Phenomenological Model of Diffraction and Resonant Scattering

Abstract

Diffraction phenomena are shown to play an important role in ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{\ensuremath{-}}p$ elastic scattering, even in the region of $\ensuremath{\sim}1 \frac{\mathrm{GeV}}{c}$, 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 \ensuremath{\sim}16 down to $\ensuremath{\sim}0.8 \frac{\mathrm{GeV}}{c}$, and that the scattering amplitudes throughout this region are predominantly imaginary. The slope of the diffractionlike peak is shown to increase sharply at incident ${K}^{\ensuremath{-}}$ momenta, corresponding to the formation of known, highly elastic resonances. A model is then formulated to apply to ($\ensuremath{\pi},K$)-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 ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{\ensuremath{-}}p$ elastic-scattering data from 0.8 to $1.2 \frac{\mathrm{GeV}}{c}$, where two dominant resonant states are known, the ${{Y}_{1}}^{*}(1760)$ and ${{Y}_{0}}^{*}(1820)$. 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).