Regge Model with Scale-Invariance for Nucleon Compton Scattering, Electroproduction, and Electron-Positron Annihilation

Abstract

A Regge model satisfying the requirement of scale invariance is constructed for the Compton amplitude. Using the $P$, $P^{\prime }$, and $A_2$ Regge trajectories, we obtain good fits to the total photon-nucleon cross sections and to the differential cross section $\frac{d\sigma }{\mathrm{dt}}$ for proton Compton scattering. The model is then applied to electroproduction in the deep-inelastic region and successfully describes the data on the proton and neutron structure functions, the breaking of scale invariance at small -$q^2$ and the behavior of the ratio $\frac{W_2^n}{W_2^p}$, as a function of -$q^2$ for fixed hadronic mass squared. Predictions are given for the differential cross section for the crossed-channel process $e^{+}+e^{-}\to \mathrm{proton}+\mathrm{hadrons}$, and it is found that for large $q^2$ the total annihilation cross section behaves as ${\sigma }_T\approx \frac{1}{q^2}$.