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 ${\mu }_{{\Delta }^o}=\frac{M_{\Delta }}{m_p}{\mu }_n$ and ${\mu }_{{\Delta }^{-}}=\frac{3}{2}{\mu }_{{\Delta }^o}$.

Comments: The second part of Preprint arXiv:nucl-th/0804.1322 2008; 17 pages 3 figures, 1 Table