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

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, $π^+ \to e^+ν_e$, or $π_{e2}$, (b) radiative, $π^+ \to e^+ν_eγ$, or $π_{e2γ}$, and (c) semileptonic, $π^+\to π^0 e^+ ν$, or $π_{e3}$, as well as muon radiative decay, $μ^+\to e^+ ν_{\text{e}}\barν_μγ$. 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.