  In this article, we study the $Z_c(3900)$ with the QCD sum rules in details
by including the two-particle scattering state contributions and nonlocal
effects between the diquark and antidiquark constituents. The two-particle
scattering state contributions cannot saturate the QCD sum rules at the hadron
side, the contribution of the $Z_c(3900)$ plays an un-substitutable role, we
can saturate the QCD sum rules with or without the two-particle scattering
state contributions. If there exists a barrier or spatial separation between
the diquark and antidiquark constituents, the Feynman diagrams can be divided
into the factorizable and nonfactorizable diagrams. The factorizable diagrams
consist of two colored clusters and lead to a stable tetraquark state. The
nonfactorizable Feynman diagrams correspond to the tunnelling effects, which
play a minor important role in the QCD sum rules, and are consistent with the
small width of the $Z_c(3900)$. It is feasible to apply the QCD sum rules to
study the tetraquark states, which begin to receive contributions at the order
$\mathcal{O}(\alpha_s^0)$, not at the order $\mathcal{O}(\alpha_s^2)$.
