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The emission of soft-photons and the LBK theorem, revisited

Predictions for processes involving soft photons, up to next-to-leading power (NLP) in the photon energy, can be obtained using the Low-Burnett-Kroll (LBK) theorem. The consistency of the theorem has been a recent topic of investigation since it is traditionally formulated in terms of a non-radiative amplitude, which is evaluated with unphysical momenta. We address such questions and propose a formulation of the LBK theorem which relies on the evaluation of the non-radiative amplitude with on-shell, physical momenta. We use this form to numerically study the impact of NLP contributions to cross-sections for $pp$ and $e^-e^+$ processes involving soft-photon emission.