Dynamical $CP$-violation in quasilocal quark models at nonzero chemical potential

We consider the Quasilocal Quark Model of Nambu–Jona–Lasinio type as effective theory of non-perturbative QCD with scalar-pseudoscalar four-quark interaction with derivatives in fields at finite quark chemical potential. In the presence of a strong attraction in the scalar channel the chiral symmetry is spontaneously broken and as a consequence the composite meson states are generated. For special configurations of coupling constants, the dynamical CP-violation in the pseudoscalar sector can appear as a result of complexity of dynamical mass function generated at some value of quark density.