Color dipole cross section and inelastic structure function

Understand

Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section.

• Using the parametrizations of $F_2(\xi=x \ {\rm or}\ W^2,Q^2)$ by Donnachie-Landshoff and Block et al., we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks.
• The color dipole cross section determined this way reproduces the original structure function within about 10\% for $0.1$ GeV$^2\leq Q^2\leq 10$ GeV$^2$.
• We discuss the large and small form of the dipole cross section and compare with other parameterizations.