Bethe–Salpeter-Motivated Modelling of Pseudo-Goldstone Pseudoscalar Mesons

We apply a description of bound states of fermion and antifermion by means of our approximation to the Bethe-Salpeter formalism that retains part of the information on relativistic effects provided by the full fermion propagator to the lightest pseudoscalar mesons. Therein, the pseudo-Goldstone nature of the latter quark-antiquark bound states is taken into account by appropriately formulated effective interactions. Scrutinizing the predictions of this bound-state approach for meson masses, decay constants and in-meson condensates by relying on a generalized Gell-Mann-Oakes-Renner relation shows that the light-quark-mass values required for agreement are all in the right ballpark.