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In this talk we make an exhaustive analysis of the possible chiral invariantoperators that may described the resonance decay S->pi pi. These provide at thesame time the only available chiral invariant structures for the loopultraviolet divergences in this amplitude. Independently of the order inperturbation theory, we find just one single-trace term (four if multi-traceoperators are allowed), whose renormalization renders the matrix elementfinite.

Can a resonance theory be a renormalizable theory?