Forward scattering at collider energies and eikonal unitarization of the odderon

The continuing increase of hadron total cross sections up to the highest energies currently available can most naturally be understood through an eikonal mechanism, leading to the saturation of the Froissart bound. This picture can be motivated in a nonperturbative treatment of QCD, e.g., in the large-N limit. It is then natural to ask whether this same mechanism would lead to the maximal allowed behavior for the difference of the particle-particle and antiparticle-particle cross sections, i.e., the 'maximal odderon'. We shall show in this paper that, using eikonals which are dynamically meaningful for high-energy hadron-hadron scattering at collider energies, this behavior is not possible. (orig.)