Asymptotic Predictions of Forwardπ−NDispersion Relations

Abstract

The recent Brookhaven Coulomb-interference measurements of $\alpha =\frac{\mathrm{Re}f}{\mathrm{Im}f}$ are analyzed in terms of forward $\pi -N$ dispersion relations. The results are consistent with a crossover of ${\sigma }^{\mathrm{}(-)\mathrm{}}=\frac{1}{2}({\sigma }_{-}-{\sigma }_{+})$ at high energies above 22 BeV. The $\rho$-trajectory model determined by charge-exchange experiments is compared with our analysis of the data between 8 and 20 BeV.