Electron structure: Shape, size, and generalized parton distributions in QED

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 nonzero 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 in a continuum scattering state. The shape of the electron, as determined from the transverse density and generalized parton distributions, is shown not to be round, and the continuum 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 continuum 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 ($\ensuremath{-}1/2$). Including the nonzero photon mass leads to the suppression of end-point contributions to form factors. Implications for proton structure and color transparency are discussed.