The objective of the first two chapters is the discussion of the scientific motivation for the pion beta decay experiment currently under way at the Paul Scherrer Institute in Switzerland. The explanation of some basic physics concepts will lay a firm foundation for the full understanding of the motivation for the experiment. These include the V-A structure of the weak interaction, the Conserved Vector Current hypothesis (CVC), the quark-lepton universality, the unitarity of the quark mixing matrix and the superallowed Fermi decays. Chapter 1 begins with the Dirac equation for the electron, and introduces the helicity and chirality operators as a prelude for the discussion on the V-A structure of the weak interactions. The CVC hypothesis is introduced by an analogy with electromagnetic interactions which conserve the electric charge. An alternative formulation of CVC is given using isospin and assuming that the electromagnetic isovector current and the weak vector current are different components of the same isospin current. Cabibbo universality is introduced next with some of its implications, especially the unitarity test of the Cabibbo-Maskawa-Kobayashi (CKM) quark mixing matrix. Finally, the superallowed beta decays are discussed as a particular type of nuclear beta decays involving only vector interactions. It is generally believed that if the CVC hypothesis is true, the vector coupling constants extracted from different superallowed Fermi decays would be the same after the necessary correction factors are accounted for. This universal vector coupling constant and the muon decay coupling constant give one element of the CKM matrix which, combined with the accepted values of some other elements of the matrix, allows a test of unitarity. The extent to which the unitarity test is satisfied places constraints on new physics beyond the Minimal Standard Model of elementary particles.
In chapter 2, the current state of nuclear beta decay and neutron beta decay data is presented. In particular, it is shown that a discrepancy between the nuclear decay data and the neutron decay data justifies a new precision measurement of the pion beta decay rate from which the vector coupling constant can also be extracted. In fact, the pion beta decay, proceeding solely via vector interactions, is similar to pure Fermi nuclear beta decays without the difficulties of nuclear corrections and screening effects. Therefore, the pion beta decay constitutes the most direct test of CVC. The previous experimental measurements of the pion beta decay rate are described in conjunction with the limitations in using their results to check some of the physical concepts presented above. Together, the first two chapters provide the motivation for this new precision experiment whose design and calibration are the subject of this thesis.
A description of the Ring accelerator at the Paul Scherrer Institute as it relates to the experiment is presented in chapter 3 along with the beam studies that have been conducted to date. Specifically, the beam particle rates, contaminations, profiles and spot size are discussed. After the explanation of the motivation and the description of the pion beam, a thorough description of the decay channels of the pion with the associated kinematical information is given in chapter 4. Chapter 5 begins with a general overview of the experiment followed by a description of the salient components of the apparatus together with the scientific justification of their design.
The design of the calorimeter is presented in chapter 6. There, the modularity of the shower calorimeter as a result of a geodesic triangulation is explained. In addition, a discussion on the choice of the calorimeter thickness and material is presented. In chapter 7, the experimental approach is described. The choice of the decay technique and the method of measurement are explained. The calculations of the systematic uncertainties (associated with the experimental technique) and the level of these uncertainties are also discussed. These calculations were carried out using three independent shower simulation codes, and their results showed remarkable agreement after optimization of the codes. In addition, the choice of the calorimeter granularity and the design of the event triggers are discussed. Finally, the procedure for testing the calorimeter crystals prior to assembly is presented.
In chapter 8, detector performances and calibration are discussed. First, the
active target and its performance in beam are presented. Second, the surface
treatments of the calorimeter modules as they affect the light output and light
collection uniformity are also discussed. Next, the cosmic ray tomography system
whose aim is to measure the light collection non-uniformity within the volume
of each of the calorimeter modules is described and some of its results
presented. Finally, the performance and calibration of the calorimeter are discussed.
In the concluding chapter, the current state and the outlook of the experiment are
described.