Allowed rare pion and muon decays as tests of the Standard Model

TL;DR

This paper reviews the experimental status of rare pion and muon decays, highlighting their importance for testing the Standard Model's symmetries and couplings, and discusses future prospects for precision measurements.

Contribution

It provides a comprehensive review of experimental results on rare pion and muon decays and discusses their implications for Standard Model tests and future improvements.

Findings

Current experimental data are consistent with Standard Model predictions.

Experimental accuracy lags behind theoretical precision.

Future experiments could improve tests of weak interactions.

Abstract

Simple dynamics, few available decay channels, and extremely well controlled radiative and loop corrections, make pion and muon decays a sensitive means for testing the underlying symmetries, the universality of weak fermion couplings, as well as for study of pion structure and chiral dynamics. We review the current state of experimental study of the allowed rare decays of charged pions: (a) electronic, $\pi^+ \to e^+\nu_e$, or $\pi_{e2}$, (b) radiative, $\pi^+ \to e^+\nu_e\gamma$, or $\pi_{e2\gamma}$, and (c) semileptonic, $\pi^+\to \pi^0 e^+ \nu$, or $\pi_{e3}$, as well as muon radiative decay, $\mu^+\to e^+ \nu_{\text{e}}\bar{\nu}_{\mu}\gamma$. Taken together, these data present an internally consistent picture that also agrees well with Standard Model (SM) predictions. However, even following the great strides of the recent decades, experimental accuracy 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.