Current conservation and analytic determination of the magnetic moment of the Δ resonance in the πN bremsstrahlung: II. Formulation with quark degrees of freedom. III. Magnetic moment of the Δo and Δ− resonances

Abstract

Our previous paper (Machavariani and Faessler 2010 J. Phys. G: Nucl. Part. Phys. 37 075004) is generalized within the field-theoretical formulation with the quark–gluon degrees of freedom (Huang and Weldon 1975 Phys. Rev. D11 257; Haag 1958 Phys. Rev. 112 669; Nishijima 1958 Phys. Rev. 111 995; Zimmermann 1958 Nuovo Cimento 10 598), where pions and nucleons are treated as the bound (cluster) systems of quarks. It is shown that current conservation for the on-shell πN bremsstrahlung amplitude with the composite nucleons and pions has the same form as in the usual quantum field theory (Itzykson and Zuber 1980 Quantum Field Theory (New York: McGraw-Hill); Bjorken and Drell 1965 Relativistic Quantum Fields (New York: McGraw-Hill)) without quark–gluon degrees of freedom (Machavariani and Faessler 2010). The model-independent representation of the Δ − γ′Δ vertex through the π − γ′π′, N − γ′N′, Δ − πN vertices remain the same in the quantum field theory with the quark–gluon degrees of freedom. Correspondingly, the magnetic dipole moments of the Δ+ and Δ++ resonances in the field-theoretical formulations with and without quark–gluons are identical. These results are extended for the magnetic dipole moments of the Δo and Δ− resonances which are determined via the anomalous magnetic moment of the neutron μn as and .