Pomeron decoupling theorems

We investigate the hypothesis that diffractive scattering is dominated (as $s\to \infty$) by a Pomeron Regge pole [${\alpha }_P\mathrm{}\left(t\right)\mathrm{}$]. This hypothesis is particularly attractive since a Regge pole and its attendant cuts satisfy $t$-channel unitarity. For a complete theory the constraints of $s$-channel unitarity must also be satisfied. In addition to Froissart's bound and its wellknown consequence, ${\alpha }_P\mathrm{}\left(0\right)\mathrm{}\le 1$, $s$-channel unitarity implies a large number of decoupling theorems for an isolated Pomeron pole with ${\alpha }_P\mathrm{}\left(0\right)=1\mathrm{}$. Here we systematically review these decoupling theorems. The theorems are treated in order of increasing strength so as to clearly distinguish the "strong theorems" which can be used to prove the complete decoupling of the Pomeron (e.g., ${\sigma }_{\mathrm{Tot}}\to 0$) from the "weak theorems" which cannot. This review is undertaken with two goals in view: (1) To focus attention on possible points of departure for more realistic treatments of diffractive scattering, and (2) to emphasize the importance of $s$-channel unitarity which is expected to strongly constrain diffractive production in certain regions of phase space regardless of the exact nature of the Pomeron singularity.