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

TL;DR

This paper investigates logarithmic terms in the four-dimensional soft theorem through classical scattering and one-loop quantum amplitudes, demonstrating their consistency and potential generality across theories.

Contribution

It provides a comparative analysis of classical and quantum logarithmic terms in the soft theorem, highlighting their agreement and broader applicability.

Findings

Classical and quantum results are consistent.

Logarithmic terms appear in one-loop amplitudes.

Results are expected to be general beyond scalar theories.

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.