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 $\Omega^{ -}$ ($S=-3$).
Categories: hep-ph