Alternative Method for Comparing Pion-Proton Scattering Data with Dispersion Equations

A method for comparing pion-proton scattering experiments with the predictions of the forward angle scattering dispersion equations is proposed, which allows the usual statistical measure (${\chi }^2$) of the agreement. A slight discrepancy is found between negative pion-proton data and the theory; however, the over-all agreement is considered satisfactory. Values of the coupling constant and $S$-wave zero-energy scattering lengths are determined. They are $f^2=0.08\mathrm{}\pm 0.01$, $a_1=0.193\mathrm{}\pm 0.050$, and $a_3=-0.089\mathrm{}\pm 0.048$.