Rising Meson Trajectories

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