K+pscattering analysis to 2 GeV/c

The $K^{+}p$ scattering data up to 2 GeV/c were fitted with a coupled-channel $K$-matrix parametrization in which inelasticity is represented by a single production channel for each partial wave. Several solutions are possible above laboratory kinetic energies about 1 GeV, but all are essentially the same below this energy. All solutions that we have found have a $P_{13}$ resonance pole at about total c.m. energy ($1796-i101$) MeV. Resonance poles are present in other partial waves but are at considerably higher energies or are considerably farther from the real energy axis. More reliable measurements of polarizations are needed to firmly establish the existence of resonance poles other than the $P_{13}$ one. Also, contemporary measurements of the reaction cross sections are needed.