Phenomenological Model of Diffraction and Resonant Scattering

Diffraction phenomena are shown to play an important role in $K^{-}p\to K^{-}p$ elastic scattering, even in the region of $\sim 1 \frac{\mathrm{GeV}}{c}$, where resonant effects are dominant. A brief review of existing data indicates that the differential cross sections consistently exhibit an exponential behavior at small momentum transfers from ∼16 down to $\sim 0.8 \frac{\mathrm{GeV}}{c}$, and that the scattering amplitudes throughout this region are predominantly imaginary. The slope of the diffractionlike peak is shown to increase sharply at incident $K^{-}$ momenta, corresponding to the formation of known, highly elastic resonances. A model is then formulated to apply to ($\pi ,K$)-nucleon two-body processes, in which the scattering amplitudes for each isospin state are described by a linear superposition of diffractive and resonant contributions. On a purely empirical basis, the diffractive amplitudes have been parametrized in terms of an exponential $t$ dependence. The model has been specialized to interpret $K^{-}p\to K^{-}p$ elastic-scattering data from 0.8 to $1.2 \frac{\mathrm{GeV}}{c}$, where two dominant resonant states are known, the ${Y_1}^{*}\mathrm{}\left(1760\right)\mathrm{}$ and ${Y_0}^{*}\mathrm{}\left(1820\right)\mathrm{}$. A good fit to the data yields a reliable set of six resonant parameters (masses, widths, and elasticities) for these states, and three parameters describing the diffractive contribution (real and imaginary part of the forward-scattering amplitude, and slope of the diffraction peak).