High-EnergyppElastic Diffraction Scattering from Inelastic States

Abstract

Small-angle high-energy elastic proton-proton scattering, i.e., the Pomeranchukon contribution, is determined through unitarity in terms of a model for the inelastic intermediate states. These are represented by two contributions: (i) quasielastic production of free pions, described in terms of a $c$-number source current $\beta \mathrm{}\left(k\right)\mathrm{}$ for the pions, assuming factorization of the production amplitude into a part proportional to the elastic $\mathrm{pp}$ amplitude times a part depending on $\beta \mathrm{}\left(k\right)\mathrm{}$ and the proton momenta; (ii) peripheral production of a spectrum of $N^{*}$ states by the longest range possible force-single-pion exchange. The combination of these two contributions leads to an inhomogeneous integral equation for the elastic amplitude $F(s,\theta )$ of the form