One-loop Chiral Perturbation Theory with two fermion representations

TL;DR

This paper extends Chiral Perturbation Theory to theories with fermions in two different gauge representations, accounting for an additional Nambu-Goldstone boson and calculating next-to-leading order corrections.

Contribution

It introduces a novel formulation of Chiral Perturbation Theory for multi-representation fermion theories, including the singlet Nambu-Goldstone boson and higher-order corrections.

Findings

Derived NLO corrections for pseudoscalar masses and decay constants.

Included effects of the singlet Nambu-Goldstone boson.

Generalized results to theories with more than two representations.

Abstract

We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.