Magnetic moments of the ground-state ${{\mathbf{J}}^{\mathbf{P}}=(\mathbf{3}\mathbf{/}\mathbf{2})}^{+}$ baryon decuplet

The magnetic moment - a function of the electric charge form factor $F_1(q^2)$ and the magnetic dipole form factor $F_2(q^2)$ at zero four-momentum transfer $q^2$-of the ground-state $J^P=(3\mathrm{/}2{)}^{+}$ baryon decuplet magnetic moments have been studied for many years with limited success. At present, only the magnetic moment of the ${\mathrm{\Omega }}^{-}$ has been accurately determined. We calculate nonperturbatively the magnetic moments of the \emph{physical baryon decuplet $J^P=(3\mathrm{/}2{)}^{+}$} members and in particular, we obtain ${\mu }_{{\mathrm{\Delta }}^{++}}=(+3.67\pm 0.07){\mu }_N$, ${\mu }_{{\mathrm{\Delta }}^{+}}=(+1.83\pm 0.04){\mu }_N$, ${\mu }_{{\mathrm{\Delta }}^0}=(0){\mu }_N$, and the magnetic moments of their $U$-Spin partners in terms of ${\mathrm{\Omega }}^{-}$ magnetic moment data.