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 $Σ_p = 1$ (one-quark axial current value) to $Σ_p = 0.41(12)$ consistent with the empirical value $Σ_{p, exp} = 0.33(08)$. In the case of the $Δ^+(1232)$ baryon, we find that three-quark axial currents increase the one-quark axial current value $Σ_{Δ^+} = 3$ to $Σ_{Δ^+} = 3.87(22)$. We also calculate the quark orbital angular momenta $L_u$ and $L_d$ in the proton and $Δ^+$ and interpret our results in terms of the prolate and oblate geometric shapes of these baryons consistent with their intrinsic quadrupole moments.

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