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

TL;DR

This paper develops a resonance chiral theory framework for S -> pi pi decay, demonstrating that only a finite set of operators contribute, which allows for renormalization and finiteness of the amplitude.

Contribution

It shows that the number of operators affecting the decay amplitude is finite, enabling a renormalizable and divergence-free calculation within resonance chiral theory.

Findings

Only one single-trace operator contributes to the decay amplitude.

Three multi-trace operators contribute, all chiral invariant.

Ultraviolet divergences are confined to these operators, allowing renormalization.

Abstract

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.