\(U_A(1)\) symmetry-breaking quark interactions from vacuum polarization

By considering the one-loop background field method for a quark–antiquark interaction, mediated by one (non-perturbative) gluon exchange, sixth-order quark effective interactions are derived and investigated in the limit of zero momentum transfer for large quark and/or gluon effective masses. They extend fourth-order quark interactions worked out in previous works of the author. These interactions break \(U_A(1)\) symmetry and may be either momentum-independent or momentum-dependent. Some of these interactions vanish in the limit of massless quarks, and several others—involving vector and/or axial quark currents—survive. In the local limit of the resulting interactions, some phenomenological implications are presented, which correspond to corrections to the Nambu–Jona–Lasinio model. By means of the auxiliary field method, the local interactions give rise to three meson interactions whose values are compared to phenomenological values found in the literature. Contributions for meson-mixing parameters are calculated and compared to available results.