Symmetry breaking effects in pion couplings to constituent quark currents

Pseudoscalar and axial neutral and charged pion-constituent quark coupling constants are investigated with nondegenerate quark masses in different kinematical points, off shell and on shell pions and constituent quarks. By considering a large quark mass expansion of a quark determinant in the presence of local pion field and of constituent quark background currents, gluonic effects are considered by means of an effective gluon propagator that dresses quark currents. For the neutral pion, mixing effects are introduced by means of the pion mixing to states \(P_0\) and \(P_8\), that give rise to the \(\pi ^0-\eta -\eta '\) meson mixing, and mixing of quark currents via corresponding mixing interactions. The relative behavior of charged and neutral pion coupling constants to quarks may be nearly the same—in the framework of the constituent quark model—as the pion–nucleon coupling constants if mixings are introduced. A very small pion coupling to strange quark current is also obtained. The dependence of the positive and negative pion-constituent quark coupling constant on the non-degeneracy of quark masses, for emission and absorption processes, is identified.