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, $\sqrt{s}\ga 100$ TeV. First, the profile function gets frozen in the black disk limit, $T(b)\simeq 1$ while the radius of the black disk $R_{black\;disk}$ is increasing with $\sqrt s$, providing $\sigma_{tot}\sim \ln^2s$, $\sigma_{el}\sim \ln^2s$, $\sigma_{inel}\sim \ln^2s$. In another scenario the profile function continues to grow at $\sqrt{s}\ga 100$ TeV approaching the maximal value, $T(b)\simeq 2$, that means the resonant disk mode. We discuss features of the resonant disk mode when the disk radius, $R_{resonant\;disk}\,$, increases providing the growth of the total and elastic cross sections $\sigma_{tot}\sim \ln^2s$, $\sigma_{el}\sim \ln^2s$, but a more slow increase of inelastic cross section, $\sigma_{inel}\sim \ln s$. 
V.V. Anisovich, V.A. Nikonov, J. Nyiri
hep-ph