Froissart bound, diffraction scattering of hadrons, and scaling at asymptotic energies

The Froissart bound on the total cross section, ${\ensuremath{\sigma}}_{t}$, is subjected to test against very high energy data. We have found no clear evidence for its violation. The scaling property of the differential cross section in the diffraction region is investigated. It exhibits scaling in the ISR, SPS, Tevatron, and LHC energy domain which had hitherto remained unexplored. The slope of the diffraction peak is fitted and the data are tested against the rigorous bounds.