Three quark currents and baryon spin

Abstract

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.