Abstract
The effect of the newly discovered dipion resonance at about 730 MeV and of a possible one at about 400 MeV on pion-nucleon scattering is evaluated. Partial-wave dispersion relations are solved via the $\frac{N}{D}$ decomposition by matrix-inversion methods. Two choices of "phase-space" factors are considered. The results, as compared with earlier calculations of a similar type, show marked improvement in ${P}_{33}$ and ${P}_{11}$ scattering lengths (with the Martin-Uretsky-type phase-space factor) but continue to disagree violently with experiment on the ${S}_{\frac{1}{2}}T=\frac{1}{2}$ scattering length.
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