  We derive a low-energy quantum field theory from quantum chromodynamics (QCD)
that holds in the limit of a very large coupling. All the parameters of the
bare theory are fixed through QCD. Low-energy limit is obtained through a
mapping theorem between massless quartic scalar field theory and Yang-Mills
theory. One gets a Yukawa theory that, in the same limit of strong coupling,
reduces to a Nambu-Jona-Lasinio model with a current-current coupling with
scalar-like excitations arising from Yang-Mills degrees of freedom. A
current-current expansion in the strong coupling limit yields a fully
integrated generating functional that, neglecting quark-quark current coupling,
describes all processes involving glue excitations and quark. Some processes
are analyzed and we are able to show consistency of Narison-Veneziano sum
rules. Width of the $\sigma$ resonance is computed. The decay
$\eta'\to\eta+\pi^++\pi^-$ is discussed in this approximation and analyzed
through the more elementary processes $\eta'\to\eta+\sigma$ and
$\sigma\to\pi^++\pi^-$. In this way we get an estimation of the mass of the
$\sigma$ resonance and the value of the $\eta$ decay constant. This $\eta'$
decay appears a possible source of study for the $\sigma$ resonance.
