4.1 Experimental Technique
The proposed experiment at PSI, the pion beta decay experiment, is designed
with the aim of making a precise determination of the pion beta decay rate. The
experimental method is chosen such as to achieve an overall level of
uncertainty in the range of 0.5% which would be a considerable improvement of
the present experimental uncertainty of 4%. To reach this goal, a total
systematic error of 0.3% and a statistical error of 0.4% must be achieved. As
can be seen from the previous experiments (see section 3.1) the systematic
error is composed of the errors for the efficiency of the p b
event detection and for the normalization on the absolute number
N p of decaying pions. It seems very hard to determine
these parameters with the quoted precision. A way around this problem of
absolute normalization and efficiency determination is a measurement of the
pion beta decay rate relative to the decay rate of
p ->e+ n e, which is known with high
precision (see Table 3.1). The positrons and photons from pion beta decay
produce similar showers, therefore the differences in detection efficiency for
the two processes are small and manageable. This allows a measurement of the
pion beta decay rate without the absolute knowledge of acceptances and
conversion efficiencies for both processes.
Experimentally, the branching ratio for the pion beta decay is given by
(4.1)
where R p e n and
are given in Tables 3.1 and 3.2, N p b and
N p e n are the numbers of p b and
p e n events, respectively. The corrections are ratios, for the two
processes, of the following quantities :
* Detection efficiencies
* Live time corrections
* Low energy tail corrections
* Instrumental inefficiencies
These correction factors differ from unity only by a few percent. By
calculating and measuring the associated errors, the overall systematic
uncertainty can be reduced to the proposed value of about 0.3%.
In order to achieve a statistical error of 0.4%, N p b
= 6·104 events need to be accumulated, a factor of 60 more than
detected in the previous experiment [McFa 85]. This requires a large solid
angle detector capable of handling high event rates. Assuming a detection
efficiency [epsilon] p b = 0.5[4], the number of stopped pions required is
.
(4.2)
Assuming a p + stopping rate of 106 p /s,
eq. (4.2) corresponds to 1.2·107s of beam time. The
availability of the PSI proton beam per week is about 75% of 152 hours which
corresponds to about 4·105 s/week. Thus the total required beam
time to achieve the attempted statistical precision is about 30 weeks.
[4] Includes the solid angle coverage of the
apparatus and the sensitive time gate (10...85ns after pion stop) for detecting
PIBETA events.