A unitarity bound and the components of photon-proton interactions

Abstract.

We show how and why the short distance (“hard”) interaction, which is calculated 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 unitarity bound for this process, $\sigma(\gamma^{*}p)\leq C(ln\frac{1}{x})^{\frac{5}{2}}$. We develop a simple model that consists of “soft” and “hard” contributions, which yields a qualitative description of the published experimental data over a wide range of photon virtualities ($Q^2$) and energies ($W$). This model provides a quantitative way of evaluating the relative rate of the short and long 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.