Discrimination of Rare $\pi^+$ and $\mu^+$ Decays at Rest Using Artificial Neural Networks

PEN, a new experiment aiming to measure the $\pi^+\to e^+\nu$ decay branching ratio ($\pi_{e2}$) with a relative uncertainty of $\sim 5\cdot 10^{-4}$ is being mounted at the Paul Scherrer Institute ring accelerator. The PIBETA detector was upgraded with new active degrader and fast active target detectors. Low-momentum $\pi^+$ beam tunes in the range 72-80\,MeV/c were developed producing stopping rates of up to 20k\,$\pi^+$/s. Beam detector PMT waveforms were recorded with a 2\,GHz/10 bit Acqiris digitizer. The ``system waveform functions'' for the stopping $\pi^+$'s and $\mu^+$'s and decaying $e^+$'s were determined from a set of clean Michel events. The $\pi^+\to e^+\nu$ events were distinguished from the copious Michel background using artificial neural network analysis.