Current conservation, screening and the magnetic moment of the $\Delta$ resonance: 2. Formulation with quark degrees of freedom 3. Magnetic moment of the $\Delta^o$ and $\Delta^-$ resonances

Abstract

Our previous paper \cite{MFNEW} is generalized within the field theoretical formulation with the quark degrees of freedom \cite{HW,H,N,Z}, where pions and nucleons are treated as the bound systems of quarks. It is shown that relations generated by current conservation for the on shell $\pi N$ bremsstrahlung amplitude with composite nucleons and pions have the same form as in the usual quantum field theory \cite{IZ,BD} without quark degrees of freedom \cite{MFNEW}. Consequently, the model independent relations for the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances in \cite{MFNEW} remain be the same in the quantum field theory with the quark degrees of freedom. These relations are extended for the magnetic dipole moments of the $\Delta^o$ and $\Delta^-$ resonances which are determined via the anomalous magnetic moment of the neutron $\mu_n$ as $\mu_{\Delta^o}={{M_{\Delta}}\over {m_p}} \mu_n$ and $\mu_{\Delta^{-}}={3\over 2}\mu_{\Delta^o}$.