Formalism for Partial-Wave Analysis of the Reaction Meson (0−) + Baryon (½+) → Meson (0−) + Baryon (32+)

The formalism for making a partial-wave analysis of the reactions $\pi +N\to \Delta \mathrm{}\left(1236\right)+\pi$ and $\overline{K}+N\to \Sigma \mathrm{}\left(1385\right)+\pi$ is outlined. From such an analysis, the coupling of baryon resonances to these inelastic channels can be determined. The differential cross section, decay distribution for $\Delta \to N+\pi$, and nucleon polarization are expressed as functions of the $S$-matrix elements ${S_{l^{\prime }\frac{3}{2},l\frac{1}{2}}}^J\mathrm{}\left(k\right)\mathrm{}$, which connect the initial $\pi N$ state with orbital angular momentum $l$, spin $J$, and c.m. momentum $k$ to the $\Delta \pi$ state with orbital angular momentum $l^{\prime }$.