  Analysis of differential cross sections of the TOTEM Collaboration data,
carried out without model assumptions, shows the existence of new effects in
the behavior of the hadron scattering amplitude at a small momentum transfer at
a high confidence level. The quantitative description of the data in the
framework of the high energy generalized structure (HEGS) model supports such a
phenomenon that can be associated with the specific properties of the hadron
potential at large distances. It is shown that the value of $\rho(s,t)$ at
$\sqrt{s}=13$ TeV and small $t$ exceeded $0.1$.
