Radiative Corrections to Decays with a Dalitz Pair

The radiative corrections to the process $A\to B\gamma \to B{e}^{+}{e}^{-}$ (where $A$ and $B$ are hadrons) can be separated into a part which is purely dependent upon quantum electrodynamics (the one-photon-exchange diagrams) and a part dependent upon the hadronic structure (the two-photon-exchange diagrams). Neglecting the latter because such graphs are not singular when the lepton mass is set equal to zero, we concentrate on the one-photon-exchange terms, and calculate both the radiative corrections to the total decay rate including hard photons and the radiative corrections to the differential decay rate in the soft-photon approximation. Our results are directly applicable to the decay ${\pi }^0\to e^{+}{e}^{-}\gamma$, where our assumption that the two-photon-exchange graphs can be neglected is justified because ${\pi }^0 \nrightarrow 3\gamma$ and the amplitude for ${\pi }^0\to 2\gamma \to e^{+}{e}^{-}\gamma$ is proportional to the lepton mass.