Maximum Likelihood Analysis in the PEN Experiment

The experimental determination of the $\pi^ + \to e^+\nu(\gamma)$ decay branching ratio currently provides the most accurate test of lepton universality. The PEN experiment at PSI, Switzerland, aims to improve the present world average experimental precision of $3.3 \times 10^{-3}$ to ~$5 \times 10^{-4}$ using a stopped beam approach. During runs in 2008-10, PEN has acquired over $2 \times 10^{7}$ $\pi_{e2}$ events. The experiment includes active beam detectors (degrader, mini TPC, target), central MWPC tracking with plastic scintillator hodoscopes, and a spherical pure CsI electromagnetic shower calorimeter. The final branching ratio will be calculated using a maximum likelihood analysis. This analysis assigns each event a probability for 5 processes ($\pi^ + \to e^+\nu$, $\pi^ + \to \mu^+\nu$, decay-in-flight, pile-up, and hadronic events) using Monte Carlo verified probability distribution functions of our observables (energies, times, etc). A progress report on the PEN maximum likelihood analysis will be presented.