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 $\rho =0.75014\pm 0.00017(\mathrm{stat})\pm 0.00044(\mathrm{syst})\pm 0.00011(\eta )$, where the last uncertainty arises from the correlation between $\rho$ and the decay parameter $\eta$, and $\delta =0.75067\pm 0.00030(\mathrm{stat})\pm 0.00067(\mathrm{syst})$. 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 $0.99524<P_{\mu }^{\pi }\xi \le \xi <1.00091$ 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.

Figure 1

Side view of the upstream half of the TWIST spectrometer planar chambers and support structures. Muons stopped in the target foil, which also served as a chamber cathode. The use of precision spacers and tension control ensured that the chamber wire positions were known to $30\mu \mathrm{m}$ in $z$. The spectrometer is symmetric about the target foil.

Figure 2

Reconstructed muon decay spectrum.

Figure 3

Uncalibrated data and simulation histograms in the momentum range of the decay spectrum used for energy calibration, for $-0.53<\cos \theta <-0.50$.

Figure 4

A reconstructed muon decay spectrum; the dot density is proportional to the number of positron tracks reconstructed in a $(p,\cos \theta )$ bin. The outlines show the fiducial region used for this analysis.

Figure 5

Momentum distribution of accepted events, centered stops data set. Deviation from the shape of Eq. (4) below $28\mathrm{MeV}/c$ and above $45\mathrm{MeV}/c$ comes from the acceptance constraint shown in Fig. 4. The lower plot shows the difference between data and fit for each bin, normalized by the statistical uncertainty in the difference.

Figure 6

Decay asymmetry of accepted events, centered stops data set. The lower plot shows the difference between data and fit for each bin, normalized by the statistical uncertainty in the difference.

Figure 7

Energy loss distributions for positrons across the target region (Al and PCs), showing events with small losses and integrated over the fiducial region.

Figure 8

As Fig. 7, for large energy losses.

Figure 9

Scattering angle distributions for positrons across the target region (Al and PCs), showing events with small angle scatters and integrated over the fiducial region.

Figure 10

As Fig. 9, for large angle scatters.

Figure 11

Difference between reconstruction efficiencies between data and simulation (MC) within the fiducial region as a function of momentum, for the upstream half of the detector. The difference for the downstream half is similar.

Figure 12

Difference between reconstruction efficiencies between data and simulation (MC) within the fiducial region as a function of $\cos \theta$, for the upstream half of the detector. The difference for the downstream half is similar.

Figure 13

$R_{\delta }$ as a function of delta ray cross section multiplier. Open circles are simulation; standard simulation corresponds to a multiplicative factor of 1. The linear fit was used to determine an effective multiplier for the data (dashed line). Error bars are shown but are vanishingly small.

Figure 14

$R_B$ as a function of bremsstrahlung cross section multiplier. Open circles are simulation; standard simulation corresponds to a multiplicative factor of 1. The linear fit was used to determine an effective multiplier for the data (dashed line). Error bars are shown but are vanishingly small.