High-Energy Deep-Inelastic Electron-Nucleon Scattering in a Renormalizable Theory

We have studied high-energy deep-inelastic electron-nucleon scattering in a neutral pseudoscalar-meson theory by summing an infinite set of diagrams. The diagrams analyzed are straight ladder unitary diagrams, with pions as the rungs. Explicit lower-order calculations indicate that this set of diagrams gives the leading $\ln \left|q^2\right|$ contribution, where $q^2$ is the momentum transfer squared, provided that nucleon-antinucleon pair creations and nucleon vertex corrections are ignored. The main results are: (1) The final hadrons fall naturally into two jets; (2) the Bjorken scaling law breaks down; (3) the number of pions increases as $\ln \left|q^2\right|$; and (4) a longitudinal impact-parameter space is realized. Some possible experimental consequences are deduced.