Froissart bound for virtual photon-proton scattering, nevertheless, we have become used to viewing the small-x structure function in terms of a high energy quark-antiquark pair (possibly accompanied by gluons) impinging on the target proton. Although the quark-antiquark pair is not on-shell the time evolution of the pair as it passes through the nucleon should be constrained by unitarity in much the same way that a quark-antiquark pair coming from, say, a pion state would be.

To be more specific, view deep inelastic scattering in the rest system of the proton and in the aligned jet (naive parton) model\[28,29\]. At small x the virtual photon, $\gamma^*(q),$ breaks up into a quark and antiquark pair long before reaching the proton. The relative transverse momentum of the quark and antiquark is small, of hadronic size $\mu\approx  350 MeV,$ while the longitudinal momenta are $q_z$ and $q_z\cdot
{\mu^2\over Q^2}$ respectively. Because the relative transverse momentum is small the transverse coordinate separation of the quark and antiquark can be expected to be on the order of a fermi, and the resulting cross section with the proton should be of hadronic size. The smallness of the overall cross section comes from the small probability, of order 