Factorization and the couplings of the vacuum trajectory

The decoupling theorems associated with an isolated factorizable pomeron pole of unit intercept are re-examined. It is found that the coupling of three such poles, Γ(t, t, 0), need not vanish, precisely at the point t = 0. This is demonstrated by summing only over states in the appropriate unitarity sum, and sum rule, which are consistent with the M², s/M² → ∞ limit. The triple-Regge region then makes a constant contribution to σ_total, insteadsb of the ln lns result obtained if the isolated pole is assumed to couple also to states such that s/M² = constant. The physical implications regarding factorization and the pole-cut relationship are discussed. The relationship between higher order optical theorems (Mueller discontinuities) and particular terms in the unitarity sum for the two → two absorptive part A₂₂ is exploited. Consistent contributions to the triple-Regge region contribute constant vertex corrections to pure pole behaviour in A₂₂. There is no cut contribution and the magnitude of the vertex corrections reflects the relative amount of diffractive production. The analysis is extended to multiple fireball production where pure multipole structures emerge. The series naturally terminates if the diffractive component is sufficiently small. The implications for the behaviour of the total cross section at machine energies are discussed.