The 3 flavor NJL with explicit symmetry breaking interactions: scalar   and pseudoscalar spectra and decays
  The effective quark interactions that break explicitly the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries by current-quark mass source terms are considered in NLO in $N_c$ counting. They are of the same order as the 't Hooft flavor determinant and the eight quark interactions that extend the LO Nambu-Jona-Lasinio Lagrangian, and complete the set of non-derivative and spin 0 interactions relevant for the $N_c$ scheme. The bosonized Lagrangian at meson tree level describes accurately the empirical ordering and magnitude of the splitting of states in the low lying pseudoscalar and scalar meson nonets, for which the explicit symmetry breaking terms turn out to be essential. The strong interaction and radiative decays of the scalar mesons are understood in terms of the underlying microscopic multi-quark states, which are probed differently by the strong and the electromagnetic interactions. We also obtain that the anomalous two photon decays of the pseudoscalars are in very good agreement with data. 
A. A. Osipov, B. Hiller, A. H. Blin
hep-ph