Dynamical Model of the 1535-MeVΞ*Hyperon

An attempt is made to understand the dynamical origin of the 1535-MeV ${\Xi }^{*}$ hyperon. We study the problem of scattering in the $J={\frac{3}{2}}^{+}$-state of the $\overline{K}\Lambda$-channel by the $\frac{N}{D}$ method. The influence of all other channels are ignored. The dynamical singularities of the partial-wave amplitude are assumed to arise mainly from the near by cut (due to the nucleon exchange in the crossed channel) and the far left-hand cut ($-\infty <S<~0$). The contribution of the former is evaluated explicitly in terms of the $\Lambda \mathrm{NK}$ coupling constant and that of the latter, by the method of Balázs, through the introduction of the effective range pole terms. The analysis is found to be quite insensitive to the choice of the $\Lambda \mathrm{NK}$ coupling constant. The $D$ function is found to have the desired behavior for the occurrence of a resonance or bound state in the energy region of interest. The main force for the existence of the resonance or bound state seems to arise from the singularities associated with the far left-hand cut. The best set of self-consistent solutions for the position and residue indicates the presence of a bound state in the $J={\frac{3}{2}}^{+}$ state of $\overline{K}\Lambda$ system at $S_R\approx 109{m_{\pi }}^2$ with residue ${\mathrm{K}}_{{\Xi }^{*}}\approx 10$.