Three quark currents and baryon spin

We show that three-quark axial currents as required by broken SU(6) spin-flavor symmetry reduce the quark spin contribution to proton spin from $Sigma_p = 1$ (one-quark axial current value) to $Sigma_p = 0.41(12)$ consistent with the empirical value $Sigma_{p, exp} = 0.33(08)$. In the case of the $Delta^+(1232)$ baryon, we find that three-quark axial currents increase the one-quark axial current value $Sigma_{Delta^+} = 3$ to $Sigma_{Delta^+} = 3.87(22)$. We also calculate the quark orbital angular momenta $L_u$ and $L_d$ in the proton and $Delta^+$ and interpret our results in terms of the prolate and oblate geometric shapes of these baryons consistent with their intrinsic quadrupole moments.

Spin of ground state baryons

We calculate the quark spin contribution to the total angular momentum of flavor octet and flavor decuplet ground state baryons using a spin-flavor symmetry based parametrization method of quantum chromodynamics. We find that third order SU(6) symmetry breaking three-quark operators are necessary to explain the experimental result Sigma_1=0.32(10). For spin 3/2 decuplet baryons we predict that the quark spin contribution is Sigma_3=3.93(22), i.e. considerably larger than their total angular momentum.