  This work is a follow up of recent investigations, where we study the
implications of a generalized heat kernel expansion, constructed to incorporate
non-perturbatively the effects of a non-commutative quark mass matrix in a
fully covariant way at each order of the expansion. As underlying Lagrangian we
use the Nambu -- Jona-Lasinio model of QCD, with $SU_f(3)$ and $U_A(1)$
breaking, the latter generated by the 't Hooft flavour determinant interaction.
The associated bosonized Lagrangian is derived in leading stationary phase
approximation (SPA) and up to second order in the generalized heat kernel
expansion. Its symmetry breaking pattern is shown to have a complex structure,
involving all powers of the mesonic fields allowed by symmetry. The considered
Lagrangian yields a reliable playground for the study of the implications of
symmetry and vacuum structure on the mesonic spectra, which we evaluate for the
scalar and pseudoscalar meson nonets and compare with other approaches and
experiment.
