Neutral-pion decay into an electron-positron pair: A review and update

This work aims to review several aspects of the current status of the rare $\pi^0\to e^+e^-$ decay. A particular emphasis is made on radiative corrections and detailed interpretation of related quantities, some numbers appearing in the literature are updated, and the connection with the Dalitz decay, $\pi^0\to e^+e^-\gamma$, is discussed. This comes timely as it is aligned with an announcement of a preliminary result of a new branching-ratio measurement done by the NA62 Collaboration, which brings new light into an earlier-reported discrepancy between the Standard Model prediction and the (until-recently latest) precise KTeV result.