Measuring transverse shape with virtual photons

TL;DR

This paper presents a method to determine the transverse charge density of hadrons through a Fourier transform of form factors, applicable to various virtual photon-induced transitions, providing new insights into strong interaction dynamics.

Contribution

It introduces a novel approach to analyze transverse structure in hadrons using Fourier transforms of scattering data, applicable to multiple transition processes and not limited to high momentum transfer.

Findings

Fourier transform of form factors reveals transverse charge density.

Method applicable to any virtual photon-induced transition.

Transverse resolution improves with increased q^2 range.

Abstract

A two-dimensional Fourier transform of hadron form factors allows to determine their charge density in transverse space. We show that this method can be applied to any virtual photon induced transition, such as \gamma *(q)+N -> \pi N. Only Fock states that are common to the initial and final states contribute to the amplitudes, which are determined by the overlap of the corresponding light-front wave functions. Their transverse extent may be studied as a function of the final state configuration, allowing qualitatively new insight into strong interaction dynamics. Fourier transforming the cross section (rather than the amplitude) gives the distribution of the transverse distance between the virtual photon interaction vertices in the scattering amplitude and its complex conjugate. While the measurement of parton distributions in longitudinal momentum depends on the leading twist approximation (-q^2 -> \infty limit), all q^2<0 values contribute to the Fourier transform, with the transverse resolution increasing with the available range in q^2. We illustrate the method using QED amplitudes.