#
8. Conclusion

This work has introduced the physics of the study of the decay
p ^{+}-> p ^{0}e^{+} n _{e} which is a
fundamental manifestation of the weak interaction. With the use of the just
assembled PiBeta detector the determination of its decay rate should be
achievable to 0.5% precision. Such a result will produce a critical test of the
standard model, since the theoretical calculation of the pion beta decay rate
relies on the hypothesis of the universality of the weak interaction and
unitarity of the CKM matrix. Also the detector and the considerations for its
layout have been reported.
The steps necessary to achieve good energy resolution, namely optimization of
the light yield and making the scintillator crystals uniform, as well as their
quality control have been discussed. Results obtained with a Monte-Carlo
simulation of the detector and their comparison to measurements were reported.
The angular resolution of the detector was found to be
3.6°±0.2°. On top of a track reconstruction an algorithm was
developed in order to decide about the origin of the particle(s) producing the
shower(s). With the help of this algorithm the branching ratio for radiative
pion decays in the low energy region was determined. For photons of 5 MeV
emitted with an angle of at least 20° relative to the positron the
probability was found to be (2.9±1.2)*10^{-6} which is in good
agreement with the calculated value of 2.7*10^{-6}.
After another beam period, where a liquid hydrogen target was used to produce
photons via p N-interactions, the Panofsky ratio *P* was obtained. The
analysis of the after necessary cuts well-separated photon distributions
resulted in 1.546±0.010 for *P*. Using the weighted average of the
published Panofsky ratio values, the isovector p N scattering length
*b*_{1} amounts to ^{-}0.085±0.002 inverse pion masses.