The effective field theory of extended Wilson lines

We construct the effective theory of electrically charged, spatially extended, infinitely heavy objects at leading power. The theory may be viewed as a generalization of NRQED for particles with a finite charge distribution where the charge radius and higher moments of the charge distribution are counted as $O(1)$ rather than $O(1/M)$. We show this is equivalent to a Wilson line traced by the worldline of an extended charge distribution. Our canonical use case is atomic nuclei with large charge $Z\gg 1$. The theory allows for the insertion of external operators and is sufficiently general to allow a treatment of both electromagnetic and weak mediated lepton-nucleus scattering including charged-current processes. This provides a first step towards the factorization of Coulomb regions, including structure dependence arising from a finite charge distribution, for scattering with nuclei.