Experimental study of rare charged pion decays

TL;DR

This paper reviews experimental studies of rare charged pion decays, highlighting their importance for testing fundamental symmetries, understanding pion structure, and comparing experimental results with Standard Model predictions.

Contribution

It provides a comprehensive review of recent experimental data on rare pion decays and discusses the consistency with theoretical models and future prospects for precision improvements.

Findings

Experimental data aligns well with Standard Model predictions.

The measured $ ext{BR}(R_{e/ ext{mu}}^ ext{pi})$ is $(1.2366 imes 10^{-4})$.

Experimental precision still lags behind theoretical accuracy.

Abstract

The combination of simple dynamics, small number of available decay channels, and extremely well controlled radiative and loop corrections, make charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for improving our understanding of pion structure and chiral dynamics. This paper reviews the current state of experimental study of the allowed rare decays of charged pions: (a) leptonic, $\pi^+ \to e^+\nu_e$, or $\pi_{e2}$, (b) radiative, $\pi^+ \to e^+\nu_e\gamma$, or $\pi_{e2\gamma}$, and $\pi^+ \to e^+\nu_e e^+e^-$, or $\pi_{e2ee}$, and (c) semileptonic, $\pi^+\to \pi^0 e^+ \nu$, or $\pi_{e3}$. Taken together, the combined data set presents an internally consistent picture that also agrees well with standard model predictions. The internal consistency is illustrated well by the $\pi_{e2}$ branching ratio of $(R_{e/\mu}^\pi)^{\rm PIBETA} = (1.2366 \pm 0.0064) \times 10^{-4}$ extracted in this work from the PIBETA measurement of the $\pi_{e3}$ decay and the current best value for the CKM matrix element $V_{ud}$. However, even after the great progress of the recent decades, experimental precision is lagging far behind that of the theoretical description for all above processes. We review the implications of the present state of knowledge and prospects for further improvement in the near term.