Problems of diffractive scattering

The theoretical problems concerning the description of the near constancy of the cross-sections at high energies are discussed. The attempt to formulate the problem in Regge language is described. It is shown that the Mueller extension of Regge methods to inclusive processes yields to following benefits: to the factorization of the inclusive cross-sections and to the use of sum rules added to the factorization which make it possible to derive inequalities and bounds at the theoretical level. The problems associated with the diffraction scattering namely: why the trajectory value at t = 0 is exactly one, the existence of the cuts, branch points in the angular momentum plane which were discovered after the introduction of the trajectory concept by Amati et al. and the problem of the Pomeron - Pomeron - particle coupling at t = 0 are considered. The idea that a leading pole at α = 1 at t = 0 has to be decoupled from everything including the elastic channel is discussed as well as the Froissart theory which gives the saturation of the cross-sections at high energies. (S.B.)