The structure and analytic properties of the scattering amplitude at LHC energies

Elastic proton-proton scattering is reviewed starting from the results of the LHC experiments conducted by the TOTEM and ATLAS collaborations, and the HEGS model and a simple phenomenological parametrisation are compared with the new data on the differential elastic proton-proton scattering cross section, which detect a non-exponential behaviour of the differential cross sections in the first diffraction cone. We consider the influence of various assumptions on the extraction of the elastic scattering parameters, and on the deduction of the total cross section.