Current conservation, screening and the magnetic moment of the $Δ$ resonance. -- 1. Formulation without quark degrees of freedom

Details Current conservation, screening and the magnetic moment of the $Δ$ resonance. -- 1. Formulation without quark degrees of freedom Current conservation, screening and the magnetic moment of the $Δ$ resonance. -- 1. Formulation without quark degrees of freedom

2008-04-08

arxiv.org/abs/0804.1322v2

J.Phys.G37:075004,2010

Physics

Nuclear Physics

Nuclear Theory

37 pages, 2 figures and 1 table

Scientific paper

10.1088/0954-3899/37/7/075004

The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is studied in a new form of current conservation. According to this condition, the internal and external particle radiation parts of the $\pi N$ radiation amplitude have opposite signs, i.e., they contain terms which must cancel each other. Therefore, one has a screening of the internal and external particle radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex cancel against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances and the anomalous magnetic moment of the proton $\mu_p$ is obtained, where $\mu_{\Delta}$ is expressed by $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement with the values extracted from the fit for the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.

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