Exotic Trajectories and the Pomeranchukon in a Veneziano Representation forKNandK¯NScattering

Abstract

The $\mathrm{KN}$ and $\overline{K}N$ scattering processes are studied within the framework of the Veneziano model. Apart from the normal trajectories, $\ensuremath{\rho}$, $\ensuremath{\Lambda}$, $\ensuremath{\Sigma}$, and ${Y}_{1}^{*}$, appearing in these processes, for the first time the contribution of the Pomeranchuk trajectory is included in a quantitative manner. An immediate consequence, if one is to avoid exchange degeneracy of the Pomeranchukon. is that baryon trajectories with exotic quantum numbers have to be introduced also. With reasonable parameters for the normal as well as the exotic trajectories, good agreement with a wide range of experimental data for $\mathrm{KN}$ and $\overline{K}N$ scattering is obtained. In particular, we fit ${K}^{\ensuremath{-}}p$ and ${K}^{+}n$ charge-exchange differential cross sections, ${K}^{\ensuremath{-}}p$ and ${K}^{+}p$ elastic scattering in both forward and backward directions, ${K}^{\ensuremath{-}}p$ and ${K}^{+}p$ total cross sections, and the polarization parameters for ${K}^{\ensuremath{-}}p$ and ${K}^{+}p$ elastic scattering. The parameters for the best fit imply reasonable properties of the normal as well as the exotic trajectories - the absence of parity partners of $\ensuremath{\Lambda}(1115)$, ${\ensuremath{\Lambda}}_{\ensuremath{\gamma}}(1520)$, $\ensuremath{\Sigma}(1190)$, and ${Y}_{1}^{*}(1385)$, and the correct signature property for the Pomeranchuk trajectory. The normal trajectories come out with a slope of about 1 ${\mathrm{GeV}}^{\ensuremath{-}2}$. The slope of the Pomeranchukon, which is the same for the exotic trajectories, is found from the best fits to be about 0.75 ${\mathrm{GeV}}^{\ensuremath{-}2}$, while the exotic trajectories have an intercept of about - 3.4. The properties of resonances lying on the normal and exotic trajectories are discussed.