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 \(\mathcal{O}(e^5)\) 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 \(m=1\) \cite{1903.09133, 1912.10229} and \(m=2\) cases, we propose that there exists a conservation law for every \(m\) such that the respective charge involves an \(\mathcal{O}(e^{2m+1})\) 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 \(m^{th}\) order tails to the memory term that are tied to the classical limit of these soft theorems.