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 $\mathrm{SU}(3)$-symmetric. Among the relations derived are $\ensuremath{\mu}({\ensuremath{\Xi}}^{\ensuremath{-}})+3\ensuremath{\mu}({\ensuremath{\Xi}}^{0})=6\ensuremath{\mu}(\ensuremath{\Lambda})+2\ensuremath{\mu}({\ensuremath{\Sigma}}^{+})\ensuremath{-}3\ensuremath{\mu}(p)\ensuremath{-}\ensuremath{\mu}(n)$ (independent of quark moments) and $\ensuremath{\mu}({\ensuremath{\Xi}}^{0})\ensuremath{-}\ensuremath{\mu}({\ensuremath{\Xi}}^{\ensuremath{-}})=\ensuremath{\mu}(p)+2\ensuremath{\mu}(n) (\mathrm{if} {\ensuremath{\mu}}_{\mathcal{P}}=\ensuremath{-}2{\ensuremath{\mu}}_{\mathfrak{N}})$.