Theory of Deep-Inelastic Lepton-Nucleon Scattering and Lepton Pair Annihilation Processes. II. Deep-Inelastic Electron Scattering

Abstract

This is the second in a series of four papers devoted to a theoretical study based on canonical quantum field theory of the deep-inelastic lepton processes. In the present paper we present the detailed calculations leading to the limiting behavior—or the "parton model"—for deep-inelastic electron scattering. It follows from this work that the structure functions depend only on the ratio of energy to momentum transfer $\frac{2M\nu }{q^2}$ as conjectured by Bjorken on general grounds. To accomplish this derivation, it is necessary to introduce a transverse momentum cutoff so that there exists an asymptotic region in which $q^2$ and $M_{\nu }$ can be made larger than the transverse momenta of all the virtual constituents or "partons" of the proton that are involved. We also derive the ladder approximation for the leading contribution, order by order in the strong interaction and to all orders in the coupling, to the asymptotic behavior of these structure functions with increasing ratio of energy to momentum transfer. Finally, we draw and discuss the experimental implications.