Phenomenological Analysis of Weak-Radiative Decay of theK+Meson andCP-Noninvariant Effects

Abstract

A phenomenological analysis of the pion and the photon energy spectra and the photon-pion angular correlation spectrum in the weak-radiative decay, $K^{+}\to {\pi }^{+}+{\pi }^0+\gamma$, is performed by parametrizing the direct electric ($E1\mathrm{}$) and magnetic ($M1\mathrm{}$) dipole transition amplitudes. A comparison of the calculated ${\pi }^{+}$ energy spectrum with the experimental spectrum (together with the qualitative information available from the theoretical investigations of the direct amplitudes) makes it possible to put limits on the direct amplitudes. We also make an estimate of the maximum asymmetry in the weak-radiative decays of $K^{+}$ and $K^{-}$ mesons that could be present because of possible $\mathrm{CP}$ noninvariance in these decays. This estimate is based on a model in which $\mathrm{CP}$ noninvariance arises from a relative phase (other than $\pi \pi$ scattering phase shifts) between the inner bremsstrahlung and the $E1\mathrm{}$ amplitudes. The maximum observable asymmetry in the $K^{+}$ and $K^{-}$ radiative decay rates would be about 25%.