s-WaveK+pDynamics

An investigation of the dynamics of low-energy $s$-wave $K^{+}p$ scattering has been made by the semiphenomenological application of dispersion relations. Contributions to the $s$-wave $K^{+}p$ dispersion relation from the nearby singularities due to the following processes were explicitly calculated: (a) exchange of $\Lambda$ and $\Sigma$ in the $u$ channel; (b) exchange of $\rho$, $\omega$, and $\phi$ in the $t$ channel, treated in the narrow-width approximation; and (c) exchange of an $s$-wave $T=0\mathrm{} \pi -\pi$ pair, treated as a continuum state. Other exchanges, and short-range forces, were treated phenomenologically. The amplitude in the physical region was taken from a recent phase-shift analysis of $K^{+}p$ scattering data, and the necessary coupling constants for the exchange processes were obtained from experiment, supplemented by the use of $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry when experimental data were not available. The exchange of the $s$ wave $T=0\mathrm{} \pi -\pi$ pair is shown to be potentially a very important term, and the present difficulties in calculating its exact size are discussed in detail.