Kinematic Constraints for Infinitely Rising Regge Trajectories

A kinematic constraint on the energy dependence of infinitely rising Regge trajectories is established. Under quite general conditions it is shown that asymptotically $\alpha \mathrm{}\left(s\right)\mathrm{}\le C{s}^{\frac{1}{2}}$, provided that certain channels couple to high-spin Regge recurrences. The implications of this result for dynamical models of ever-rising trajectories and for the decay rates of resonances are discussed in the light of experimental indications that $\alpha \mathrm{}\left(s\right)\mathrm{}\sim \mathrm{Cs}$.