SU(3) chiral symmetry for baryons
Abstract
Threequark nucleon interpolating fields in QCD have welldefined SU_{L}(3)×SU_{R}(3) and U_{A}(1) chiral transformation properties, viz. [(6,3)⊕(3,6)], [(3,3̄)⊕(3̄,3)], [(8,1)⊕(1,8)] and their "mirror" images, Ref. [1]. It has been shown (phenomenologically) in Ref. [2] that mixing of the [(6,3)⊕(3,6)] chiral multiplet with one ordinary ("naive") and one "mirror" field belonging to the [(3,3̄) ⊕ (3̄,3)], [(8,1) ⊕ (1,8)] multiplets can be used to fit the values of the isovector (gA(3)) and the flavorsinglet (isoscalar) axial coupling (gA(0)) of the nucleon and then predict the axial F and D coefficients, or vice versa, in reasonable agreement with experiment. In an attempt to derive such mixing from an effective Lagrangian, we construct all SU_{L}(3)×SU_{R}(3) chirally invariant nonderivative onemesonbaryon interactions and then calculate the mixing angles in terms of baryons' masses. It turns out that there are (strong) selection rules: for example, there is only one nonderivative chirally symmetric interaction between J = 1/2 fields belonging to the [(6,3) ⊕ (3,6)] and the [(3,3̄) ⊕ (3̄,3)] chiral multiplets, that is also U_{A}(1) symmetric. We also study the chiral interactions of the [(3,3̄) ⊕ (3̄,3)] and [(8,1)⊕ ( 1,8)] nucleon fields. Again, there are selection rules that allow only one offdiagonal nonderivative chiral SU_{L}(3)×SU_{R}(3) interaction of this type, that also explicitly breaks the U_{A}(1) symmetry. We use this interaction to calculate the corresponding mixing angles in terms of baryon masses and fit two lowest lying observed nucleon (resonance) masses, thus predicting the third (J = 1/2, I = 3/2) ∆ resonance, as well as one or two flavorsinglet Λ hyperon(s), depending on the type of mixing. The effective chiral Lagrangians derived here may be applied to high density matter calculations.
 Publication:

International Conference on the Structure of Baryons (BARYONS' 10)
 Pub Date:
 October 2011
 DOI:
 10.1063/1.3647400
 Bibcode:
 2011AIPC.1388..326D
 Keywords:

 QCD;
 symmetry breaking;
 flavour model;
 quarks;
 12.38.Aw;
 11.30.Qc;
 11.30.Hv;
 14.65.Jk;
 General properties of QCD;
 Spontaneous and radiative symmetry breaking;
 Flavor symmetries