The recent, extremely precise measurements of Carter et al. led to widely different values of the mass and width of the $\pi N$ 3-3 resonance depending on the particular resonance formulas used. We had shown, however, that the position of the $S$-matrix pole in the complex plane had a unique value $M_{33}=1211-50i$ MeV. We report here that the residue of the pole $\frac{R}{(M_{33}-W)}$ in $T [=\frac{\mathrm{}(S-1\mathrm{})\mathrm{}}{2i}]$ has the unique value $R=53\mathrm{}{e}^{-i0.81\mathrm{}}$ MeV. We are unable to interpret these four fundamental parameters $M_{33}$ and $R$. We thus present it as a basic, important problem to understand these parameters in a model-independent manner.

• Received 15 January 1973

DOI:https://doi.org/10.1103/PhysRevD.7.2789