Baryon fields with U{sub L}(3)xU{sub R}(3) chiral symmetry. III. Interactions with chiral [(3,3)+(3,3)] spinless mesons

Three-quark nucleon interpolating fields in QCD have well-defined SU{sub L}(3)xSU{sub R}(3) and U{sub A}(1) chiral transformation properties, viz. [(6,3)+(3,6)], [(3,3)+(3,3)], [(8,1)+(1,8)], 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 [(6,3)+(3,6)] chiral multiplet with one ordinary (naive) and one mirror field belonging to the [(3,3)+(3,3)], [(8,1)+(1,8)] multiplets can be used to fit the values of the isovector (g{sub A}{sup (3)}) and the flavor-singlet (isoscalar) axial coupling (g{sub A}{sup (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{sub L}(3)xSU{sub R}(3) chirally invariant nonderivative 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)+(3,6)] and the [(3,3)+(3,3)] chiral multiplets, that is also U{sub A}(1) symmetric. We alsomore » study the chiral interactions of the [(3,3)+(3,3)] and [(8,1)+(1,8)] nucleon fields. Again, there are selection rules that allow only one off-diagonal nonderivative chiral SU{sub L}(3)xSU{sub R}(3) interaction of this type, that also explicitly breaks the U{sub 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.« less