Influence ofK¯-Nucleon Interactions on Pion-Hyperon Scattering

Abstract

Scattering amplitudes for coupled $\pi \Lambda$, $\pi \Sigma$, and $\overline{K}N$ channels are obtained by an extension of the method of Amati, Stanghellini, and Vitale. The method is shown to be essentially equivalent to the $\frac{N}{D}$ method in the region of nonrelativistic baryon energies, under the assumption that the only important forces arise from the Born singularities. All possibilities for the $\Sigma \Lambda$ and $\overline{K}\Lambda$ relative parities are considered. The aim is to see to what extent earlier calculations, which neglect the $\overline{K}-N$ interactions, are modified by its inclusion. If the $\overline{K}N$ coupling constants are as strong as the $\pi N$ coupling, significant quantitative and qualitative modifications are obtained: an $I=1\mathrm{}$, $J=\frac{3}{2}$ resonance with the properties of the ${Y_1}^{*}$ may be obtained for $P\left(\Sigma \Lambda \right)=\pm 1$; an $I=0\mathrm{}$ resonance with the location and width of the ${Y_0}^{*}$ may be obtained for $P\left(\Sigma \Lambda \right)=-1\mathrm{}$, in the $P_{\frac{1}{2}}$ state, and for $P\left(\Sigma \Lambda \right)=+1\mathrm{}$, in the $P_{\frac{3}{2}}$ state. If the $\overline{K}N$ couplings are significantly weaker than the $\pi N$ coupling, a $P_{\frac{3}{2}}$ resonance with the properties of the ${Y_1}^{*}$ is obtained only if $P\left(\Sigma \Lambda \right)=+1\mathrm{}$ and if the $\Sigma \Sigma \pi$ coupling is very weak; in this case one obtains no $I=0\mathrm{}$ resonance identifiable with the ${Y_0}^{*}$. An $I=0\mathrm{}$, $P_{\frac{3}{2}}$ resonance at 1520 MeV may be obtained with a wide variety of couplings for $P\left(\Sigma \Lambda \right)=+1\mathrm{}$; the predicted width of this resonance is very large ($\frac{\Gamma }{2}>50\mathrm{}$ MeV). Resonances in other states,...