${\Omega }^{-}$, ${\Xi }^{\ast -}$, \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 ${\Delta }^{-}$, ${\Xi }^{\ast -}$, ${\Sigma }^{\ast -}$ 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 $q^2\le 0$. We relate the electric charge form factor $F_1(q^2)$ of the \emph{physical} decuplet $S\ne -3$, $U$-spin =3/2 quartet members to that of the ${\Omega }^{-}$ ($S=-3$).

Comments: corrected typos in Eqs. (2) and (10)