Bi-local baryon interpolating fields with two flavours

TL;DR

This paper constructs bi-local baryon interpolating fields with two flavors, analyzing their symmetries, identities, and chiral properties to identify independent operators for excited nucleon states.

Contribution

It introduces a systematic derivation of independent baryon operators considering Fierz identities and chiral symmetry, specifically for two-flavor systems.

Findings

Derived Fierz identities reduce operator redundancies.

Classified baryon fields into chiral multiplets.

Identified operators for excited nucleon states.

Abstract

We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with given values of spin (Lorentz group representation), chiral symmetry ($U_L(2) \times U_R(2)$ group representation) and isospin appropriate for the first angular excited states of the nucleon.