and improved constraints on the weak interaction

The TWIST Collaboration has completed its measurement of the three muon decay parameters $\rho$, $\delta$, and $P_{\mu }\xi$. This paper describes our determination of $\rho$, which governs the shape of the overall momentum spectrum, and $\delta$, which controls the momentum dependence of the parity-violating decay asymmetry. The results are $\rho =0.74977\pm 0.00012(\mathrm{stat})\pm 0.00023(\mathrm{syst})$ and $\delta =0.75049\pm 0.00021(\mathrm{stat})\pm 0.00027(\mathrm{syst})$. 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 $\rho$, $\delta$, and $P_{\mu }\xi$ 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.

Figure 1

Conceptual drawing of the TWIST spectrometer. It shows the superconducting solenoid within the steel yoke, with the drift chambers and proportional chambers symmetrically placed upstream and downstream of the central stopping target.

Figure 2

A cross section of the TWIST detector, including an example event of a downstream decay. PCs provide timing information and DCs determine the position of particles. The angle between the decay positron and the $z$ axis, defined along the beam direction, is $\theta =\pi -{\theta }_s$. The muon polarization direction is opposite to that of the $z$ axis.

Figure 3

Residuals normalized by the statistical uncertainty from the muon decay parameters fit between simulation and data. Only bins with their center contained in the fiducial regions are used in the fitting procedure.

Figure 4

Measurement of the angle-dependent momentum mismatch at the decay positron kinematic end point for set 84, taken with the Al target under nominal conditions.

Figure 5

Integrated $\Delta \theta$ distributions for the silver target module in data and simulation.

Figure 6

Integrated momentum loss $(\Delta p)|\cos \theta |$ distributions for the silver target module in data and simulation. The right panel shows the distribution of high momentum loss events, due primarily to bremsstrahlung. The discontinuity between the two panels is because of the change in bin size.

Figure 7

Number of events with two tracks versus the momentum difference between the two reconstructed tracks. The left-hand side shows nominal data set 74 and the corresponding simulation. The right side shows nominal and exaggerated simulations. The bottom plots correspond to the ratio of the two distributions above.

Figure 8

Distributions of number of muon tracks ending in a wire plane, versus plane number (top panel), normalized to number ending in PC 6 (plane number 28), for different data and simulation conditions. The bottom panel shows the differences of selected pairs of distributions.

Figure 9

Results of the $\rho$ and $\delta$ measurement for each data set, fitted separately for the Ag sets (left panels) and for the Al sets (right panels). Only statistical uncertainties are shown here.

Figure 10

Summary of the central values and total uncertainties of $\rho$ and $\delta$ from this analysis, along with the previous published measurements [6, 7, 8, 38, 39].