Experimental study of rare charged pion decays
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, $π^+ \to e^+ν_e$, or $π_{e2}$, (b) radiative, $π^+ \to e^+ν_eγ$, or $π_{e2γ}$, and $π^+ \to e^+ν_e e^+e^-$, or $π_{e2ee}$, and (c) semileptonic, $π^+\to π^0 e^+ ν$, or $π_{e3}$. 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 $π_{e2}$ branching ratio of $(R_{e/μ}^π)^{\rm PIBETA} = (1.2366 \pm 0.0064) \times 10^{-4}$ extracted in this work from the PIBETA measurement of the $π_{e3}$ 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.