Isobar Mechanism for Pion-Baryon Higher Resonances

Peierls isobar mechanism is extended to pion-hyperon interactions on the assumption that ${Y_1}^{*}$ is the $\pi \Lambda$ isobar whose mass lies below the $\overline{K}N$ threshold and of spin parity $P_{\frac{3}{2}}$. It is shown that this mechanism, when combined with experimental data currently available, does suggest that a pion-hyperon resonance in the $I=1\mathrm{}$ channel at c.m. energy 1645 Mev with spin-parity assignment $D_{\frac{3}{2}}$ is possible. This resonance state is expected to reflect in the total $K^{-}-p$ and $K^{-}-n$ (pure $I=1\mathrm{}$) cross sections as resonance peaks centered at around 685-Mev/c $K$-meson lab momentum. Experimental implications of this isobar model for pion-baryon interactions as well as certain mathematical difficulties associated with the over-all validity of such a mechanism are also discussed.