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, $pi^+ to e^+ u_e$, or $pi_{e2}$, (b) radiative, $pi^+ to e^+ u_egamma$, or $pi_{e2gamma}$, and $pi^+ to e^+ u_e e^+e^-$, or $pi_{e2ee}$, and (c) semileptonic, $pi^+to pi^0 e^+ u$, 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.
Simple dynamics, few available decay channels, and highly controlled radiative and loop corrections, make pion and muon decays a sensitive means of exploring details of the underlying symmetries. We review the current status of the rare decays: pi+ -
> e+ nu, pi+ -> e+ nu gamma, pi+ -> pi0 e+ nu, and mu+ -> e+ nu nu-bar gamma. For the latter we report new preliminary values for the branching ratio B(E_gamma >10 MeV, theta_(e-gamma) > 30deg) = 4.365 (9)_stat (42)_syst x 10^{-3}, and the decay parameter eta-bar = 0.006 (17)_stat (18)_syst, both in excellent agreement with standard model predictions. We review recent measurements, particularly by the PIBETA and PEN experiments, and near-term prospects for improvement. These and other similar precise low energy studies complement modern collider results materially.
Building on the rare pion and muon decay results of the PIBETA experiment, the PEN collaboration has undertaken a precise measurement of B_{pi e2} = R^pi_{e/mu}, the pi^+ -> e^+ u(gamma) decay branching ratio, at the Paul Scherrer Institute, to reduc
e the present 40times experimental precision lag behind theory to ~ 6-7times. Because of large helicity suppression, R^pi_{e/mu} is uniquely sensitive to contributions from non-(V-A) physics, making this decay a particularly suitable subject of study. Even at current precision, the experimental value of B_{pi e2} provides the most accurate test of lepton universality available. During runs in 2008-10, PEN has accumulated over 2times 10^7 pi_{e2} events; a comprehensive maximum-likelihood analysis is currently under way. The new data will also lead to improved precision of the earlier PIBETA results on radiative pi and mu decays.
We review the recent measurements of the rare pion decays: Pi+ -> Pi0 e+ Nu [pion beta, Pi_(e3), or Pi_beta decay], radiative decay Pi+ -> e+ Nu Gamma [Pi_(e2Gamma) or RPD], and Pi+ -> e+ Nu [Pi_(e2)] decay, as well as the radiative muon decay, Mu ->
e Nu Nu-bar Gamma, their theoretical implications, and prospects for further improvement.
A new measurement of $B_{pi e2}$, the $pi^+ to e^+ u(gamma)$ decay branching ratio, is currently under way at the Paul Scherrer Institute. The present experimental result on $B_{pi e2}$ constitutes the most accurate test of lepton universality availa
ble. The accuracy, however, still lags behind the theoretical precision by over an order of magnitude. Because of the large helicity suppression of the $pi_{e2}$ decay, its branching ratio is susceptible to significant contributions from new physics, making this decay a particularly suitable subject of study.
A new measurement of $B_{pi e2}$, the $pi^+ to e^+ u(gamma)$ decay branching ratio, is currently under way at the Paul Scherrer Institute. The present experimental result on $B_{pi e2}$ constitutes the most accurate test of lepton universality availa
ble. The accuracy, however, still lags behind the theoretical precision by over an order of magnitude. Thanks to the large helicity suppression of $pi_{e2}$ decay, the branching ratio is susceptible to significant contributions from new physics, making this decay a particularly suitable subject of study.
The Nab collaboration will perform a precise measurement of a, the electron-neutrino correlation parameter, and b, the Fierz interference term in neutron beta decay, in the Fundamental Neutron Physics Beamline at the SNS, using a novel electric/magne
tic field spectrometer and detector design. The experiment is aiming at the 10^{-3} accuracy level in (Delta a)/a, and will provide an independent measurement of lambda = G_A/G_V, the ratio of axial-vector to vector coupling constants of the nucleon. Nab also plans to perform the first ever measurement of b in neutron decay, which will provide an independent limit on the tensor weak coupling.
