Realistic transverse images of the proton charge and magnetization densities

Abstract

We develop a technique, denoted as the finite radius approximation (FRA), that uses a two-dimensional version of the Nyquist-Shannon sampling theorem to determine transverse densities and their uncertainties from experimental quantities. Uncertainties arising from experimental uncertainties on the form factors and lack of measured data at high ${Q}^{2}$ are treated. A key feature of the FRA is that a form factor measured at a given value of ${Q}^{2}$ is related to a definite region in coordinate space. An exact relation between the FRA and the use of a Bessel series is derived. The proton Dirac form factor is sufficiently well known such that the transverse charge density is very accurately known except for transverse separations $b$ less than about 0.1 fm. The Pauli form factor is well known to ${Q}^{2}$ of about 10 GeV${}^{2}$, and this allows a reasonable, but improvable, determination of the anomalous magnetic moment density.