Radial and orbital Regge trajectories in heavy quarkonia

Abstract

The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectory for the squared excitation energy $E^2(nl)$ (ERT), and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from experimental mass differences and their values in bottomonium: the intercept $a(b\bar{b})=0.131$GeV${}^2$, the slope of the orbital ERT $b_l(b\bar{b})=0.50$\,GeV${}^2$, and the slope of the radial ERT, $b_n(b\bar{b})=0.724$\,GeV${}^2$, appear to be smaller than those in charmonium, where $a(c\bar{c})=0.381$\,GeV${}^2$, $b_l(c\bar{c})=0.686$\,GeV${}^2$, and the radial slope $b_n(c\bar{c})=1.074$\,GeV${}^2$, which value is close to that in light mesons, $b_n(q\bar{q})=1.1(1)$\,GeV${}^2$. For the resonances above the $D\bar{D}$ threshold the masses of the ${\chi }_{c0}(nP)$ with $n=2,3,4$, equal to 4218\,MeV, 4503\,MeV, 4754\,MeV, are obtained, while above the $B\bar{B}$ threshold the resonances ${\rm Y}(3{}^3{D}_1)$ with the mass 10693\,MeV and ${\chi }_{b1}(4{}^3{P}_1)$ with the mass 10756\,MeV are predicted.

Comments: 7 pages, no figures