New mass relations for heavy quarkonia

By assuming the existence of (quasi)linear Regge trajectories for heavy quarkonia in the low energy region, we derive a new meson mass relation which shows good agreement with experiment for both charmed and b-flavored mesons. We show that for this relation to avoid depending on the values of the Regge slopes of these (quasi)linear trajectories, it must be of sixth power in meson masses. It may be reduced to a quadratic Gell-Mann--Okubo-type formula by fitting the values of the slopes. For charmed mesons, such a formula holds with an accuracy of ~ 1%, and is in qualitative agreement with the relation obtained previously by the application of the linear mass spectrum to an SU(4) meson multiplet.