A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSEs) studies have long emphasised this importance, and have proved that QCD's Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken, while the decay constants of their radial excitations vanish. Such features are readily illustrated using a rainbow-ladder truncation of the DSEs. In this connection we find (in GeV): fηc(1S)=0.233, mηc(2S)=3.42; and support for interpreting η(1295), η(1470) as the first radial excitations of η(548), η′(958), respectively, and K(1460) as the first radial excitation of the kaon. Moreover, such radial excitations have electromagnetic diameters greater than 2 fm. This exceeds the spatial length of lattices used typically in contemporary lattice-QCD.
Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
