Momentum Dependence of Diffraction Slopes in Meson-Nucleon Scattering

The slopes $B\left(k\right)\mathrm{}$ of the exponential forward peak for ${\pi }^{\pm }p$ and $K^{\pm }p$ elastic scattering have been surveyed in the region $0.3\lesssim P_{\mathrm{lab}}\lesssim 20.0$ GeV/c. Plots of the momentum dependence of $B\left(k\right)\mathrm{}$ reveal striking enhancements at momenta corresponding to the location of known high-spin, high-elasticity resonances. There are indications that the background behavior of $B\left(k\right)\mathrm{}$, 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 $K^{+}p\to K^{+}p$ interactions, where resonance formation is weak (or absent), but also in ${\pi }^{\pm }p\to {\pi }^{\pm }p$ and $K^{-}p\to K^{-}p$ interactions, where many prominent resonant states are formed. An explanation for the behavior of $B\left(k\right)\mathrm{}$ is presented, based on the properties of the logarithmic derivative of the differential cross section in the forward direction. As a quantitative illustration, $B{\mathrm{}\left(k\right)\mathrm{}}_{K^{-}}$ 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 $B{\mathrm{}\left(k\right)\mathrm{}}_{K^{-}}$ and $K^{-}p$ total-cross-section data could be obtained throughout the entire momentum region. The information which can be derived from the experimental study of $B\left(k\right)\mathrm{}$ is discussed; this has bearing on the determination of resonance properties and on the behavior of the spin-flip amplitude.