Impact analysis of TOTEM data at the LHC: black disk limit exceeded
  We discuss the profile of the impact--parameter dependent elastic scattering amplitude. Extraction of impact-parameter dependence from the dataset with inclusion of the experimental data on elastic scattering at the LHC energies helps to reveal the asymptotics of hadron interactions. Analysis of the data clearly indicates that the impact-parameter elastic scattering amplitude exceed the black disk limit at the LHC energy 7TeV and the inelastic overlap function reaches its maximum value at $b>0$ 
A. Alkin, E. Martynov, O. Kovalenko, S.M. Troshin
hep-ph hep-ex