Effective Range Analysis ofs-WaveK−pReactions

Abstract

An effective range analysis of $s$-wave ${K}^{\ensuremath{-}}p$ reaction data is carried out. Two specific problems are investigated. First, a survey is made of solutions which, in addition to fitting the above threshold data, yield a $\ensuremath{\pi}\ensuremath{\Lambda}$ resonance having the characteristics of the ${{Y}_{1}}^{*}$. The only acceptable solutions found were for even $K\ensuremath{\Sigma}N$ parity and did not lead to a ${{Y}_{0}}^{*}$ resonance. Other features of these solutions are discussed, as well as the validity and applicability of the effective range approximation to describe the energy dependence of the $\overline{K}N$ data. Second, using the (nonperturbative) uncoupled phase procedure developed in the preceding paper, we investigate effective range solutions for the above threshold ${K}^{\ensuremath{-}}p$ data which, in the absence of influence of the $\overline{K}N$ channel, would have the pion-hyperon scattering amplitudes predicted by global symmetry of the pion-baryon interaction. The concept of global symmetry is found to be compatible with the present ${K}^{\ensuremath{-}}p$ data. The actual $\ensuremath{\pi}Y$ phases, however, are quite different from the global symmetry uncoupled phases in states coupled to the $\overline{K}N$ $s$ wave, and there are solutions in which the ${{Y}_{0}}^{*}$ arises as a quasi-bound state resonance. Going beyond the physical predictions of these surveys, we conclude that there are at present almost enough $\overline{K}N$ data above threshold to justify a search for effective range solutions (then predicting whether either ${{Y}_{1}}^{*}$ or ${{Y}_{0}}^{*}$ is in the same partial wave as a $\overline{K}N$ $s$ state). Moreover, it is clear that such solutions will be quite different from the results of a constant scattering-length analysis of low-energy data.