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