Quarks, Gluons and Ghosts at Finite Temperatures within a Bethe–Salpeter–Dyson–Schwinger Approach

Abstract

A framework based on the rainbow approximation to the Dyson–Schwinger and Bethe–Salpeter equations with effective parameters adjusted to lattice data is suggested to calculate the masses of the ground and excited states of mesons and pseudo-scalar glueballs as QCD bound states of quarks and gluons. The structure of the truncated Bethe–Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson–Schwinger equations is analysed in the Landau gauge. Both the Bete–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 mesons and pseudoscalar glueballs exhibit a rich mass spectrum that also includes the ground and excited states predicted by the lattice calculations. The obtained mass spectrum contains also several intermediate excitations unexpected within the lattice approaches.