Chiral Lagrangians with tensor sources

TL;DR

This paper extends Chiral Lagrangians to include tensor sources, enabling the calculation of tensor current-related Green functions and form factors, with a focus on operator basis minimality and phenomenological applications.

Contribution

It introduces tensor sources into Chiral Lagrangians, identifies a minimal operator basis at O(p^6), and explores applications in vector meson resonances and pion decay.

Findings

Only four new operators at O(p^4)

Approximately a hundred operators at O(p^6)

Validated the operator basis with phenomenological examples

Abstract

The implementation of tensor sources in Chiral Lagrangians allows the computation of Green functions and form factors involving tensor currents, that is, quark bilinears of the form \bar{q}_i\sigma^{\mu\nu}q_j. Whereas only four new terms show up at O(p^4), we find around a hundred of them at O(p^6). So it becomes essential to ensure that this set o operators is indeed minimal and non-redundant (i.e., it is a basis). We discuss two phenomenological applications in the context of vector meson resonances and the radiative pion decay.