Beam particle tracking with a low-mass mini time projection chamber in the PEN experiment

The international PEN collaboration aims to obtain the branching ratio for pion electronic decay $\pi^+ \to e^+\nu_e(\gamma)$, aka $\pi_{e2}$, a relative precision of $5\times 10^{-4}$ or better. apparatus comprises number detection systems, all contributing vital information event reconstruction. This paper discusses design, performance, and Monte Carlo simulation mini time projection chamber (mTPC) used pion, muon, positron beam particle tracking. We also review use extracted trajectory coordinates in analysis, particular constructing observables critical discriminating background processes, maximizing fiducial volume target which vertices can be accepted extraction without introducing bias.