Measuring transverse shape with virtual photons
  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. 
Paul Hoyer, Samu Kurki
hep-ph hep-ex nucl-ex