Impact-ParameterK-Matrix Approach to High-Energy Peripheral Interactions

An approximate dispersion-theoretic treatment of peripheral inelastic processes is introduced with the aid of a $K$-matrix formalism based on the impact-parameter representation of Blankenbecler and Goldberger. The method allows the use of one-meson exchange poles as a framework for constructing a multichannel scattering amplitude which satisfies unitarity in the high-energy region, allowing for an indefinitely large number of open channels. The reaction matrix is time-reversal symmetric and exhibits any other symmetries of the pole terms. Applications are numerically worked out for models of high-energy $\overline{K}p$ and $\mathrm{np}$ charge exchange, and in the former case satisfactory agreement with experiments is achieved. A qualitative discussion is given of peripheral isobar production models. The high-energy $\overline{p}p$ and $\overline{K}p$ diffraction scattering is examined, as well as the agreement of the small-momentum-transfer behavior with a simple model not involving Regge poles. The method sheds no light on the difference between $\overline{p}p$ and $\mathrm{pp}$ scattering at high energies.