Study ofπNandKNElastic and Inelastic Scatterings and Their Polarizations by a Multiple-Regge-Pole Model

Abstract

The presently available data on pion-nucleon scattering for incident momenta from 6 to 18 $\frac{\mathrm{GeV}}{c}$ and for small values of momentum transfer [$|t|<1 {(\frac{\mathrm{GeV}}{c})}^{2}$] are analyzed using a model characterized by the dominance of several meson Regge poles in the crossed channels. Among the processes considered are ${\ensuremath{\pi}}^{+}p$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p$ elastic scattering and the charge-exchange reactions ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\eta}}^{0}n$. All the contributing meson trajectories, $P$, ${P}^{\ensuremath{'}}$, $\ensuremath{\rho}$, and ${A}_{2}$, are taken into account. The following $\mathrm{KN}$ reactions: ${K}^{\ensuremath{-}}p$, ${K}^{\ensuremath{-}}n$, ${K}^{+}p$, ${K}^{+}n$ elastic scattering and the ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{0}n$ charge-exchange reaction, are also analyzed with the contributing trajectories $P$, ${P}^{\ensuremath{'}}$, $\ensuremath{\rho}$, ${A}_{2}$, and $\ensuremath{\omega}$. We find that both ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ data for pion-nucleon reactions can be very well fitted by the model with energy-independent residue functions. The polarization data are well fitted, and determine the residue functions of $P$, ${P}^{\ensuremath{'}}$, and $\ensuremath{\rho}$. These parameters are then used to fit the $\mathrm{KN}$ data to obtain the residue function of $\ensuremath{\omega}$. The polarizations of the $\mathrm{KN}$ scatterings for which data are still lacking are predicted by the model. In connection with the speculation that the ${P}^{\ensuremath{'}}$ trajectory may behave like the $\ensuremath{\rho}$ trajectory, three alternative trajectories are assumed for ${P}^{\ensuremath{'}}$, and their corresponding residue functions determined by the given data. The results are plotted, and we find that the "predicted" polarizations are not very sensitive to the variation of the ${P}^{\ensuremath{'}}$ trajectory. Our results show that the nonflip residue functions of both $\ensuremath{\omega}$ and $\ensuremath{\rho}$ cross the $t$ axis near $0<|t|<0.1 {(\frac{\mathrm{GeV}}{c})}^{2}$, while those of $P$ and ${P}^{\ensuremath{'}}$ do not. We have established the relative sign between different trajectories. We would also like to point out that in the fittings more constraints derived from the sum rules are verified in the present work.