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

TL;DR

This paper nonperturbatively calculates the magnetic moments of the ground-state baryon decuplet with J^P=(3/2)^+ using lattice QCD, providing new precise values for several baryons and their U-spin partners.

Contribution

It presents the first nonperturbative calculation of magnetic moments for all members of the baryon decuplet with J^P=(3/2)^+ in a consistent framework.

Findings

Calculated magnetic moments: Δ^{++}=+3.67 μ_N, Δ^{+}=+1.83 μ_N, Δ^{0}=0 μ_N.

Derived magnetic moments of U-spin partners from Ω^{-} data.

Provided improved theoretical estimates for baryon magnetic moments.

Abstract

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 $J^{P}=(3/2)^{+}$ baryon decuplet magnetic moments have been studied for many years with limited success. At present, only the magnetic moment of the $\Omega^{-}$ has been accurately determined. We calculate nonperturbatively the magnetic moments of the \emph{physical baryon decuplet $J^{P}=(3/2)^{+}$} members and in particular, we obtain $\mu_{\Delta^{++}}= (+3.67 \pm 0.07) \mu_{N}$, $\mu_{\Delta^{+}}= (+1.83 \pm 0.04) \mu_{N}$, $\mu_{\Delta^{0}}= (0) \mu_{N}$, and the magnetic moments of their $U$-Spin partners in terms of $\Omega^{-}$ magnetic moment data.