Study of Rare Pion and Muon Decays with the PIBETA Detector

The PIBETA detector at PSI is used to study the signals and backgrounds to rare pion and muon decays. We report the measured decay rates for \pi^+\to e^+\nu\gamma, \mu^+\to e^+\nu\nu\gamma, and \mu^+\to e^+\nu\nu e^+e^- processes, and discuss the effectiveness of the PIBETA detector in testing the limits for the lepton-family-number non-conserving muon decays. The extracted branching ratios are based on the statistics of 3.5\cdot 10^12 stopped \pi^+’ s collected in 1999 with pion beam intensities between 5\cdot 10^4\, \pi^+/s and 1\cdot 10^6\, \pi^+/s.