Correspondence Arguments for High-Energy Collisions

We assume that in deep-inelastic processes such as $e^{-}p\to e^{-}+\mathrm{hadrons}$, ${\nu }_{\mu }p\to {\mu }^{-}+\mathrm{hadrons}$, $e^{+}{e}^{-}\to \mathrm{hadrons}$, or $\mathrm{pp}\to \mathrm{hadrons}$ of high transverse momentum, the dynamics is continuously and smoothly connected to their limiting cases. For example, the process $\gamma p\to \mathrm{hadrons}$ is a limit of $e^{-}p\to e^{-}+\mathrm{hadrons}$, exclusive channels are limiting cases of inclusive spectra, and $\mathrm{pp}\to \mathrm{low}-p_T$ hadrons is a limiting case of $\mathrm{pp}\to \mathrm{high}-p_T$ hadrons. The demand that these limits be smooth we call correspondence (with apologies to Bohr). Correspondence evidently is closely related to the concept of duality, although much cruder at least in the way we practice it. We first apply the correspondence method to some familiar examples. However, the main applications are to the processes $e^{-}p\to e^{-}+\mathrm{hadrons}$, $\nu p\to \mu +\mathrm{hadrons}$, and $e^{+}{e}^{-}+\mathrm{hadrons}$. We find several properties of hadron inclusive distributions and exclusive channels to be roughly independent of $Q^2$, in particular (a) the scaled inclusive momentum distribution in colliding-beam processes, (b) hadron inclusive distributions (and therefore multiplicity) at a given $s$ in electroproduction, (c) the ratio of nondiffractive exclusive electroproduction cross sections (such as $e^{-}p\to e^{-}{\pi }^{+}n$) to total electroproduction cross sections at fixed $s$, and (d) the ratio of the cross section for coherent electroproduction of all vector states to the total electroproduction cross section. Some semiquantitative estimates are given.