Momentum Dependence of Diffraction Slopes in Meson-Nucleon Scattering

Abstract

The slopes $B(k)$ of the exponential forward peak for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ and ${K}^{\ifmmode\pm\else\textpm\fi{}}p$ elastic scattering have been surveyed in the region $0.3\ensuremath{\lesssim}{P}_{\mathrm{lab}}\ensuremath{\lesssim}20.0$ GeV/c. Plots of the momentum dependence of $B(k)$ reveal striking enhancements at momenta corresponding to the location of known high-spin, high-elasticity resonances. There are indications that the background behavior of $B(k)$, when considered over such a wide momentum interval, might be smoothly rising in all cases; thus, the forward peak associated with background diffraction effects would appear to shrink not only in ${K}^{+}p\ensuremath{\rightarrow}{K}^{+}p$ interactions, where resonance formation is weak (or absent), but also in ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ and ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{\ensuremath{-}}p$ interactions, where many prominent resonant states are formed. An explanation for the behavior of $B(k)$ is presented, based on the properties of the logarithmic derivative of the differential cross section in the forward direction. As a quantitative illustration, $B{(k)}_{{K}^{\ensuremath{-}}}$ was derived in terms of a simple phenomenological model, which involves a linear superposition of diffractive-like and resonant amplitudes. In this way a fit to the $B{(k)}_{{K}^{\ensuremath{-}}}$ and ${K}^{\ensuremath{-}}p$ total-cross-section data could be obtained throughout the entire momentum region. The information which can be derived from the experimental study of $B(k)$ is discussed; this has bearing on the determination of resonance properties and on the behavior of the spin-flip amplitude.