Weak Radiative Decay of theΣ+andΛHyperons

Unitarity is found to give a reliable, model-independent lower bound on the branching ratio $\left[\frac{\mathrm{rate}(\Lambda \to n\gamma )}{\mathrm{rate}(\Lambda \to \mathrm{all})}\right]>\mathrm{}8.5\mathrm{}\times {10}^{-4\mathrm{}}$. This value is nearly as large as the experimentally determined branching ratio for the decay ${\Sigma }^{+}\to p\gamma$. Dispersion-theoretic techniques supplemented with current algebra, PCAC, and pole models are then used to determine the real as well as imaginary parts of the amplitudes for the radiative decays of the $\Lambda$ and ${\Sigma }^{+}$ hyperons. Input consists of the experimental nonleptonic decay amplitudes and pion-nucleon phase shifts. The theoretical predictions are very sensitive to the hyperon magnetic moments, and until these are better known, these results for the radiative decays can only be qualitatively compared with experiment.