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The European Physical Journal C
ISSN: 1434-6044 (printed version)
ISSN: 1434-6052 (electronic version)
Abstract Volume 5 Issue 2 (1998) pp 303-315
DOI 10.1007/s100529800845
theoretical physics:
A unitarity bound and the components of photon-proton interactions
E. Gotsman (1)(2), E.M. Levin (1)(2)(3), U. Maor (1)
(1) School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978, Israel (e-mail: gotsman@post.tau.ac.il, leving@post.tau.ac.il, maor@post.tau.ac.il)
(2) DESY Theory, Notkestr. 85, D-22603, Hamburg, Germany
(3) Theory Department, Petersburg Nuclear Physics Institute, 188350, Gatchina, St. Petersburg, Russia
Received: 7 August 1997 / Revised version: 11 December 1997 / Published online: 10 March 1998
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.
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Online publication: August 25, 1998
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