Can a resonance theory be a renormalizable theory?

TL;DR

This paper analyzes resonance decay operators in chiral theories, identifying the unique structures necessary for renormalization and ensuring finite matrix elements across all perturbation orders.

Contribution

It provides a comprehensive classification of chiral invariant operators relevant for resonance decay and their role in renormalization.

Findings

Only one single-trace operator is needed for renormalization.

The identified operators ensure finiteness of the decay amplitude.

The analysis is valid at all orders in perturbation theory.

Abstract

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.