On the Forward Scattering Amplitude of the Virtual Longitudinal Photon at Zero Energy

Abstract

The theorem is proved, determining the forward scatterring amplitude of virtual longitudinal photon at zero energy on any hadronic target in the limit of small photon virtualities $Q^2$. The theorem is strict, based only on Lorenz and gauge invariance. No assumptions about the strong interaction, besides the gap in the mass spectrum, are used. Two terms in the expansion over $Q^2$ are calculated. The estimation is given up to what $Q^2$ the elastic term can represent the whole amplitude of longitudinal virtual photon-proton scattering.