Real parts of forward elastic hadronic amplitudes

Abstract

We compute the real parts of forward elastic hadronic scattering amplitudes using derivative analyticity relations and recent measurements of total cross sections at the Fermi National Accelerator Laboratory. The results on the ratios of real to imaginary parts, $\ensuremath{\rho}(s)$, for $pp$, $\overline{p}p$, ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$, and ${K}^{\ifmmode\pm\else\textpm\fi{}}p$ are compared with the available experimental data. The agreement with the data is reasonably good. The real parts are predicted to change signs at energies $s\ensuremath{\simeq}180,430,120,250, <20 \mathrm{and} 145$, ${\mathrm{GeV}}^{2}$ for $\overline{p}p$, $pp$, ${\ensuremath{\pi}}^{\ensuremath{-}}p$, ${\ensuremath{\pi}}^{+}p$, ${K}^{\ensuremath{-}}p$, and ${K}^{+}p$, respectively.