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

Abstract

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 $$\bar{s}s$$ s ¯ s exotic $$1^{-+}$$ 1 - + states, and identify orbital angular momentum content in the excitations of the $$\rho $$ ρ meson. Comparing our covariant model results, the $$\rho $$ ρ 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 $$m_\pi \sim 1.4$$ m π ∼ 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 $$m_\pi $$ m π .