Baryon Fields with U_L(3) \times U_R(3) Chiral Symmetry: Axial Currents of Nucleons and Hyperons

TL;DR

This paper reformulates the chiral properties of baryons with SU(3) symmetry, explicitly derives axial and vector currents, and investigates how mixing of chiral multiplets influences axial current matrix elements of nucleons and hyperons.

Contribution

It provides a detailed explicit derivation of chiral transformations and currents for baryons in SU(3) symmetry, including the effects of multiplet mixing on axial currents.

Findings

Explicit chiral transformations of baryon multiplets are derived.

Vector and axial-vector currents close the SU(3) chiral algebra.

Strong correlation found between axial current components and experimental data.

Abstract

We use the conventional F and D octet and decimet generator matrices to reformulate chiral properties of local (non-derivative) and one-derivative non-local fields of baryons consisting of three quarks with flavor SU(3) symmetry that were expressed in SU(3) tensor form in Ref. [12]. We show explicitly the chiral transformations of the [(6,3)\oplus(3,6)] chiral multiplet in the "SU(3) particle basis", for the first time to our knowledge, as well as those of the (3,\bar{3}) \oplus (\bar{3}, 3), (8,1) \oplus (1,8) multiplets, which have been recorded before in Refs. [4,5]. We derive the vector and axial-vector Noether currents, and show explicitly that their zeroth (charge-like) components close the SU_L(3) \times SU_R(3) chiral algebra. We use these results to study the effects of mixing of (three-quark) chiral multiplets on the axial current matrix elements of hyperons and nucleons. We show, in particular, that there is a strong correlation, indeed a definite relation between the flavor-singlet (i.e. the zeroth), the isovector (the third) and the eighth flavor component of the axial current, which is in decent agreement with the measured ones.