New asymptotic conservation laws for electromagnetism

We obtain the subleading tail to the memory term in the late time electromagnetic radiative field generated due to a generic scattering of charged bodies. We show that there exists a new asymptotic conservation law which is related to the subleading tail term. The corresponding charge is made of a mode of the asymptotic electromagnetic field that appears at $$ \mathcal{O} $$ O (e5) and we expect that it is uncorrected at higher orders. This hints that the subleading tail arises from classical limit of a 2-loop soft photon theorem. Building on the m = 1 [41, 42] and m = 2 cases, we propose that there exists a conservation law for every m such that the respective charge involves an $$ \mathcal{O} $$ O (e2m+1) mode and is conserved exactly. This would imply a hierarchy of an infinite number of m-loop soft theorems. We also predict the structure of mth order tails to the memory term that are tied to the classical limit of these soft theorems.