Regularization Methods in Chiral Perturbation Theory

TL;DR

This paper analyzes regularization and renormalization ambiguities in chiral perturbation theory, emphasizing the importance of Ward identities in ensuring unambiguous, testable predictions at the one-loop level for Goldstone boson interactions.

Contribution

It provides a comprehensive analysis of regularization ambiguities in chiral perturbation theory and shows how Ward identities constrain regulators to produce unique, unambiguous results.

Findings

Ward identities enforce unique results in one-loop chiral perturbation theory.

Proper treatment of tadpoles is crucial for consistent results.

Regulators constrained by Ward identities lead to unambiguous predictions.

Abstract

Chiral lagrangians describing the interactions of Goldstone bosons in a theory possessing spontaneous symmetry breaking are effective, non-renormalizable field theories in four dimensions. Yet, in a momentum expansion one is able to extract definite, testable predictions from perturbation theory. These techniques have yielded in recent years a wealth of information on many problems where the physics of Goldstone bosons plays a crucial role, but theoretical issues concerning chiral perturbation theory remain, to this date, poorly treated in the literature. We present here a rather comprehensive analysis of the regularization and renormalization ambiguities appearing in chiral perturbation theory at the one loop level. We discuss first on the relevance of dealing with tadpoles properly. We demonstrate that Ward identities severely constrain the choice of regulators to the point of enforcing unique, unambiguous results in chiral perturbation theory at the one-loop level for any observable which is renormalization-group invariant. We comment on the physical implications of these results and on several possible regulating methods that may be of use for some applications.