An analysis of the new LHC data through the dispersion relations

We present an analysis of the new experimental data obtained by the TOTEM and ATLAS Collaborations at the LHC at $s=7$ and 8 TeV and at small momentum transfer. We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the total cross section. In particular, the determination of the phase of the elastic scattering amplitude will play an important role, and we shall study it via dispersion relations. We shall also examine the origin of the dependence on momentum transfer of the slopes of the different parts of the scattering amplitude in different models. We shall also give the results of another similar analysis based on a Regge-trajectory approach for the hadron scattering amplitude.