Diffractive elastic scattering and hadronic radii: Geometric and Pomeron approaches

A parametrization based on geometric concepts is proposed for the spin-independent part of the amplitude $A_{12}\mathrm{}(s,t)\mathrm{}$ for elastic scattering of hadrons 1 and 2 at center-of-mass energies $\sqrt{s}\gtrsim 20$ GeV. The dependence on the squared momentum transfer $t$ is described by the form factors $F_i(t,R_i^2\mathrm{}(s\left)\right)$ for each hadron and contain energy-dependent complex radii $R_i\mathrm{}\left(s\right)\mathrm{}$. Data on differential cross sections for $\mathrm{pp}$, $p\overline{p}$, and $\pi p$ as well as the energy dependence of the total cross section and the slope parameter are reproduced with few adjustable parameters. When our parametrization for $A_{12}\mathrm{}(s,t)\mathrm{}$ is compared to the one from the Pomeron approach strong similarities emerge.