π−−pScattering and the Dispersion Relation

Theoretical values for $D_{-}\left(\omega \right)$ in the theory of pion dispersion relations have been recalculated with a suitable modification of the experimental values for ${{\sigma }_{\mathrm{tot}}}^{-}$. This modification is supported by the results obtained from a recent phase-shift analysis. Agreement with the experimental values for $D_{-}\left(\omega \right)$ is achieved for pion kinetic energies ≲220 Mev. It may be concluded that the theoretical values for $D_{-}\left(\omega \right)$ have a strong dependence on the detailed shape of the peak of ${{\sigma }_{\mathrm{tot}}}^{-}$ near the resonance.