Models of Elastic pp Scattering at High Energies – Possibilities, Limitations, Assumptions, and Open Ques-tions

The simplest collision process, the elastic scattering of protons, has been measured at various energies and in a broad interval of scattering angles. Its theoretical description is, however, much more delicate, than it may seem at first glance. The widely used eikonal model allowed one to analyze the pp elastic scattering data at an ISR energy of 52.8 GeV and the TOTEM data at a much higher LHC energy of 8 TeV. The results represent the most detailed elaborated impact parameter analysis of pp data which has ever been performed. They have helped to identify several deeper open questions and problems concerning all widely used theoretical frameworks used for the description of the elastic pp scattering. The problems should be further studied and solved to derive some important proton characteristics which may be obtained with the help of the elastic scattering.