A Lagrangian for the Chiral (1/2,0) Circle Plus (0,1/2) Quartet Nucleon Resonances

Abstract

We study the nucleon and three N* resonances properties in an effective linear realization chiral SU(L)(2) x SU(R)(2) and U(A)(1) symmetric Lagrangian. We place the nucleon fields into the so-called naive (1/2, 0) circle plus (0, 1/2) and mirror (0, 1/2) circle plus (1/2, 0) (fundamental) representations of SU(L)(2) x SU(R)(2), two of each - distinguished by their U(A)(1) chiral properties, as defined by an explicit construction of the nucleon interpolating fields in terms of three quark (Dirac) fields. We construct the most general one-meson-baryon chiral interaction Lagrangian assuming various parities of these four nucleon fields. We show that the observed masses of the four lowest-lying nucleon states can be well reproduced with the effective Lagrangian, after spontaneous symmetry breakdown, without explicit breaking of U(A)(1) symmetry. This does not mean that explicit U(A)(1) symmetry breaking does not occur in baryons, but rather that it does not have a unique mass prediction signature that exists, e. g. in the case of spinless mesons. We also consider briefly the axial couplings with chiral representation mixing.