Vacuum polarization induced flavor, chiral and $U_A$(1) symmetry breakings corrections to quark (effective) interactions

The one loop background field method for the quark-antiquark interaction, mediated by nonperturbative one-gluon exchange from the QCD effective action, is considered to provide vacuum polarization contributions to flavor-dependent quark (effective) interactions. Background quark currents are dressed by a gluon cloud leading to the emergence of constituent quark currents. Pion cloud is also obtained dynamically. These resulting contributions are resolved either in form factors or coupling constants for the long-wavelength limit. Quark mass non-degeneracy, flavor symmetry breaking (FSB), leads to pseudoscalar meson mixing interactions and to quark mixing interactions. These mixing(s) induce a sizeable role of FSB in the sea quark-antiquark states by means of the quark condensates. Also, 6th order ($U_A(1)$ breaking) quark interactions are derived with different Lorentz and flavor structures, among which interactions with the same shape as the 't Hooft interactions induced by instantons. Consequences for observables usually calculated with NJL-type models are presented.