Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach

Abstract

We investigate the light quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass of sbars exotic 1-+ states, and identify orbital angular momentum content in the excitations of the rho meson. Comparing our covariant model results, the rho and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of $m_{\pi }$ ~ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of $m_{\pi }$.

26 pages, 21 figures, 3 tables, revised version according to reviewer comments

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• Mass Calculations of Light Quarkonium, Exotic $J^{PC}=0^{+-}$ Hybrid Mesons from Gaussian Sum-Rules
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• Composition of low-lying $\mathbf{J}={\frac{3}{2}}^{\pm }\mathbf{\Delta }$-baryons
• Chiral crossover transition from the Dyson-Schwinger equations in a sphere
• Exposing the effect of $p$-wave in pion triplet under the strong magnetic field
• Pseudo-scalar {\boldm $q\bar{q}$} bound states at finite temperatures within a Dyson-Schwinger--Bethe-Salpeter approach
• The rainbow modified-ladder approximation and degenerate pion
• Broad resonance structure in $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ and higher $\rho$-meson excitations
• Partial wave analysis for the in-hadron condensate
• S- and D-wave vector charmonia
• Global Dyson-Schwinger-Bethe-Salpeter Approach to Mesons with Open Flavour