Vibrational trajectories for heavy quarkonia

We show that vibrational states vS (v≥0) of the heavy mesons provide a special window to the nature of the confining quark potential, extending here the studies of Kang, Schnitzer, and others of the case of linear confinement in the 3+1 dimensions. Linear confinement potentials yield an initial bending, followed by an approximate saturation of the spectroscopic interval Δv=Mv2-Mv-12 as a function of v, in contrast with many other forms of confinement potentials with their characteristically different forms of Δv. This feature of the linear potentials is roughly in accord with the available experimental data, and has some similarities with characteristics of the 't Hooft trajectories occurring in his (1+1)-dimensional theory of mesons