Geometric interpretation of hadron-proton total cross sections and a determination of hadronic radii

Abstract

Hadron-proton total cross sections ${\sigma }_{\mathrm{hp}}^t$ and slope parameters $b_{\mathrm{hp}}$ from elastic scattering are found to be closely related. If effective radii $R_i$ are defined by $b_{\mathrm{hp}}$=$R_h^2$+$R_p^2$, we find from the data ${\sigma }_{\mathrm{hp}}^t$=${\mathrm{gR}}_h^2$ $R_p^2$. This geometric factorization property, which holds for c.m. energies √s ≥15 GeV, is understood within the eikonal approach. Total cross sections ${\sigma }_{\mathrm{hp}}^t$ can be used to deduce hadronic radii of mesons and baryons.