Radiative corrections to the Dalitz decay ${\pi }^0\to e^{+}{e}^{-}\gamma$ revisited

Abstract

We have recalculated the Mikaelian and Smith radiative corrections to the Dalitz decay ${\pi }^0\to e^{+}{e}^{-}\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the radiative photon. In contrast to the previous calculations, we did not neglect the terms of order higher than $\mathcal{O}(m^2)$ and also included the one-photon-irreducible contribution at one-loop level and the virtual muon loop contribution. The results can then be used also for heavier particles in the final state.

Comments: 15 pages, 5 figures, 1 table and 3 ancillary files (C++ code); v2: accepted version for publication in Phys. Rev. D.; extended discussion, one table and muon loop contribution added, C++ code updated