Regge Trajectories of Mesons in the Quark Model

We examine a model in which mesons are produced as quasibound states in the quark-antiquark system by using the multichannel $N{D}^{-1\mathrm{}}$ equations. The $\rho$ meson is considered as a particular example. The parameters of the model can be adjusted to produce the $\rho$ meson with the experimentally observed mass and width. We continue the solution as a function of $l$ to compute the Regge trajectory of the $\rho$. In contrast to attempts to compute the $\rho$ trajectory by using a single-channel formalism in which the "force" producing the $\rho$ is the exchange of the $\rho$ meson, we are able to compute trajectories which are approximately linear and have ${\alpha }_{\rho }\mathrm{}\left(0\right)\mathrm{}\approx 0.5$. We present a reason for this difference and examine the model dependence of the results. The apparently equal slopes of the known Regge trajectories can be explained within this model if the particles on the trajectories are produced as quasibound states in the quark-antiquark system.