Diractive Production at Collider Energies I: Soft Diraction and Dino's Paradox

One of the more interesting developments from recent collider experiments is the nding that hadronic total cross sections as well as elastic cross sections can be described by the exchange of a \soft Pomeron" pole in the near-forward limit. The most important consequence of Pomeron being a pole is the factorization property. However, due to Pomeron intercept being greater than 1, the extrapolated single di raction dissociation cross section based on a classical triple-Pomeron formula is too large leading to a potential unitarity violation at Tevatron energies. It is our desire here to examine carefully the notion of Pomeron ux renormalization, proposed by Goulianos, and to suggest an alternative resolution. Our treatment lies in a proper implementation of nal-state screening correction, with \ avoring" for Pomeron as the primary dynamical mechanism for setting the relevant energy scale. In our scheme, which we shall occasionally refer to as \unitarization of Pomeron ux", initial-state screening remains unimportant, consistent with the pole dominance picture for elastic and total cross section hypothesis at Tevatron energies. Since factorization remains intact, umambiguous predictions for double Pomeron exchange, doubly di raction dissociation, etc., both at Tevatron and at LHC energies, can be made.