$\Omega^{-}$, $\Xi^{* -}$, $\Sigma^{* -}$ and $\Delta^{-}$ decuplet baryon magnetic moments

Abstract

The properties of the ground state $U$-Spin $={3/2}$ baryon decuplet magnetic moments $\Delta^{-}$, $\Xi^{* -}$, $\Sigma^{* -}$ and $\Omega^{-}$ and their ground state spin 1/2 cousins $p$, $n$, $\Lambda$, $\Sigma^{+}$, $\Sigma^{0}$, $\Sigma^{-}$, $\Xi^{+}$, and $\Xi^{-}$ have been studied for many years with a modicum of success. The magnetic moments of many are yet to be determined. Of the decuplet baryons, only the magnetic moment of the $\Omega^{-}$ has been accurately determined. We calculate the magnetic moments of the \emph{physical} decuplet $U$-Spin $={3/2}$ quartet members without ascribing any specific form to their quark structure or intra-quark interactions.Comment: 11 pages.V5 "This research" column of Table I. modified as all results must be in nuclear magneton units. In Eq.~(35), factor $(m/m_{\Omega^{-}})$ replaced with $(m/m_{\Delta^{-}})$. $\mu_{\Delta^{-}}$ . Next two paragraphs after Eq.~(35)now read $\mu_{\Delta^{-}}= (-1.83\pm 0.04)\,\mu_{N}$.Corrected Table I. is reported. Mass units reported as $GeV/c$ now read $GeV/c^{2}$. Conclusions unchange