Infrared radiative corrections: Extended treatment applicable to resonant scattering

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Abstract
The calculation of infrared radiative corrections to scattering cross sections, to which a great deal of attention has been devoted in the past, is reconsidered here and carried to a higher order of accuracy within the context of a specific relativistic model. Earlier work, initiated by Low [Phys. Rev. 110, 974 (1958)] and developed further by others, which led to soft-photon approximations for bremsstrahlung amplitudes, is extended to apply to virtual- as well as real-photon emission and absorption processes. As in the earlier work the requirement of gauge invariance plays a central role in the analysis. Evaluation of the new correction term obtained here requires, as input, the physical (on-mass-shell) amplitude for scattering in the absence of radiative interactions. The new term is expected to lead, in most cases, to only small modifications of the results obtained by standard methods; verification of this expectation would provide a useful check on the range of validity of these standard procedures. It is pointed out that for scattering in the neighborhood of a very narrow resonance the new correction term, which properly accounts for rapid variations of the scattering amplitude with energy, could become numerically significant. In an attempt to examine this possibility in a very preliminary yet quantitative manner the radiative correction terms derived here have been evaluated with the aid of a simple Breit-Wigner representation of the radiation-free scattering amplitude, and some typical results are reported.