The Systematics of the PEN experiment, A Precision Measurement of Pion Electronic Decay Branching Ratio

The ratio of decay rates $\Gamma(\pi\rightarrow e\bar{\nu}(\gamma))/\Gamma(\pi\rightarrow \mu \bar{\nu}(\gamma))$ provides a key confirmation of the V$-$A nature of the electroweak interaction. Currently, the experimental value of this ratio is $R^{\text{exp}}_{e/\mu}= (1.2327 \pm 0.0023)\times 10^{-4}$, whereas the theoretically determined value according to Standard Model physics is $R^{\text{SM}}_{e/\mu}= (1.2356 \pm 0.0001)\times 10^{-4}$.  This ratio proves one of the most sensitive tests for lepton universality and can be used to give bounds on non V$-$A physics. For this reason, the PEN collaboration performed a precision measurement of the $\pi^+\rightarrow \text{e}\nu_\text{e}(\gamma)$ branching ratio with the goal of obtaining a relative uncertainty of $5\times 10^{-4}$ or better. The PEN detector consisted of an active target and beam counters, a mini-time projection chamber, 2 cylindrical multi-wire proportional chambers, a plastic scintillating hodoscope, and a spherical 240 module pure CsI calorimeter. Precise descriptions of decays in flight, chamber efficiencies, Monte Carlo acceptances, and the shape of CsI calorimeter low energy tail, the biggest systematic challenge, are required for determination of the branching ratio.  These issues will be discussed.