Mass Spectrum of Pseudo-Scalar Glueballs from a Bethe-Salpeter Approach with the Rainbow-Ladder Truncation

We suggest a framework based on the rainbow approximation to the Dyson-Schwinger and Bethe-Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe-Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson-Schwinger equations is analyzed in Landau gauge. Both, the Bethe-Salpeter and Dyson-Schwinger equations, are solved numerically within the same rainbow-ladder truncation with the same effective parameters which ensure consistency of the approach. We found that with a set of parameters, which provides a good description of the lattice data within the Dyson-Schwinger approach, the solutions of the Bethe-Salpeter equation for the pseudo-scalar glueballs exhibit a rich mass spectrum which also includes the ground and excited states predicted by lattice calculations. The obtained mass spectrum contains also several intermediate excitations beyond the lattice approaches. The partial Bethe-Salpeter amplitudes of the pseudo-scalar glueballs are presented as well.