Nonstatic Relations between Magnetic Moments in the Quark Model

Abstract

Relations between baryon magnetic moments are derived which are independent of orbital corrections, relativistic corrections, and two-body exchange corrections (and generally any two-body correction) in the quark model, provided that the wave-function contributions leading to these corrections are $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric. Among the relations derived are $\mu \left({\Xi }^{-}\right)+3\mathrm{}\mu \left({\Xi }^0\right)=6\mathrm{}\mu \left(\Lambda \right)+2\mathrm{}\mu \left({\Sigma }^{+}\right)-3\mathrm{}\mu \mathrm{}\left(p\right)-\mu \mathrm{}\left(n\right)\mathrm{}$ (independent of quark moments) and $\mu \left({\Xi }^0\right)-\mu \left({\Xi }^{-}\right)=\mu \mathrm{}\left(p\right)+2\mathrm{}\mu \mathrm{}\left(n\right)\mathrm{} (\mathrm{if} {\mu }_{\mathcal{P}}=-2\mathrm{}{\mu }_{\mathfrak{N}})$.