Hadron collisions at ultrahigh energies: black disk or resonant disk modes?

The analysis of current ultrahigh energy data for hadronic total cross sections and diffractive scattering cross sections points to a steady growth of the optical density with energy for elastic scattering amplitudes in the impact parameter space, $b$. At LHC energy the profile function of the $pp$-scattering amplitude, $T(b)$, reaches the black disk limit at small $b$. Two scenarios are possible at larger energies, $\sqrt{s}\text{ga}100$ TeV. First, the profile function gets frozen in the black disk limit, $T(b)\simeq 1$ while the radius of the black disk $R_{blackdisk}$ is increasing with $\sqrt{s}$, providing ${\sigma }_{tot}\sim {\ln }^{2}s$, ${\sigma }_{el}\sim {\ln }^{2}s$, $\sigma_{inel}\sim \ln^2s$\mathrm{.}Inanotherscenariotheprofilefunctioncontinuestogrowat$\sqrt{s}\ga 100$TeVapproachingthemaximalvalue,$T(b)\simeq 2$, that means the resonant disk mode. We discuss features of the resonant disk mode when the disk radius, $R_{resonantdisk}$, increases providing the growth of the total and elastic cross sections ${\sigma }_{tot}\sim {\ln }^{2}s$, $\sigma_{el}\sim \ln^2s$,butamoreslowincreaseofinelasticcrosssection,$\sigma_{inel}\sim \ln s$.