The effective field theory of extended Wilson lines

TL;DR

This paper develops an effective field theory for extended, charged, heavy objects like atomic nuclei, generalizing NRQED to include finite charge distributions and enabling detailed analysis of electromagnetic and weak interactions with nuclei.

Contribution

It introduces a Wilson line-based effective theory for extended charges, accounting for finite charge radii, and applies it to nuclear and lepton-nucleus scattering processes.

Findings

Framework for including charge distribution effects in scattering

Application to electromagnetic and weak interactions with nuclei

First step towards factorization of Coulomb regions with structure dependence

Abstract

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.