Implications of Direct- and Crossed-Channel Regge Self-Consistency

Abstract

By comparing the $t$-channel Regge-pole amplitude with the $s$-channel Regge amplitude, we apply self-consistency for near-forward scattering. Under certain plausible assumptions, this enables us to evaluate the high-energy behavior of the Regge-trajectory function as $\ensuremath{\alpha}(s)\ensuremath{\rightarrow}{(s\mathrm{ln}s)}^{\frac{1}{2}}$, and that of the residue function as $\ensuremath{\beta}(s)\ensuremath{\rightarrow}{s}^{{\ensuremath{\alpha}}_{c}(0)\ensuremath{-}\frac{1}{2}}{(\mathrm{ln}s)}^{\ensuremath{-}\frac{1}{2}}$. We also determine that two trajectories will have the same shape if their derivatives at $s=0$ are the same, since this derivative alone determines the trajectory shape completely. The resonance content of these trajectories at high $s$ is also examined and found to be empty in the usual sense.