arXiv:0912.4338v2 [hep-ph] 2 Mar 2010 Baryon Fields with U L (3) × U R (3) Chiral Symmetry: Axial Currents of Nucleons and Hyperons Hua-Xing Chen 1 , ∗ V. Dmitraˇ sinovi´ c 2 , † and Atsushi Hosaka 3‡ 1 Department of Physics and State Key Laboratory of Nuclear Physics and Technology Peking University, Beijing 100871, China 2 Vinˇ ca Institute of Nuclear Sciences, lab 010, P.O.Box 522, 11001 Beograd, Serbia 3 Research Center for Nuclear Physics, Osaka University, Ibaraki 567–0047, Japan 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) ⊕ (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)⊕( 3, 3), (8, 1)⊕(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 SUL(3) × SUR(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. PACS numbers: 14.20.-c, 11.30.Rd, 11.40.Dw Keywords: baryon, chiral symmetry, axial current, F /D values I. INTRODUCTION Axial current “coupling constants” of the baryon flavor octet [1] are well known by now, see Ref. [2][20]. The zeroth (time-like) components of these axial currents are generators of the SU L (3) × SU R (3) chiral symmetry that is one of the fundamental symmetries of QCD. The general flavor SU F (3) symmetric form of the nucleon axial current contains two free parameters, the so called F and D couplings, which are empirically determined as F =0.459 ± 0.008 and D=0.798 ± 0.008, see Ref. [2]. The conventional models of (linearly realized) chiral SU L (3) × SU R (3) symmetry, Refs. [4, 5], on the other hand appear to fix these parameters at either (F =0,D=1), which case goes by the name of [(3, 3) ⊕ ( 3, 3)], or at (F =1,D=0), which case goes by the name of [(8, 1) ⊕ (1, 8)] representation. Both of these chiral representations suffer from the shortcoming that F +D=1= g (3) A =1.267 without derivative couplings. But, even with derivative interactions, one cannot change the value of the vanishing coupling, e.g. of F =0, in [(3, 3) ⊕ ( 3, 3)], or of D=0, in [(8, 1) ⊕ (1, 8)]. Rather, one can only renormalize the non-vanishing coupling to 1.267. Attempts at a reconciliation of the measured values of axial couplings with the (broken) SU L (3) × SU R (3) chiral symmetry go back at least 40 years [4–10], but, none have been successful to our knowledge thus far. As noted above, perhaps the most troublesome problem are the SU (3) axial current’s F ,D values, which problem has repercussions for the meson-baryon interaction F ,D values, with far-reaching consequences for hyper-nuclear physics and even astrophysics. Another, perhaps equally important and difficult problem is that of the flavor-singlet axial coupling of the nucleon [11]. This is widely thought * Electronic address: hxchen@rcnp.osaka-u.ac.jp † Electronic address: dmitra@vinca.rs ‡ Electronic address: hosaka@rcnp.osaka-u.ac.jp