Radiative Modes ofK-Meson Leptonic Decay

The gamma-ray spectra for the decays $K\to \mu \nu \gamma$ and $K\to e\nu \gamma$ as well as $\pi \to \mu \nu \gamma$ and $\pi \to e\nu \gamma$ are calculated in full: Terms in the spectra proportional to lepton mass are retained so that the results are applicable to the muon decay mode, and the calculations take into account both inner bremsstrahlung radiation and radiation arising from structure in the meson vertex. The latter contributions are expressed in terms of two form factors.