Radiative Pionic Decays ofΣ±Hyperons

Abstract

The radiative decays ${\Sigma }^{\pm }\to n+{\pi }^{\pm }+\gamma$ are analyzed on the assumption that the pole approximation is valid for the decays ${\Sigma }^{\pm }\to n+{\pi }^{\pm }$. It is shown that the matrix elements for these radiative decays are essentially the same as those for the phenomenological inner-bremsstrahlung diagrams as long as the anomalous magnetic moments of the $\Sigma$ and $\Lambda$ hyperons are at most of the order of magnitude of the nucleon magnetic moments. This is true independently of the signs and magnitudes of the strong and weak vertices involved. The branching ratios of ${\Sigma }^{\pm }\to n+{\pi }^{\pm }+\gamma$ to ${\Sigma }^{\pm }\to n+{\pi }^{\pm }$ depend on whether the pion in ${\Sigma }^{\pm }\to n+{\pi }^{\pm }$ is in the $S$- or the $P$-wave state, in general agreement with what was pointed out by previous authors. However, in contrast with the results of the previous calculation, the present analysis shows that the anomalous magnetic moments of ${\Sigma }^{\pm }$ and the neutron noticeably contribute to the branching ratios. Therefore, in order to check the underlying theoretical assumptions so as to determine the pion-wave assignment in ${\Sigma }^{\pm }\to n+{\pi }^{\pm }$, it is necessary to have either very accurate data for ${\Sigma }^{\pm }\to n+{\pi }^{\pm }+\gamma$ or an experimental determination of the anomalous magnetic moments of ${\Sigma }^{\pm }$.