$\mu d$ formation

The process $\mu p + d \mbox{$\rightarrow$}\mu d + p$ can be experimentally monitored by

1. observation of diffusion of the $\mu d$ atom
2. observation of the $p\mu d$ fusion channel going to

Figure 19: Display of a typical $\mu d$ diffusion event seen in the y-z plane. Such events can be readily fished out, since the backtracking vector misses the point of expected muon decay (=$\mu$ stop + elapsed lifetime seen by the scintillators below) by several cm. Note the long muon lifetime (10 $\mu s$ in this example) which is typical for such events!

Fig. 19 shows a typical event from our 1999 run where only natural hydrogen (c$_d$ = 140 ppm) was used. Under this condition, $\mu^-$ transfer to deuterium occurs at a rate of $\sim$5% and is found quite easily, while in $\mu^+$ runs it is absent. The number of muon diffusion events at well defined conditions is - after a proper calibration is made - a direct measurement of c$_d$. Details of the $\mu d$ diffusion distribution and the procedures which we will use to calibrate it are shown below (chapter 5.4.3).

Fig. 20 shows the result of a $\mu d$ diffusion search in data from our test runs. These are plots of diffusion distance versus decay time. The outlying points in the left image are from the diffused $\mu d$ atoms in a $\mu^-$ run. For reference only a single event at t=0 leaks through in a $\mu^+$ run shown on the right. The amount of these outlying events will allow us to accurately calibrate the amount of deuterium in the runs and to check our models of the $\mu d$ distribution. Note that in these analyses an approximately 95% efficient TPC electron tracking algorithm was used to eliminate events where an electron track was found near the $\mu$-stop even though the wire chamber tracking pointed several cm away. For this reason it is important that we have reasonable electron efficiency in the TPC but do not need 100%.

Figure 20: Tracked $\mu d$'s from test runs, $\mu^-$ events (left) $\mu^+$ events/background study (right).

Several clean candidates of process 2) were observed in the TPC during special runs using 3 hardware thresholds. More statistics of these events will be collected during future test runs, which is necessary to judge whether sufficient background suppression is achievable at the level of 1 ppm deuterium anticipated for the final run.