Fermion Quarks of Spin32

Abstract

The usual quark model of baryons requires quarks to obey effective Bose statistics if they are to be in space-symmetric states. We show that if quarks had spin $\frac{3}{2}$ they could obey the usual Fermi statistics, even with space-symmetric wave functions. Using spin-$\frac{3}{2}$ quarks, we construct a completely antisymmetric three-quark state of total spin $\frac{3}{2}$ corresponding to the baryon decuplet, and a mixed symmetry state of total spin ½ corresponding to the baryon octet. A simple dynamical assumption about the spin dependence of quark-quark forces limits the $s$-wave baryon states to the octet and decuplet, and saturates the quark binding at three. We find very little difference in the experimentally tested quark-model predictions when spin-$\frac{3}{2}$ quarks are used. The main differences we do find are: the well-known prediction that $-\frac{{\mu }_p}{{\mu }_n}=\frac{3}{2}$ is lost with spin-$\frac{3}{2}$ quarks, and they must have anomalous magnetic moments. The predicted ${\Sigma }^{+}$ moment is essentially unchanged, but the ${\Xi }^{-}$ and ${\Omega }^{-}$ moments change when spin-$\frac{3}{2}$ quarks are used, and their measurement would test the spin of the quark. With spin-$\frac{3}{2}$ quarks, mass relations within $\mathrm{SU}\left(3\right)\mathrm{}$ multiplets are kept while the less well satisfied relations connecting octet to decuplet mass differences get broken by a small amount.