Covariant nonlocal chiral quark models with separable interactions

We present a comparative analysis of chiral quark models which include nonlocal covariant four-fermion couplings. We consider two alternative ways of introducing the nonlocality, as well as various shapes for the momentum-dependent form factors governing the effective interactions. In all cases we study the behavior of model parameters and analyze numerical results for constituent quark masses and quark propagator poles. Advantages of these covariant nonlocal schemes over instantaneous nonlocal schemes and the standard NJL model are pointed out.