Infinitely Rising Regge Trajectories and Crossing Symmetry

It is found that, in a crossing-symmetric model of a scattering amplitude $A(s,t)\mathrm{}$ which is dominated by Regge-pole exchange, the restrictions imposed by analyticity on the Regge trajectory $\alpha \mathrm{}\left(s\right)\mathrm{}$ and by analyticity and polynomial boundedness in $s$ for fixed $t$ on $A(s,t)\mathrm{}$, suggest uniquely the asymptotic behavior $\alpha \mathrm{}\left(s\right)\mathrm{}\sim \frac{s}{\ln s}$ as $s\to \infty$, if the large-$s$ and large-$t$ limits of $\ln A(s,t)\mathrm{}$ are uniform. The use of a double-dispersion relation for $\ln A(s,t)\mathrm{}$ is proposed.