Generating functional of ChPT at one loop for non-minimal operators

TL;DR

This paper calculates the divergent part of the one-loop effective action in Chiral Perturbation Theory with photons, addressing non-minimal operators and extending results to SU(2) and SU(3) cases.

Contribution

It introduces a method to evaluate the one-loop effective action for non-minimal operators in ChPT, including gauge dependence and different symmetry groups.

Findings

Derived the divergent part of the one-loop effective action for non-minimal operators.

Extended calculations to both SU(2) and SU(3) cases.

Compared results with existing literature for validation.

Abstract

The divergent part of the one-loop effective action in Chiral Perturbation Theory with virtual photons has been evaluated in an arbitrary covariant gauge. The differential operator, that emerges in the functional determinant, is of a non-minimal type, for which the standard heat kernel methods are not directly applicable. Both SU(2) and SU(3) cases have been worked out. A comparison with existing results in the literature is given.