Masses of $J^{PC}=1^{-+}$ exotic quarkonia in a Bethe-Salpeter-equation approach

We investigate the properties of mesons with the exotic $J^{PC}=1^{-+}$ quantum numbers. Starting out from the light-quark domain, where the ${\pi }_1$ states are used as references, we predict the masses of analogous quarkonia for $c\overline{c}$ and $b\overline{b}$ configurations. We employ a covariant Dyson-Schwinger–Bethe-Salpeter-equation approach with a rainbow-ladder truncated model of quantum chromodynamics.

Figure 1

Light isovector quarkonium spectra of mesons with $J\le 2$ including exotic quantum numbers, fitted to exotic-vector-related splittings. Calculated values (blue circles) are compared to experimental data (red boxes) from Ref. [54].

Figure 2

Charmonium spectra, fitted to axial-vector-related splittings. Calculated values (blue circles) are compared to experimental data (red boxes) from Refs. [54, 60, 61, 62]. The horizontal dashed line marks the lowest open-flavor threshold.

Figure 3

Bottomonium spectra, fitted to axial-vector-related splittings. Calculated values (blue circles) are compared to experimental data (red boxes) from Refs. [54, 60]. The lowest open-flavor threshold is above all masses plotted in this figure.