Confinement, form factors, and deep-inelastic scattering in two-dimensional quantum chromodynamics

Abstract

We clarify the gauge invariance, infrared structure, and completeness of 't Hooft's solution for the meson sector of two-dimensional quantum chromodynamics. Electromagnetic form factors of mesons are then shown to obey an asymptotic power law, whose power is dynamically determined and is not related to the shortdistance behavior of the theory. Following a review of the total annihilation cross section for producing hadrons, we discuss deep-inelastic lepton scattering. As expected, Bjorken scaling is obtained, but we show how the sum over hadronic final states reproduces the parton model precisely. The Drell-Yan-West relation and Bloom-Gilman duality are fulfilled for the relation between the scaling function and form factors. We conclude by speculating on the applicability of our picture of form factors to the real, four-dimensional world. We argue that this is a viable alternative to dimensional scaling and, phenomenologically, the differences between our predictions and the dimensional counting rules are slight for light quarks. Finally, we attempt to abstract those features of the model which may guide us toward a solution to the four-dimensional problem.