# Radial and orbital Regge trajectories in heavy quarkonia

## TL;DR

This paper investigates heavy quarkonium spectra using Regge trajectories and relativistic Hamiltonians, extracting parameters from experimental data and predicting masses of higher resonances.

## Contribution

It introduces a combined approach using Regge trajectories and relativistic Hamiltonians to analyze heavy quarkonia spectra and predicts masses of higher resonances.

## Key findings

- Parameters of Regge trajectories differ between bottomonium and charmonium.
- Predicted masses for higher resonances above D and B meson thresholds.
- Values of Regge trajectory slopes are similar to those in light mesons.

## 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 $\Upsilon(3\,^3D_1)$ with the mass 10693\,MeV and $\chi_{b1}(4\,^3P_1)$ with the mass 10756\,MeV are predicted.