Abstract
We calculate in closed analytical form the one-loop radiative corrections to electron–pion scattering e−π− → e−π−. Concise expressions (in terms of dimensionless Mandelstam variables) are given for the pertinent interference terms between the tree diagram and the one-loop diagrams related to photonic vertex correction, vacuum polarization and two-photon exchange. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft-photon radiation below an energy cutoff λ. We evaluate the finite part of the soft-photon correction factor in the center-of-mass frame. For all contributions we keep the full dependence on the electron mass. The results for the loop amplitudes can also be applied to pion-pair production e−e+ → π+π−. The radiative corrections to the corresponding total cross section are calculated with consideration of the pion structure via a vector meson dominance form factor. We find that such an additional charge form factor (inserted into the photonic vertex correction of the pion) changes the radiative corrections to the total cross section by about −0.2%.
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