Studies for the PIENU experiment and on the direct radiative capture of muons in zirconium

The branching ratio of pions decaying to positrons and muons R = (π→eυ + π→eυγ)/(π→μυ + π→μυγ) has been calculated with very high precision in the Standard Model of particle physics. So far, the theoretical value of R = 1.2352(1) x 10-⁴ is 40 times more precise than the current experimental value of R = 1.230(4) x 10-⁴. To test this variable with respect to deviations from the Standard Model, the experimental precision needs to be improved, which is why the PIENU experiment aims at a precision of less than 10-³, i.e. an improvement of an order of magnitude over the current precision. At this level, mass scales ∼ TeV/c² can be probed for evidence of new pseudo-scalar interactions. The data collected with the experimental setup also allows for a search of sterile neutrinos. When determining the branching ratio, various systematic corrections are applied. The largest among these is due to electro-magnetic shower leakage out of the calorimeters and radiative decays. It was calculated to be (2.25 ± 0.06) % in this thesis. In the second part of the thesis, an experiment on the direct radiative capture of muons in zirconium is described. One theoretical extension to the Standard Model involves a new light and weakly interacting particle in the muon sector which does not conserve parity. This can be studied experimentally with polarized muons that undergo the direct radiative capture into the 2S state of a medium mass target nucleus. During this capture, longitudinal muon polarization is conserved and the muons instantly undergo the 2S-1S transition emitting a second photon. Studying the angular distribution of this second photon indicates whether or not the process is parity violating, which would manifest physics beyond the Standard Model. The direct radiative capture of a muon into an atom in the 1S or 2S state has not been observed yet. Therefore, data was taken in 2012 to study the radiative capture of muons in zirconium. The analysis method of this data set is described with a blind analysis technique.Science, Faculty ofPhysics and Astronomy, Department ofGraduat