Effective Range Analysis ofs-WaveK−pReactions

An effective range analysis of $s$-wave $K^{-}p$ 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 $\pi \Lambda$ resonance having the characteristics of the ${Y_1}^{*}$. The only acceptable solutions found were for even $K\Sigma N$ 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 $K^{-}p$ 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 $K^{-}p$ data. The actual $\pi Y$ 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.