The electron in three-dimensional momentum space

TL;DR

This paper derives three-dimensional momentum space distribution functions for the electron and photon within a dressed electron using perturbation theory, light-front formalism, and gauge considerations.

Contribution

It introduces a comprehensive method to compute transverse-momentum-dependent distributions for the dressed electron, including gauge-invariant results and numerical visualizations.

Findings

Derived leading-twist TMDs for electron and photon

Compared light-front and diagrammatic approaches

Provided gauge-invariant distribution functions with numerical plots

Abstract

We study the electron as a system composed by an electron and a photon, using lowest order perturbation theory. We derive the leading-twist transverse-momentum-dependent distribution functions for both the electron and photon in the dressed electron, thereby offering a three-dimensional description of the dressed electron in momentum space. To obtain the distribution functions, we apply both the formalism of light-front wave function overlap representation and the diagrammatic approach. We perform the calculations both in light-cone gauge and Feynman gauge, and we present a detailed discussion of the role of the Wilson lines to obtain gauge-independent results. We provide numerical results and plots for many of the computed distributions.