Decay of the Pi Meson

It is known experimentally that, relative to the normal pion decay mode π→μ+ν, the branching ratios ρ and ρ_γ for the alternate decay modes π→e+ν and π→e+ν+γ are very small (ρ, ρ_γ5×10^-5). We investigate the question of whether these limits on the branching ratios are consistent with the idea that pion decay occurs through a universal Fermi interaction via disintegration into a virtual nucleon pair: π→virtualnucleonpair→μ(or e)+ν. A value for ρ consistent with the experiments can be obtained if the pseudoscalar coupling constant gP in the universal Fermi interaction is small compared to the axial vector coupling constant gA. An estimate of ρ_γ is made assuming that the photodecay occurs through the axial vector coupling, and it is found that there is probably no disagreement with experiment on this score. However, the photodecay can also occur through the tensor interaction (forbidden for π→μ+ν and π→e+ν). Using the experimental value gAgT0.02 obtained from beta-decay experiments, we estimate ρ_γ0.025, a result which is inconsistent with the experimental value. It is shown that the disagreement cannot be removed by using a linear combination of all possible Fermi couplings. An upper limit on gP for beta decay, valid even in the absence of a universal Fermi interaction, is obtained.