Resonance Pole with $J^P={\frac{3}{2}}^{+}$ in a Coupled-Channel Analysis of $K^{+}p$ Elastic Scattering Data

Energy-dependent partial-wave amplitudes based on a coupled-channel ($K^{+}p, K\Delta$) $K$- matrix formalism are obtained for elastic $K^{+}p$ scattering up to $P_{\mathrm{lab}}=2\mathrm{}$ GeV/c. The data used include new high-precision differential cross sections. A total of 42 parameters describing the $l<~4$ partial waves are used to fit 3822 data points and the best solution found has a ${\chi }^2$ per degree of freedom of 1.33. This solution exhibits a $T$-matrix $Z^{*}$ resonance pole in the $P_3$ partial wave with mass coordinates 1787-$i100\mathrm{}$ MeV.