Waveform Analysis for a Precision Pion Decay Measurement

The PEN experiment aims to measure the $\pi^+$ $\rightarrow$ $e^+\nu(\gamma)$ ($\pi_{\rm e2}$ decay) branching ratio at PSI, with an uncertainty of $\Delta B/B \simeq 5\times 10^{-4}$, or better, using a large-angle detector system featuring a pure CsI calorimeter. A critical element of the data analysis requires distinguishing $\pi\to$ $e \nu$ events from the $\pi\to\mu\to e$ decay chain. A digitized waveform for a large subset of pion decay events must be reliably sorted into one of the two categories in order to reveal the low-energy ``tail'' of the calorimeter response to the $\pi_{\rm e2}$ 69\,MeV $e^+$'s, otherwise masked by the muon decay positrons. Most events contain pulses which overlap. An analysis program was designed to distinguish between the different decay types with a high resolution extraction of closely spaced peaks. The peak to peak (or overlapping pulse) separation methods and their relative merits will be discussed.