Next-to-eikonal corrections to soft-gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-toeikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using pathintegral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple softgluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class oflog(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion