  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 pure
Yang-Mills theory, being mixing effects due to the next-to-leading order. A
full effective theory for QCD is obtained and the width of the $\sigma$
resonance decay is straightforwardly computed. This appears as the lowest
glueball state. Vacuum gluon condensate is computed that consistently support
studies on the identification of this meson as a glueball.
