$\Omega^-$, $\Xi^{*-}$, $\Sigma^{*-}}$ and $\Delta^-}$ decuplet baryon electric charge form factor $F_1(q^2)$

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 $U$-spin =3/2 baryon decuplet $\Delta^{-}$, $\Xi^{*\,-}$, $\Sigma^{*\,-}$ 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---only the magnetic moment of the $\Omega^{-}$ has been accurately determined. In a recent study by us utilizing the infinite momentum frame, we calculated the magnetic moments of the \emph{physical} decuplet $U$-Spin =3/2 quartet members in terms of that of the $\Omega^{-}$ without ascribing any specific form to their quark structure or intra-quark interactions. That study determined $F_{2}(q^{2})$ and was conducted nonperturbatively where the decuplet baryon momenta were all collinear. In this follow-up research---again utilizing the infinite momentum frame but now allowing for non-collinear momenta---we are able to determine $F_{1}(q^{2})$ where $q^{2}\leq 0$. We relate the electric charge form factor $F_{1}(q^{2})$ of the \emph{physical} decuplet $S\neq -3$, $U$-spin =3/2 quartet members to that of the $\Omega^{-}$ ($S=-3$).