Abstract
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} (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} (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.
Highlights
This asymptotic conservation law was proved in [20]
We show that there exists a new asymptotic conservation law which is related to the subleading tail term
We predict the structure of mth order tails to the memory term that are tied to the classical limit of these soft theorems
Summary
Our aim is to study late time radiation emitted in a general classical scattering process. The current corresponding to an extended object can be written as the contribution from pointlike object plus corrective terms that depend on internal structure of the object like its charge distribution. These correspond to higher order moments and are subleading at large r. These corrections originating from internal structure of the scattering objects do not contribute to the modes that are of interest to us We illustrate this in appendix C by showing that dipole term does not affect the subleading tail term in (4.7) and the Q1, Q2 charges given in (3.20) and (5.12) respectively. We show in appendix C that these modes are not affected by non-minimal couplings. we can study scattering of minimally coupled, spin zero point particles without any loss of generality
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