General Parametrization of Trajectory and Residue Functions for Daughter Regge Poles

Abstract

We present the most general parametrizations for the trajectory and residue functions for daughter Regge poles which are consistent with analyticity and unitarity. Our results are confined to the scattering of spinless particles, but are valid for arbitrary external masses and nonparallel trajectories. We show that except in the special case of pairwise-equal external masses, an infinite number of Lorentz poles contribute to the scattering amplitude at $s=0$. We obtain a simple parametrization of the scattering amplitude for $s\ensuremath{\sim}0$, $t\ensuremath{\rightarrow}\ensuremath{\infty}$, which involves powers of both $t$ and $\mathrm{ln}t$.