In a 4d EFT, all effective operators which can contribute to the soft factor are constructed, and their contribution analysed using a double complex deformation (one soft shift and two BCFW shifts). This approach reproduces many results already known in the literature (the photon and graviton soft theorems, for example). It also sheds light on the question of whether loop corrections from massive particles could modify these soft theorems. If one integrates out the massive particles of a theory, one is left with effective operators - and unless these operators are of the form given here, then they do not contribute to the soft theorem.

Recently, the connection between soft theorems and asymptotic symmetries has experienced a resurgence of interest. To say that a soft factor is not modified by any effective operators (for instance from integrating out massive particles) is analogous to saying that the corresponding asymptotic symmetry is not anomalous (in a theory with those massive particles). Whether asymptotic symmetries are preserved to a given loop order (or, indeed, non-perturbatively), is important because it determines their utility in constructing UV complete S matrices.