Radiative pion decay (${\pi }^{+}\to {\ell }^{+}{\nu }_{\ell }\gamma$)

A charged pion decays to a charged antilepton, its associated neutrino, and a photon. Inner bremsstrahlung from charged external states interferes with structure-dependent radiation. An experimentally resolved photon needs an energy cut: the real-radiation rate alone diverges in the soft limit, whereas a suitably inclusive combination with virtual radiative corrections is finite.^[ref]