Exciting flavored bound states

We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing function from lattice QCD and Dyson-Schwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited $D_{(s)}$ mesons, which indicates a non-Hermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.

Figure 1

Lowest Chebyshev moment, ${}^0{E}_{P_1}(p^2)$, associated with the leading Dirac structure $E_{P_1}(p^2)$ of the meson’s BSA (22) for the first radial excitations $\pi (1300)$, $\eta (1760)$, and ${\eta }_c(2S)$. The interaction parameters are $\omega =0.6$ and $\omega D=(1.1\mathrm{GeV}{)}^3$.