Soft-Photon Theorems and RadiativeKl3Decays

We apply the soft-photon theorems of Low, Adler and Dothan, and Burnett and Kroll to the radiative decays $K^{-}\to {\pi }^0{l}^{-}\overline{\nu }\gamma$ and ${\overline{K}}^0\to {\pi }^{+}{l}^{-}\overline{\nu }\gamma$ ($l=e or \mu$) to obtain the leading terms in the respective matrix elements. Numerical results for the photon spectra and for the decay rate (as a function of the minimum photon energy) are given in terms of the conventional $K_{l3\mathrm{}}$ parameters $f_{+}\mathrm{}\left(0\right)\mathrm{}$, $\xi$, ${\lambda }_{+}$, and ${\lambda }_{-}$.