Survey of $J=0$, 1 mesons in a Bethe-Salpeter approach

The Bethe-Salpeter equation is used to comprehensively study mesons with $J=0$, 1 and equal-mass constituents for quark masses from the chiral limit to the $b$-quark mass. The survey contains masses of the ground states in all corresponding $J^{PC}$ channels including those with “exotic” quantum numbers. The emphasis is put on each particular state’s sensitivity to the low- and intermediate-momentum, i.e., long-range part of the strong interaction.

Figure 1

The form of the effective interaction (3) for the three values of the parameter $\omega$ used herein.

Figure 2

Dependence of meson masses on $m_{\pi }$ (more generally, $m_{\pi }$ denotes the pseudoscalar-meson mass for a given current-quark mass). Vertical dotted lines correspond to positions for light, strange, and charm $\overline{q}q$ states.

Figure 3

Dependence of meson masses on $\omega$. Dotted lines correspond to experimental data [21, 79]. Note that there is no flavor mixing in RL truncation, i.e. there is no experimental number for an $\overline{s}s$ pseudoscalar meson.

Figure 4

Dependence of meson leptonic decay constants on $\omega$. Dotted lines correspond to experimental data [77, 79]. Note that there is no flavor mixing in RL truncation, i.e. there is no experimental number for an $\overline{s}s$ pseudoscalar-meson decay constant. Furthermore, measurements for the ${\eta }_b$ decay constant have not yet been reported.