New properties of elastic $pp$ and $p\bar{p}$ scattering at high energies

Data-driving determination of the new properties of elastic scattering at small angles on the basis on all existing experimental data for $d\sigma/dt$ of $pp$ and $p\bar{p}$ at $\sqrt{s} \geq 540$ GeV allows us to obtain the main characteristics of the nonstandard terms of the elastic scattering amplitude. It was shown that the oscillation term has a different sign for $pp$ and $p\bar{p}$ reactions; hence, it is part of the Odderon amplitude. The energy dependence of the oscillation term and the term with an extremely large slope is determined. The period of the oscillation term agrees with the scaling properties predicted by the Auberson - Kinoshita - Martin (AKM) theorem. The high quality quantitative description of all data at $\sqrt{s} \geq 540$ GeV in the framework of the HEGS model supports such a phenomenon which can be connected with peripheral hadron interaction.