Baryon fields with UL(3) X UR(3) chiral symmetry: Axial currents of nucleons and hyperons

Abstract

We use the conventional F and D octet and decimet generator matrices to reformulate chiral properties of local (nonderivative) and one-derivative nonlocal fields of baryons consisting of three quarks with flavor SU(3) symmetry that were expressed in SU(3) tensor form by Chen et al. [Phys. Rev. D 78, 054021 (2008)]. We show explicitly the chiral transformations of the [(6, 3) circle plus (3, 6)] chiral multiplet in the SU(3) particle basis, for the first time to our knowledge, as well as those of the (3, (3) over bar) circle plus ((3) over bar, 3), (8, 1) circle plus (1, 8) multiplets, which have been recorded before by Bardeen and Lee [ Phys. Rev. 177, 2389 (1969)] and Lee [Phys. Rev. 170, 1359 (1968)]. We derive the vector and axial-vector Noether currents, and show explicitly that their zeroth (chargelike) components close the SU(L) X 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.