Mass spectrum and decay constants of radially excited vector mesons

We calculate the masses and weak decay constants of flavorless and flavored ground and radially excited $J^P=1^{-}$ mesons within a Poincaré covariant continuum framework based on the Bethe-Salpeter equation. We use in both the quark’s gap equation and the meson bound-state equation an infrared massive and finite interaction in the leading symmetry-preserving truncation. While our numerical results are in rather good agreement with experimental values where they are available, no single parametrization of the QCD inspired interaction reproduces simultaneously the ground and excited mass spectrum, which confirms earlier work on pseudoscalar mesons. This feature being a consequence of the lowest truncation, we pin down the range and strength of the interaction in both cases to identify common qualitative features that may help to tune future interaction models beyond the rainbow-ladder approximation.

Figure 1

The solid indigo curves correspond to the effective coupling strength $\mathcal{G}$ in Ref. [25] with $wD=(0.8\mathrm{GeV}{)}^3$; the dash-dotted magenta curve depicts the effective strength in the Maris-Tandy model [24]; the dotted red curve corresponds to the effective strength extracted from lattice QCD data by using the maximum entropy method (MEM); see Ref. [59] for details.