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We prove a theorem in QCD stating that in the limit of strong coupling,$g\to\infty$, the observed spectrum of glueballs in QCD is the same of a pureYang-Mills theory, being mixing effects due to the next-to-leading order. Afull effective theory for QCD is obtained and the width of the $\sigma$resonance decay is straightforwardly computed. This appears as the lowestglueball state. Vacuum gluon condensate is computed that consistently supportstudies on the identification of this meson as a glueball.

Observability of glueball spectrum in QCD and the width of $\sigma$ resonance