Impact-parameter analysis of the new TOTEM pp data at 13 TeV: black disk limit excess

We revisit a discussion on the impact-parameter dependence of proton-proton elastic scattering amplitude with improved uncertainty calculation. This analysis allows to reveal the asymptotic properties of hadron interactions. New data indicates that the impact-parameter elastic scattering amplitude is slightly above the black disk limit at 13~TeV c.m.s. energy of the LHC reaching a value of $$\mathrm{I}\mathrm{m}$,H(s,0) = 0.512\pm 0.001\ $\text{(sys+stat)}$ \pm 0.004
$\text{(norm)}$$ confirming that black disk limit is violated at current collision energy, however it was not exceeded at 7~TeV. The growth trend of the impact-parameter amplitude imaginary part, extrapolated from previous and new data, indicates that it is unlikely that the amplitude is close to saturation. New analysis is consistent with smooth energy evolution of the elastic scattering amplitude and supersedes the earlier conclusion on the black disk limit excess observed at 7~TeV.