Unitarisation dependence of diffractive scattering in light of high-energy collider data

We study the consequences of high-energy collider data on the best fits to total, elastic, inelastic, and single-diffractive cross sections for $pp$ and $p \bar{p}$ scattering using different unitarisation schemes. We find that the data are well fitted both by eikonal and U-matrix schemes, but that diffractive data prefer the U-matrix. Both schemes may be generalised by means of an additional parameter; however, this yields only marginal improvements to the fits. We provide estimates for $\rho$, the ratio of the real part to the imaginary part of the elastic amplitude, for the different fits. We comment on the effect of the different schemes on present and future cosmic ray data.