Discovery of the Odderon by TOTEM experiments and the FMO approach

This paper is an extended version of the talk by B. Nicolescu at the XLVIII International Symposium on Multiparticle Dynamics (ISMD2018) at Singapore, 3-7 September, 2018. Theoretical basis and history of the Froissaron and Maximal Odderon (FMO) approach for elastic $pp$ and $\bar pp$ scattering is presented. Precise formulation of the FMO model at any momentum transfer squared $t$ is given. The model is applied to description and analysis of the experimental data in a wide interval of energy $\sqrt{s}$ and $t$. The special attention is given for the latest TOTEM data at 13 TeV, both at $t=0$ and at $t\neq 0$ and to their interpretation in the FMO model. It is emphasized that the last TOTEM results can be considered as clear evidence for the first experimental observation of the Odderon, predicted theoretically about 50 years ago.