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We develop a resonance chiral theory without any a priori limitation on thenumber of derivatives in the hadronic operators. Through an exhaustive analysisof the resonance lagrangian and by means of field redefinitions, we find thatthe number of independent operator contributing to the S -> pi pi decayamplitude is finite: there is only one single-trace operator (the cd term) andthree multi-trace terms. The deep implication of this fact is that theultraviolet divergences that appear in this amplitude at the loop level canonly appear through these chiral invariant structures. Hence, a renormalizationof these couplings renders the amplitude finite.

Renormalizable Sectors in Resonance Chiral Theory: S -> pi pi Decay Amplitude