The structure functions for deep-inelastic lepton processes including (along with other hadron charges and ${\mathrm{SU}}_3$ quantum numbers) $e^{-}+p\to e^{-}+\mathrm{anything},"$ $e^{-}+e^{+}\to p+\mathrm{anything},"$ $\nu +p\to e^{-}+\mathrm{anything},"$ $\overline{\nu }+p\to e^{+}+\mathrm{anything}"$ are studied in the Bjorken limit of asymptotically large momentum and energy transfers, $q^2$ and $M_{\nu }$, with a finite ratio $w\equiv \frac{2M_{\nu }}{q^2}$. A "parton" model is derived from canonical field theory for all these processes. It follows from this result that all the structure functions depend only on $w$, as conjectured by Bjorken for the deep-inelastic scattering. 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 partons that are involved. Upon crossing to the $e^{+}{e}^{-}$ annihilation channel and deriving a parton model for this process, we arrive at the important result that the deep-inelastic annihilation cross section to a hadron plus "anything" is very large, varying with colliding $e^{+}{e}^{-}$ beam energy at fixed $w$ in the same way as do point-lepton cross sections. General implications for colliding-ring experiments and ratios of annihilation to scattering cross sections and of neutrino to electron inelastic scattering cross sections are computed and presented. Finally, we discuss the origin of our transverse momentum cutoff and the compatibility of rapidly decreasing elastic electromagnetic form factors with the parton model constructed in this work.

• Received 20 June 1969

DOI:https://doi.org/10.1103/PhysRev.187.2159