  In view of the expectation that the existence of complex poles is a signal of
confinement, we investigate the analytic structure of the gluon, quark, and
ghost propagators in the Landau gauge QCD and QCD-like theories by employing an
effective model with a gluon mass term of the Yang-Mills theory, which we call
the massive Yang-Mills model. In this model, we particularly investigate the
number of complex poles in the parameter space of the model consisting of gauge
coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and
various numbers of quark flavors $N_F$ within the asymptotic free region. Both
the gluon and quark propagators at the best-fit parameters for $N_F=2$ QCD have
one pair of complex conjugate poles, while the number of complex poles in the
gluon propagator varies between zero and four depending on the number of quark
flavors and quark mass. Moreover, as a general feature, we argue that the gluon
spectral function of this model with nonzero quark mass is negative in the
infrared limit. In sharp contrast to gluons, the quark and ghost propagators
are insensitive to the number of quark flavors within the current
approximations adopted in this paper. These results suggest that details of the
confinement mechanism may depend on the number of quark flavors and quark mass.
