Heavy pseudoscalar mesons in a Schwinger-Dyson--Bethe-Salpeter approach

The mass spectrum of heavy pseudoscalar mesons, as quark–antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum-dependent masses of the constituents. This dependence is prior found by solving the Schwinger-Dyson equation for quark propagators in rainbow-ladder approximation. Such approximation is known to provide fast convergence of numerical methods and accurate results for lightest mesons. However, as the meson mass increases, the method becomes less stable and special attention must be devoted to details of means of solving the corresponding equations. We focus on the pseudoscalar sector and show that our numerical scheme describes fairly accurately the π, K, D, D s and η c ground states. The excited states are considered as well. Our calculations are directly related to future physics at FAIR.