Towards a nonperturbative foundation of the dipole picture: I. Functional methods

This is the first of two papers in which we study real and virtual photon–proton scattering in a nonperturbative framework. We classify different contributions to this process and identify the leading contributions at high energies. We then study the renormalisation of the photon–quark–antiquark vertex that occurs in the leading contributions. We find something like the dipole picture in one of these contributions but also find two correction terms which can potentially become large at small photon virtualities. In the second paper we will discuss the additional approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results found here.