Chiral Properties of Baryon Fields with Flavor SU(3) Symmetry

TL;DR

This paper explores the chiral symmetry properties of local three-quark baryon fields within flavor SU(3), revealing how their Lorentz and flavor structures influence allowed chiral representations and implications for phenomenological models.

Contribution

It explicitly constructs independent local three-quark baryon fields with definite Lorentz and flavor representations and analyzes their chiral symmetry properties.

Findings

Allowed chiral representations are strongly correlated with Lorentz group representations.

Chiral symmetry breaking affects the possible chiral representations of baryon fields.

Implications for phenomenological Lagrangians with chiral symmetry are discussed.

Abstract

We investigate chiral properties of local (non-derivative) fields of baryons consisting of three quarks with flavor SU(3) symmetry. We construct explicitly independent local three-quark fields belonging to definite Lorentz and flavor representations. Chiral symmetry is spontaneously broken and therefore the baryon fields can have different chiral representations. It turns out that the allowed chiral representations are strongly correlated with the Lorentz group representations due to the color and spatial structure of the local three-quark fields. We discuss some implications of the allowed chiral symmetry representations on phenomenological Lagrangians with chiral U(3)_L \otimes U(3)_R symmetry.