Lorentz Pole Structure andt=0Kinematic Constraints in Forward Vector-Meson Production

We determine the behavior near $t=0\mathrm{}$ of the helicity amplitudes for $\pi N\to \mathrm{VN}$, $\pi \pi \to \mathrm{VV}$, and $\mathrm{NN}\to \mathrm{NN}$ consistent with (1) the $t=0\mathrm{}$ kinematic constrains (conspiracy relations), (2) the classification of Regge poles into $O(3, 1)$ families at $t=0\mathrm{}$, and (3) the requirement of factorization for individual poles of definite quantum numbers. We show that from the $t$ dependence thus determined, one is able to derive the rule for the energy dependence of forward scattering amplitudes proposed by Sawyer.