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

TL;DR

This paper develops an effective chiral Lagrangian framework to describe nucleon and N* resonances, successfully reproducing their masses without explicit U_A(1) symmetry breaking.

Contribution

It introduces a novel chiral Lagrangian incorporating naive and mirror nucleon representations, explaining resonance masses without explicit U_A(1) breaking.

Findings

Reproduces lowest-lying nucleon masses with the effective Lagrangian

Shows U_A(1) symmetry breaking is not necessary for mass splitting

Analyzes axial couplings with chiral mixing

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) + (0, 1/2) and "mirror" (0, 1/2) + (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.