Rising Meson Trajectories

Abstract

An integral equation for rising meson Regge trajectories is derived and solved for the $\ensuremath{\rho}$ trajectory. The equation is a simple extension of a method previously described in which dispersion relations for $\ensuremath{\alpha}(s)$ and the reduced residue $b(s)$ are coupled by unitarity. In the present method, the trajectory dispersion relation is subtracted twice, which causes trajectories to rise $\ensuremath{\sim}s$. The solutions depend on two parameters and represent almost straight trajectories with imaginary parts.