Towards a nonperturbative foundation of the dipole picture: II. High energy limit

This is the second of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. In the first paper we have identified the leading contributions to this process at high energies and have derived expressions for them which take into account the renormalisation of the photon-quark-antiquark vertex. In the present paper we investigate the approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results derived in the first paper. We discuss the gauge invariance of different contributions to the scattering amplitude and point out some subtleties related to gauge invariance in the correct definition of a perturbative photon wave function. As a phenomenological consequence of the dipole picture we derive a bound on the ratio of the cross sections for longitudinally and transversely polarised photons. This bound is independent of any particular model for the dipole-proton cross section and allows one to test the validity of the assumptions leading to the dipole picture in particular at low photon virtualities. We conclude that the naive dipole model formula should be supplemented by two additional terms which can potentially become large at small photon virtualities.