A study of radiative lepton decays of the Z boson

This thesis is devoted to the analysis of the data collected by the ALEPH detector at the large electron-positron (LEP) particle accelerator at CERN which studies the production and decay of the Z boson. The data was collected between 1990 and 1993 and corresponds to the production of about 1,422,000 Z events. Such a large data sample enables a detailed study of Z -> l+ l- + n photons (n>=1) events to be undertaken, where the aim is to observe physics beyond the standard model which enhances the number of events with an l+ l- + n gamma final states, e.g. compositeness. The thesis focuses on Z -> mu+ mu- + m gamma (m=1 or 2) and Z -> tau+ tau- gamma decays. The analysis of the former decay involves comparing the data with a number of electroweak theoretical predictions. Any discrepancies would indicate the presence of physics beyond the standard model. The latter decay is used to obtain a limit for the anomalous magnetic moment of the tau. The analysis of Z -> mu+ mu- + m gamma events indicates that the Monte Carlo has some inadequacies; it overpredicts the number of events with either low energy photons or photons close to the muons. The data has a small excess in the region of phase space in which physics beyond the standard model is most likely to be observed. This excess is, however, more likely due to the deficiencies of the Monte Carlo. The other theoretical predictions are generally in good agreement with the data and show the necessity of including initial state radiation and s channel photon exchange when considering final states with a detected photon. The standard model prediction for the value of the anomalous magnetic moment of the tau, denoted by F^tau_2(0), is 11773(3)*10^-7. The current experimental limit of F^tau_2(0)<0.0062 does not rule out the possibility that the tau is composite. The analysis of Z -> tau+ tau- gamma events produces the limit F^tau_2(0)<0.051. Whilst this result is worse than the current limit it is based on simpler theoretical assumptions.