Chiral Perturbation Theory with tensor sources

TL;DR

This paper develops a comprehensive chiral Lagrangian including tensor sources up to order p^6, identifying new terms and ensuring a complete, non-redundant operator basis for meson interactions.

Contribution

It introduces the first systematic construction of a chirally-invariant Lagrangian with tensor sources up to p^6 order, including detailed operator counting and redundancy analysis.

Findings

78 terms at p^6-order for two flavors

113 terms at p^6-order for three flavors

First odd-parity operators appear at p^8-order

Abstract

We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \bar{\psi}\sigma_{\mu\nu}\psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p^2). With this choice, we build the even-parity effective Lagrangian up to the p^6-order (NLO). While there are only 4 new terms at the p^4-order, at p^6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p^8-order (NNLO).