Baryon fields with UL(3) x UR(3) chiral symmetry. III. Interactions with chiral [(3, (3)over-bar) ⊕ ((3)over-bar, 3)] spinless mesons

Three-quark nucleon interpolating fields in QCD have well-defined SUL(3) x SUR(3) and U-A(1) chiral transformation properties, viz. left perpendicular(6, 3) circle plus (3, 6)right perpendicular, left perpendicular(3, (3) over bar) circle plus ((3) over bar, 3)right perpendicular, left perpendicular(8, 1) circle plus (1, 8)right perpendicular, and their mirror images; see [H. X. Chen, V. Dmitrasinovic, A. Hosaka, K. Nagata, and S. L. Zhu, Phys. Rev. D 78, 054021 (2008)]. It has been shown (phenomenologically) in [H. X. Chen, V. Dmitrasinovic, and A. Hosaka, Phys. Rev. D 81, 054002 (2010)] that mixing of the left perpendicular(6, 3) circle plus (3, 6)right perpendicular chiral multiplet with one ordinary (naive) and one mirror field belonging to the [(3, (3) over bar) circle plus ((3) over bar, 3)], [(8, 1) circle plus (1, 8)] multiplets can be used to fit the values of the isovector (g(A)((3))) and the flavor-singlet (isoscalar) axial coupling (g(A)((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 SUL(3) x SUR(3) chirally invariant non-derivative one-meson-baryon 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) circle plus (3, 6)] and the [(3, (3) over bar) circle plus ((3) over bar, 3)] chiral multiplets, that is also U-A(1) symmetric. We also study the chiral interactions of the [(3, (3) over bar) circle plus ((3) over bar, 3)] and [(8, 1) circle plus (1, 8)] nucleon fields. Again, there are selection rules that allow only one off-diagonal nonderivative chiral SUL(3) x SUR(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) Delta resonance, as well as one or two flavor-singlet Lambda hyperon(s), depending on the type of mixing. The effective chiral Lagrangians derived here may be applied to high density matter calculations.