Measurement of the parameter ${\xi }^{\prime \prime }$ in polarized muon decay and implications on exotic couplings of the leptonic weak interaction

The muon decay parameter ${\xi }^{\prime \prime }$ has been determined in a measurement of the longitudinal polarization of positrons emitted from polarized and depolarized muons. The result, ${\xi }^{\prime \prime }=0.981\pm 0.045_{\text{stat}}\pm 0.003_{\text{syst}}$, is consistent with the Standard Model prediction of unity, and provides an order of magnitude improvement in the relative precision of this parameter. This value sets new constraints on exotic couplings beyond the dominant $V\text{−}A$ description of the leptonic weak interaction.

Figure 1

Variation of the enhancement factor $k(P_{\mu },x,\cos \theta )$ as a function of the positron emission angle, $\theta$, for three values of the reduced energy $x$. Upper panel: for $P_{\mu }=0.95$. Lower panel: for $P_{\mu }=0.10$.

Figure 2

Vertical profile of the $\pi \mathrm{E}3$ beam line at the Paul Scherrer Institute showing the quadrupoles, the dipoles, and the Wien filter.

Figure 3

General view of the three magnets that are assembled into the spectrometer. The filter accepts only high energy decay positrons, stopping the remainder. The tracker is used for energy analysis, and the lens transports the positrons to the polarimeter (Fig. 6). The red lines are tracks for $50\mathrm{MeV}/c$ positrons generated via Monte Carlo simulation and the blue lines are secondary particles. The arrow on the implantation target shows the average direction of the muon polarization.

Figure 4

Front view of the arrangement of four SSDs on the frame of one of the three planes of detectors located inside the tracker (Fig. 3). The boards with the front-end electronics were connected perpendicular to these planes.

Figure 5

Typical normalized positron energy spectra as deduced from the momentum measurement with the SSD located inside the tracker magnet for positrons transmitted through the spectrometer. The distributions correspond to muons implanted in the Al target (left curve) and S target (right curve). The full circles are for positrons that underwent Bhabha scattering in the polarimeter and the open circles for positrons that annihilated in flight. The solid lines show calculated shapes assuming muon polarizations $P_{\mu }^{\mathrm{Al}}=0.937$ and $P_{\mu }^{\mathrm{S}}=0.382$.

Figure 6

Top view of the positron polarimeter with tracings of a scattering event occurring in the first magnetized foil of the Vacoflux foil loop. The plastic scintillators (in red) PS1 and PS2 detect incoming positrons, while the hodoscope scintillators HOD-X and HOD-Y in coincidence with the segmented BGO determine the scattering type. The MWPC are labeled (1)–(5). The Vacoflux foil loop mounted around the yoke provides polarized electrons ($P_e$).

Figure 7

Front view of the hodoscope and the calorimeter showing the position of the scintillator detectors: HOD-X (in green), HOD-Y (in red) and top and bottom cosmic rays telescopes (in black) relative to the hexagonal front face of the BGO modules of the calorimeter (in magenta).

Figure 8

Two-dimensional distribution of events selected by the AIF trigger plotted as a function of the measured $\cos \varphi$, where $\varphi$ is the angle between the two photons in the laboratory system and of the ratio $E_1/E_2$ between the smallest and the largest energies of the photons. The sweeping distribution at the left corresponds to AIF events following Eq. (8). The line shows the cut limit applied to both AIF and BHA events.

Figure 9

Experimental superratios, Eq. (9), for the two targets and the two orientations of the scattering foils as a function of the positron energy for AIF (upper panel) and BHA (lower panel). The dotted lines show the values of the function $\phi (A_{i,\alpha }^{\pm })$ which is the superratio calculated from the analyzing power assuming a positron polarization $P_L=1$ (Sec. 4f). The solid lines correspond to the fit of the superratios (Sec. 4h).

Figure 10

Calculated analyzing powers $A_{i,\alpha }^{-}$, corresponding to the negative magnetization current, as a function of the positron energy for AIF events (upper panel) and BHA events (lower panel). The open (closed) circles are for events from scattering foil 1 (2). The values for the positive magnetization current, $A_{i,\alpha }^{+}$, have a similar trend but with opposite signs and are not shown.

Figure 11

Energy dependent part of the enhancement factor in Eq. (21) as deduced from the rates of AIF events (upper panel) and BHA events (lower panel) selected for the eight $\alpha$ configurations presented in Fig. 9. The enhancement factors for the two magnetization currents were averaged. The dotted lines between the points are to guide the eye.

Figure 12

Distribution of residuals normalized to their statistical error as obtained from a fit of the superratios by a function with nine free parameters. The red curve is the fit of the residuals by a normal distribution.

Figure 13

The values of $\mathrm{\Delta }$ with their errors obtained after inversion of Eq. (23) for AIF events (upper panel) and BHA events (lower panel). The band delimited by the dotted lines indicate the $\pm 1\sigma$ interval of the fitted value of $\mathrm{\Delta }$.

Figure 14

Measurements of the decay parameter ${\xi }^{\prime \prime }$ as a function of the year of publication.

Figure 15

Constraints at 90% C.L. on exotic couplings $g_{RL}^T$ and $g_{RL}^V$ obtained from the present experiment (solid green curve), assuming $g_{RR}^V=g_{RR}^S=g_{RL}^S=0$, and compared to the current limits (dashed red lines).

Figure 16

Constraints at 90% C.L. on exotic couplings $g_{RL}^T$ and $g_{RL}^S$ obtained from the present experiment (solid green curve), assuming $g_{RR}^V=g_{RR}^S=g_{RL}^V=0$, and compared to the current limits (dashed red lines).