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

TL;DR

This paper extends previous work on the magnetic moments of Delta resonances by formulating the problem with quark degrees of freedom, showing current conservation relations remain consistent and deriving new magnetic moment relations for neutral and negatively charged Delta states.

Contribution

It introduces a field theoretical formulation with quark degrees of freedom to analyze Delta resonance magnetic moments, confirming the invariance of current conservation relations and deriving new magnetic moment formulas.

Findings

Relations for magnetic moments of Delta resonances are preserved with quark degrees of freedom.

Magnetic moments of $\Delta^o$ and $\Delta^-$ are expressed via the neutron's magnetic moment.

The model confirms consistency with previous quantum field theory results.

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 $\mu_{\Delta^{-}}={3\over 2}\mu_{\Delta^o}$.