We study the dipole picture of high-energy virtual-photon-proton scattering.
It is shown that different choices for the energy variable in the dipole cross
section used in the literature are not related to each other by simple
arguments equating the typical dipole size and the inverse photon virtuality,
contrary to what is often stated. We argue that the good quality of fits to
structure functions that use Bjorken-x as the energy variable - which is
strictly speaking not justified in the dipole picture - can instead be
understood as a consequence of the sign of scaling violations that occur for
increasing Q^2 at fixed small x. We show that the dipole formula for massless
quarks has the structure of a convolution. From this we obtain derivative
relations between the structure function F_2 at large and small Q^2 and the
dipole-proton cross section at small and large dipole size r, respectively.Comment: 27 page
