Decay Rate ofΣ+→p+γfrom Unsubtracted Dispersion Relations

Assuming unsubtracted dispersion relations, we set up integral representation for the weak photonic amplitudes $F_1$ and $F_2$. The integrals involve the magnetic and electric dipole amplitudes $M_{1-}$ and $E_{0+}$ of the photo-pion production and the pion-nucleon scattering phase shifts of the states $P_{11}$, $P_{31}$, $S_{11}$, and $S_{31}$. The integrals were carried out on a computer and the relative decay rate of ${\Sigma }^{+}\to p\gamma$ to its total rate was found to be 0.71×${10}^{-3\mathrm{}}$, which is comparable with the latest experimental value (1.9±0.4)×${10}^{-3\mathrm{}}$.