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The mass spectrum of heavy pseudoscalar mesons, described as quark-antiquarkbound systems, is considered within the Bethe-Salpeter formalism with momentumdependent masses of the constituents. This dependence is found by solving theSchwinger-Dyson equation for quark propagators in rainbow-ladder approximation.Such an approximation is known to provide both a fast convergence of numericalmethods and accurate results for lightest mesons. However, as the meson massincreases, the method becomes less stable and special attention must be devotedto details of numerical means of solving the corresponding equations. We focuson the pseudoscalar sector and show that our numerical scheme describes fairlyaccurately the $\pi$, $K$, $D$, $D_s$ and $\eta_c$ ground states. Excitedstates are considered as well. Our calculations are directly related to thefuture physics programme at FAIR.

A Combined Solution of the Schwinger-Dyson and Bethe-Salpeter Equations for Mesons as $q\bar q$ Bound States