Decays of theK−patom and the Λ(1405)

To investigate differences between some recent calculations on the decays of the ${\mathit{K}}^{\mathrm{-}}$p atom, we calculate the pionic decays ${\mathit{K}}^{\mathrm{-}}$p→Λ${\mathrm{\pi }}^0$, ${\mathrm{\Sigma }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$, ${\mathrm{\Sigma }}^0$ ${\mathrm{\pi }}^0$, and ${\mathrm{\Sigma }}^{\mathrm{-}}$ ${\mathrm{\pi }}^{+}$ in an isobar model and compare them with experimental rates determined from measured branching ratios together with the imaginary part of the K¯N scattering amplitude. The comparison shows that the coupling constants at the strong-interaction vertices are reduced significantly from the on-shell values. These coupling constants are then applied to an isobar-model calculation of the radiative transition rates. Comparing these with results from a recent experiment gives values for the radiative decay widths of the Λ(1405): ${\mathrm{\Gamma }}_{\mathrm{\Lambda }\mathrm{}\left(1405\right)\mathrm{}\to \mathrm{\Lambda }\gamma }$=27±8 keV and ${\mathrm{\Gamma }}_{\mathrm{\Lambda }\mathrm{}\left(1405\right)\mathrm{}\to \mathrm{\Sigma }}^0$γ=10±4 or 23±7 keV.