Search for two body muon decay signals

Lepton family number violation is tested by searching for ${\mu }^{+}\to e^{+}{X}^0$ decays among the $5.8\times {10}^8$ positive muon decay events analyzed by the TWIST collaboration. Limits are set on the production of both massless and massive $X^0$ bosons. The large angular acceptance of this experiment allows limits to be placed on anisotropic ${\mu }^{+}\to e^{+}{X}^0$ decays, which can arise from interactions violating both lepton flavor and parity conservation. Branching ratio limits of order ${10}^{-5}$ are obtained for bosons with masses of $13–80\mathrm{MeV}/{\mathrm{c}}^2$ and with different decay asymmetries. For bosons with masses less than $13\mathrm{MeV}/{\mathrm{c}}^2$ the asymmetry dependence is much stronger and the 90% limit on the branching ratio varies up to $5.8\times {10}^{-5}$. This is the first study that explicitly evaluates the limits for anisotropic two body muon decays.

Figure 1

Spectrum of decay positron momenta and angles reconstructed from the TWIST spectrometer in bins of $0.01\times 0.5\mathrm{MeV}/\mathrm{c}$. Events used by this analysis are contained within the regions defined by the dashed line.

Figure 2

The distribution of the momentum loss $\mathrm{\Delta }p$ between the momentum of a simulated positron track at the time of decay and its momentum reconstructed from the positron track as a function of $\cos \theta$. This distribution, generated with $30\mathrm{MeV}/\mathrm{c}<p<35\mathrm{MeV}/\mathrm{c}$ is used to model a two body decay signal within that range after applying an offset in momentum. Similar distributions are derived for all other 5 MeV ranges.

Figure 3

Demonstration of the effect of two body decay (TBD) signals on the endpoint. Figure a(b) shows the decay probability for momentum near the endpoint of upstream(downstream) spectra for data and Monte Carlo (MC) simulation with various two body decay signals added. The enhanced sensitivity to $A=1$ decays in the downstream spectrum is clear. Figure c shows a two body decay signal corresponding to a branching ratio, $B=-225\mathrm{ppm}$, in comparison with the uncalibrated difference between data and MC (after the muon decay parameter fit, with no two body decay signal imposed) and the change in the shape of the spectrum produced by the momentum calibration (a $4.3\mathrm{keV}/\mathrm{c}$ offset at $\cos \theta =-3/4$), in the upstream spectrum as determined by the energy calibration fit.a) −0.8 < cosθ < −0.7 b) 0.7 < cosθ < 0.8 c) Signal and Residuals, −0.8 < cosθ < −0.7

Figure 4

Confidence intervals set on branching ratios for ${\mu }^{+}\to e^{+}{X}^0$ decays determined from the muon decay spectrum for signals well separated from the endpoint. Statistical and energy calibration uncertainties are included.

Figure 5

FC confidence intervals determined at the endpoint as a function of the momentum calibration offset. The black dotted line shows the best a priori estimate of the momentum calibration as determined from Table 1.