Phenomenological Model of Diffraction and Resonant Scattering

Diffraction phenomena are shown to play an important role in K^-p→K^-p elastic scattering, even in the region of ~1 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 ~0.8 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 (π,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→K^-p elastic-scattering data from 0.8 to 1.2 GeV/c, where two dominant resonant states are known, the Y₁*(1760) and Y₀*(1820). 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).