decays are of prime importance to the pion beta experiment because, as explained in chapter 7, these events are used for normalization of the pion beta processes. Therefore, the pion beta experiment will not only measure the branching ratio of pion beta events but also that of decays. With twenty-five detector modules, a fraction of the calorimeter () was put together with five overlapping clusters (shown in table ) to make a single arm trigger. The beam line set-up consisted of a 4 cm active degrader (S1), a 5 cm active target (S2) and the box containing the calorimeter modules as shown in figure . A very thin (0.3 cm) plastic scintillator counter was placed in front of the array and used as veto for hadronic processes.
Table: The cluster definitions during the test run of 1994. There was only one supercluster which was the entire array. These definitions were not exactly the same ones presented in section 7.4.3. However, the scheme was the same, i.e., each module was shared at most three times. Electronically, the PMT signals were split the number of times they were shared and sent to the adders where the cluster and supercluster signals were produced with a high and a low discrimination levels.
The stopped pion was defined as the coincidence between the beam counter S0 (see figure 3.6 where S0 is the scintillator counter located behind the lead collimator), the active degrader S1 and the RF, timed appropriately for pion selection: . The stopped pion initiated a delayed pion gate (DG) of 60 ns during which the decays were registered as the coincidences . The signal was the supercluster signal --- with high discrimination level but with the timing of the low discrimination level signal which enabled a good timing resolution and the elimination of some prompt events which might otherwise have slipped into the DG --- obtained as the ``OR'' of the five cluster signals.
Figure: The beam line set-up to measure decays. 116 MeV/c 's traversed the plastic scintillator degrader and stopped within the active target. decays were detected in the array of twenty-five crystals which subtended of solid angle. The concrete shielding and parts of secondary beam channel in the area are also shown. Behind the wooden box of CsI detectors, is the climatization apparatus.
The low and high discrimination levels were set at 3 MeV and 25 MeV respectively. The high discrimination level eliminated a significant fraction of the accidental Michel events and reduced the computer dead time. The absence of the prompt veto, which was provided by the S1 counter, led to the domination of the spectrum by prompt events. The electronic diagram is shown in figure with the trigger for events. However, data were also collected for prompt and Michel processes, in which case the event trigger was modified to and respectively.
Figure: The electronic diagram for the trigger. The upper and lower discrimination levels were 25 and 3 MeV respectively: this meant that of the accidental Michel events were cut away in the trigger. The delayed pion gate was opened 15 ns after a valid pion stop.
As previously mentioned, the endpoint of the Michel spectrum had been used for gain calibration of the CsI detectors, and the prompt events provided a timing calibration and a reliable way to time in various signals. The delayed muon gate DG was also initiated by the stopped pion but delayed by
about 250 ns with respect to the pion stop time.
Table: The rates measured during the taking at an average proton current of . The computer live time was .
As displayed in figure , 250 ns after the pion stop time, the number of events was negligible and the DG was only sensitive to Michel events. The temporal distributions (shown in figure ) of and Michel events are given by the following relations respectively:
where is the rate of pion stops, is the fraction of solid angle subtended by the CsI array, is the delay of DG with
Figure: The experimental arrangement for the study of decays.
respect to the pion stop time (t=0), is the length of the delayed pion gate, and are the mean lifetimes of the pion and muon respectively, and is the branching ratio. Some of the measured rates are compiled in table . The expected trigger rate (102 Hz) was the fraction of with energies above the upper discrimination level of . The rate of in the CsI array was given by equation . The explicit calculation gave , consistent with the on-line observations.
A cut on the energy spectrum of the plastic veto detector in front of the CsI not only eliminated the very energetic hadronic interactions but also some of the double Michel events . The double Michel processes form a broad energy spectrum extending up to with the most probable energy close to the peak. The suppression of these events dictated the need for the two cylindrical MWPC's with double track resolution as explained in chapter 5. However, the test run of 1994 was not equipped with MWPC's. As a result, the measured spectrum shown in figure rides on some double Michel background which was not cut away by the plastic veto detector alone. The reduction of the beam intensity by a factor of three resulted in an additional suppression of the double Michel events by a factor of ten.
The measured spectrum is well separated from the Michel background and the resolution could be improved by compensating for the energy dispersion in due to the energy losses of the positrons in the target and the plastic veto. To that end, two ADC inputs were implemented for the target S2 and the degrader S1. One of the ADC inputs was in time with the trigger while the other was delayed. The delayed ADC inputs measured the charge which preceded the pulse in time with the trigger and allowed full energy reconstructions in S1 and S2 signals. The energy scales for the degrader and the target were absolutely calibrated using the measured peak positions of the light outputs in S1 and S2 and the expected energies deposited in these counters by the beam positrons, muons and pions. Electron equivalent energies [Mad-78] were used in the calibration for muons and pions. For the degrader S1, the fully reconstructed energy was used to identify the beam particle which preceded the event. On the other hand, for the target S2, the reconstructed energy was used to identify the Michel events from decays as shown in figure : in fact, the cascades were expected to deposit an additional 4.118 MeV in the target relative to the events due to muon stops.
Figure: The separation between Michel decays and the events. The mean energy of the Michel events in the target is higher by than that of the events due to the 4.118 decay muons.
Therefore, the correlations between the full target energy and (triggered on one of the crystals for better energy resolution and cut on positrons in the plastic veto detector) revealed two groups of particles with one group having --- this result is obtained from the absolute calibration and the energy distribution of the active target cut on Michel and events in the CsI array --- more than the other group in S2.
Figure: The measured pion decay curve versus expectation (dashed line).
The expected light output from the 4.118 MeV muons in target was in agreement with measurement.
The goal of the test was to measure the response of the calorimeter to decays. In that respect, the test run was very instructive and encouraging. The result of figure shows a clean separation between the Michel and the events. The resolution will certainly be improved with the elimination of the double Michel events using MWPC's with good double track resolution. From the measurements of the responses of the array to monoenergetic positrons, electrons, and decays, it can be concluded that the pion beta shower calorimeter, operated under controlled temperature and humidity and equipped with excellent CsI modules with good surface treatment, is capable of detecting decays with good energy and timing resolutions which are necessary to isolate this process from the background. The other reaction of interest to the pion beta experiment is the pion beta decay. This process ultimately produces two photons of which are expected to be detected in the shower calorimeter. It has therefore been necessary to check the response of the calorimeter to photons of similar energies. Such photons were produced during the test run of 1994 via the charge exchange reaction , and the data are currently being analyzed.
With the number of decays measured and the number of pions stopped in target, an estimate of the branching ratio can be made. It should be stressed that the measurement of the branching ratio was not the goal of the test run and as a result, the experiment was not fully equipped for a precise determination of . Of the particles stopped in the target, were pions and decays were registered in the array. Taking into account the fraction of solid angle subtended by the array, the fraction of pions still alive at the time the delayed pion gate is opened (0.56), and correction factors such as the computer live time (), positron annihilation , shower backsplash , and the veto inefficiency , the estimated branching ratio is .