Electron Structure: Shape, Size and GPDs in QED

TL;DR

This paper investigates the electron's shape, size, and internal structure using perturbation theory, revealing it is not perfectly round and varies between free and bound states, with implications for understanding proton structure.

Contribution

It introduces a detailed analysis of the electron's shape and internal distributions, including the effects of photon mass and polarization, extending the understanding of electron and proton structures.

Findings

The bound electron is larger than the free electron.

The electron's shape is non-round, especially when bound.

Virtual electron and photon carry nearly total angular momentum.

Abstract

The shape of the electron is studied using lowest-order perturbation theory. Quantities used to probe the structure of the proton: form factors, generalized parton distributions, transverse densities, Wigner distributions and the angular momentum content are computed for the electron-photon component of the electron wave function. The influence of longitudinally polarized photons, demanded by the need for infrared regularization via a non-zero photon mass, is included. The appropriate value of the photon mass depends on experimental conditions, and consequently the size of the electron (as defined by the slope of its Dirac form factor) bound in a hydrogen atom is found to be about four times larger than when the electron is free. The shape of the electron, as determined from the transverse density and generalized parton distributions is shown to not be round, and the free electron is shown to be far less round than the bound electron. An electron distribution function (analogous to the quark distribution function) is defined, and that of the bound electron is shown to be suppressed compared to that of the free electron. If the relative transverse momentum of the virtual electron and photon is large compared with the electron mass, the virtual electron and photon each carry nearly the total angular momentum of the physical electron (1/2), with the orbital angular momentum being nearly (-1/2). Including the non-zero photon mass leads to the suppression of end-point contributions to form factors. Implications for proton structure and color transparency are discussed.