Manifest Gauge Invariance for Structure Dependent Radiative Corrections to Processes Involving Atoms and Nuclei

TL;DR

This paper presents a method to construct gauge-invariant representations of correlation functions in atomic and nuclear reactions, enabling more accurate and consistent radiative correction calculations especially for heavy targets.

Contribution

The paper introduces a novel representation that makes gauge invariance explicit and separates dominant contributions in processes involving heavy nuclei or atoms.

Findings

Enables gauge-invariant approximation schemes for bound state reactions.

Separates dominant contributions in heavy target limit.

Analyzes elastic electron scattering and weak interaction processes.

Abstract

Radiative corrections to reactions involving atoms or nuclei can become sensitive to the structure of the bound state. Generically, one encounters correlation functions of multiple currents which must satisfy Ward identities. At intermediate steps, however the Ward identities are obscured, and often violated by physically motivated approximation schemes. In this paper we outline a method to construct a representation of the aforementioned correlators that manifests gauge invariance in the limit of a heavy target (i.e., when recoil energy can be neglected). This representation then enables manifestly gauge invariant approximation schemes. Furthermore, the proposed representation naturally separates the largest contributions that dominate scattering amplitudes in the limit of a heavy constituent (e.g., proton) mass. We analyze elastic electron scattering from nuclei in detail, and also discuss radiative corrections to processes mediated by the weak interaction.