Rising cross sections and scaling

Abstract

A parametrization for hadronic total cross sections, which incorporates a logarithmically rising term, is proposed. The new parameters present in it are restricted, using a scaling assumption for ${q}^{2}$ in the timelike region. The resulting expression contains only one parameter in addition to the usual Regge parameters. In the energy range between $10 \mathrm{and} 400 \frac{\mathrm{GeV}}{c}$ this model gives very good fits for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$, ${K}^{\ifmmode\pm\else\textpm\fi{}}p$, $pp$, and $\overline{p}p$ total cross sections. Above $400 \frac{\mathrm{GeV}}{c}$, the agreement with recent data on the $pp$ total cross section is only qualitative. The model also predicts the vanishing of the ratio of real to imaginary parts of the $pp$ forward elastic amplitude at $360 \frac{\mathrm{GeV}}{c}$ in agreement with experimental data, the increase of this ratio to a maximum value, and a vanishing asymptotic limit.