Do we understand elastic scattering up to LHC energies?

The measurements of high energy (bar sign)pp and pp elastic at ISR, SPS, and Tevatron colliders have provided usefull informations on the behavior of the scattering amplitude. A large step in energy domain is accomplished with the LHC collider presently running, giving a unique opportunity to improve our knowledge on the asymptotic regime of the elastic scattering amplitude and to verify the validity of our theoretical approach, to describe the total cross section σtot(s), the total elastic cross section σel(s), the ratio of the real to imaginary parts of the forward amplitude ρ(s) and the differential cross section dσ (s,t)/dt.