Theory of Deep-Inelastic Lepton-Nucleon Scattering and Lepton Pair Annihilation Processes. IV. Deep-Inelastic Neutrino Scattering

This is the last in a series of four papers devoted to a theoretical study based on canonical 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 neutrino scattering, i.e., $\nu +p\to e^{-}+\mathrm{anything},\text{'}\text{'}$ $\overline{\nu }+p\to e^{+}+\mathrm{anything},\text{'}\text{'}$ where "anything" refers to all possible hadrons. In particular, we show 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. Experimental implications, including sum rules and the relation of $\nu$ and $\overline{\nu }$ cross sections to each other as well as to deep-inelastic electron scattering cross sections, are derived and discussed.