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

Understand

We develop a resonance chiral theory without any a priori limitation on the number of derivatives in the hadronic operators.

• Through an exhaustive analysis of the resonance lagrangian and by means of field redefinitions, we find that the number of independent operator contributing to the S -> pi pi decay amplitude is finite: there is only one single-trace operator (the cd term) and three multi-trace terms.
• The deep implication of this fact is that the ultraviolet divergences that appear in this amplitude at the loop level can only appear through these chiral invariant structures.
• Hence, a renormalization of these couplings renders the amplitude finite.