Global pile-up free spectra

Fig. 13 shows results on the lifetime fit from our last experiment. The runs were sorted in consecutive groups according to time, beam conditions, target fillings etc. The lower figure for $\mu ^{-}$ gives consistent results for all counters within run groups. The behavior of the observed $\lambda$ is consistent with the decline of the target purity with time and purity recovery by refilling. The $\mu ^{+}$ spectra show a significant discrepancy between lower and upper electron telescope and a poor reduced $\chi ^{2}$ . This behavior is much improved in the up/down sum spectrum.

**Figure 13:** Results for lifetime fits for different run groups of the run in April 2000. Results are given in deviation $\Delta \lambda /\lambda _{0}\protect$ of the measured decay rate from the PDG value for $\lambda _{0}$ . Negative values correspond to increased decay rate. Filled points correspond to the results for the lower electron telescope, the upper electron telescope and the sum of both (from left to right). Open circles denote the fit's reduced $\chi ^{2}/50\protect$ .
$\resizebox*{0.7\textwidth}{0.4\textheight} {\includegraphics{stat.eps}}$

A closer look at the time spectra (Fig. 14) reveals that this effect is due to $\mu ^{+}$ SR. The observed frequency over the runs is consistent with muonium precession in a magnetic field of 0.2-0.4 G. Some variation of this field value suggest the contribution of stray fields in addition to the earth magnetic field. The deviation of 10 $^{-3}$ of the sum fit from $\lambda _{0}$ is not inconsistent with the expected effect of free muons which can be estimated based on the observed muonium rotation as

which gives a correction to $\lambda _{0}$ of some 10 $^{-3}$ , using $\alpha \approx 0.1$ and $\omega _{\mu }\approx 0.015$ . Thus either a rather careful matching of upper and lower counter or fitting is required to reduce this effect. In our final setup we will keep the $\mu ^{+}$ SR effect under control by applying an external magnetic field of 70 Gauss to define the field direction and precession frequency.

**Figure 14:** Time spectra for $\mu ^{-}$ (left) and $\mu ^{+}$ (right) of global pileup free data set. Binwidth 200ns. Lower rows show deviations from a pure exponential fit for $\mu$ selection by external beam telescope (second row) and muon tracking (third row). For $\mu ^{-}$ the initial spike due to wall stops disappears in row three, for $\mu ^{+}$ the precession signal is evident.
$\resizebox*{0.7\textwidth}{0.4\textheight} {\includegraphics{time.eps}}$

The accidental to signal level for pile-up free spectra is already $\sim 10^{-4}$ for a simple coincidence between a MWPC and electron telescope. It can be further improved by using the 4 MWPC's above the TPC to precisely track the decay electron back to the end of the muon track. This and tracking the muon to the proper entrance wire reduce our backgrounds to around 10 $^{-5}$ , see Fig. 15.

**Figure 15:** Time distribution of fully tracked $\mu$ -e events with global pile-up protection. The accidental level is below 10 $^{-5}$ of the good signal at time 0.
$\resizebox*{0.5\textwidth}{0.3\textheight} {\includegraphics{e1_pu_xyz.eps}}$