Asymptotic regimes for hadron diffractive scatterings and coulomb interaction. Arguments for the black disk mode

Comparative analysis of the interplay of hadron and Coulomb interactions in $pp^\pm$ scattering amplitudes is performed in a broad energy interval, $\sqrt{s}=1-10^6$ TeV, for two extreme cases: for the asymptotic interactions of hadrons in black disk and resonant disk modes. The interactions are discussed in terms of the $K$-matrix function technique. In the asymptotic regime the real part of the hadronic amplitude is concentrated in both cases on the boundary of the disks in the impact parameter space but the LHC energy region is not asymptotic for the resonant disk mode that lead to a specific interplay of hadronic and coulombic amplitudes. For the $pp$ scattering at $\sqrt{s}\sim 10$ TeV an interplay of the hadron and Coulomb interactions in the resonant disk modes is realized in a shoulder in $d\sigma_{el}/d{\bf q}^2$ at ${\bf q}^2\sim 0.0025-0.0075$ GeV$^2$. The absence of such a shoulder in the data at 8 TeV can be considered as an argument against the resonant disk mode.