Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions

Abstract

We explore the logarithmic terms in the soft theorem in four dimensions by analyzing classical scattering with generic incoming and outgoing states and one loop quantum scattering amplitudes. The classical and quantum results are consistent with each other. Although most of our analysis in quantum theory is carried out for one loop amplitudes in a theory of (charged) scalars interacting via gravitational and electromagnetic interactions, we expect the results to be valid more generally.Comment: LaTeX file, 61 pages, 25 figures; v2: references updated, other minor changes; v3: few sign errors corrected, no change in the main results on the classical wave-for