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.
Highlights
In recent years, a large number of new resonances was observed in heavy quarkonia (HQ) [1,2,3,4,5,6,7,8], and among them, the resonances Xð4500Þ and Xð4700Þ with JPC 1⁄4 0þþ [6], being the highest excitations in the meson sector, are interesting
One of the main goals of the present paper is to show that the heavy quark mass can be taken not as a fitting parameter but extracted from experimental mass differences, if both the orbital and the radial ERT’s in the ðE2; nÞ and ðE2; nlÞ
In our study of HQ, we have used the Afonin-Pusenkov conception [41] about the Regge trajectories (RTs), defined through the excitation energy, Eðn; lÞ 1⁄4 MðnlÞ − 2mQ, which later was developed in Refs. [42,43,44]
Summary
The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectories for the squared excitation energy E2ðnlÞ (ERT) and using the relativistic Hamiltonian with the universal interaction. For the resonances above the DDthreshold, we predict Mðχc0ðnPÞÞ (in MeV) as 3415, 3862(8), 4196(12), 4475(15), and 4720(17); Mðχc1ðnPÞÞ (in MeV) as 3511, 3943(7), 4274(11), and 4553(15); and Mðχc2ÞðnPÞÞ (in MeV) as 3556, 3.928(4), 4223(6), and 4474(8) for nr 1⁄4 0, 1, 2, 3, which are in good agreement with the experimental masses, and for the n3D3 states the masses Mðψ3ðn3D3ÞÞ (in MeV) as 3857(8), 4197(11), 4479(13), and 4700(13) are predicted.
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