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 $etatoeta+pi^++pi^-$ is discussed in this approximation and analyzed through the more elementary processes $etatoeta+sigma$ and $sigmatopi^++pi^-$. 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.
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