We have measured the pi+-->e+ nugamma branching ratio over a wide region of phase space, based on a total of 65 460 events acquired using the PIBETA detector. Minimum-chi2 fits to the measured (E(e+), E(gamma) energy distributions result in the weak form factor value of F(A)=0.0119(1) with a fixed value of F(V)=0.0259. An unconstrained fit yields F(V)=0.0258(17) and F(A)=0.0117(17). In addition, we have measured a=0.10(6) for the dependence of F(V) on q2, the e+ nu pair invariant mass squared, parametrized as F(V)(q2)=F(V)(0)(1+aq(2)). The branching ratio for the kinematic region E(gamma)>10 MeV and theta(e(+)gamma)>40 degrees is measured to be B(expt)=73.86(54)x10(-8). Earlier deviations we reported in the high-E(gamma)-low-E(e+) kinematic region are resolved without a tensor term. We also derive new values for the pion polarizability alpha(E)=2.78(10)x10(-4) fm3 and neutral pion lifetime tau(pi0)=(8.5+/-1.1)x10(-17) s.

The lowest order radiative corrections to the width and spectra of the radiative e2 decay are calculated. We take into account the virtual photon emission contribution as well as soft and hard real photon emission contributions. The result turns out to be consistent with the standard Drell-Yan picture for the width and spectra in the leading logarithmical approximation which permits us to generalize it to all orders of perturbation theory. Explicit expressions of nonleading contributions are obtained. The contribution of the short distance is found to be in agreement with standard model predictions. It is presented as a general normalization factor. We check the validity of the Kinoshita-Lee-Nauenberg theorem about the cancellation in the total width of the mass singularities at the zero limit of the electron mass. We discuss the results of the previous papers devoted to this problem. The Dalitz plot distribution is illustrated numerically.A rather detailed calculation of the lowest order RC was carried out in Ref. ͓4͔. Nonclear manipulations with a soft

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:, and µ + → e + ννγ. For the latter we report new preliminary values for the branching ratio B(Eγ > 10 MeV, θeγ > 30 • ) = 4.365 (9)stat (42)syst × 10 −3 , and the decay parameterη = 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.

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