Reggeon Structure,s-Channel Unitarity, and the Mandelstam Cut

We study in detail the allowed $s$-channel intermediate states in the unitarity equations for the Mandelstam and Amati-Fubini-Stanghellini diagrams. The aim is to contrast them with Abarbanel's analysis of the full unitarity equation. On this basis we argue that Abarbanel's ansatz for the general production amplitude is incomplete. The details of our calculation depend strongly on the off-mass-shell behavior of the ladder diagrams which we analyze in some detail. Our analysis is also generalized to present arguments against the inclusive-sum-rule proof of the vanishing of the triple-Pomeron vertex at $t=0\mathrm{}$.