A unitarity bound and the components of photon - proton interactions

We show how and why the small distance (“hard”) interaction, calculable in perturbative QCD, provides a mass cutoff in Gribov’s formula for photon-proton collisions. This enables us to find a new and more restrictive bound for this process, $\sigma ({\gamma }^{\ast }p)\le C(ln1\mathrm{/}x{)}^{5\mathrm{/}2}$.A simple model the published experimental data over a wide range of photon virtualities ($Q^2$) and energies ($W$), is developed. This model provides a quantitative way of evaluating the relative rate of the small and large distance contributions, in the different kinematic regions. The main results of the analysis are (i) that even at $Q^2 =0$ and high energies the short distance contribution is not small, and it provides a possible explanation for the experimental rise of the photoproduction cross section; and (ii) at large values of $Q^2$, the long distance processes still contribute to the total cross section.