Discrepancy betweenπ−-Proton Scattering and a Dispersion Equation

The ${\pi }^{-}$-proton scattering is reanalyzed following Puppi and Stanghellini. The use of more recent data in evaluating the very sensitive principal value integral and a more detailed error analysis lead, with the same coupling constant, $f^2=0.08\mathrm{}$, and the same $S$-wave scattering lengths, $a_1=0.165\mathrm{}$ and $a_3=-0.105\mathrm{}$, to much less disagreement than they found. However, a residual discrepancy of the same general character remains. It is pointed out that the analysis is very sensitive to the experimental charge exchange scattering, and two alternatives to using this data are suggested. The importance of $D$ waves, in extending the analysis to energies above 300 Mev, is demonstrated. It is shown that contributions from energies above ∼2 Bev, and reasonable changes in $f^2$, $a_1$, and $a_3$, cannot contribute significantly towards resolution of the discrepancy.