Spin budget of the proton at NNLO and beyond

We revisit the scale evolution of the quark and gluon spin contributions to the proton spin, 1/2 Delta Sigma and Delta G, using the three-loop results for the spin-dependent evolution kernels available in the literature. We argue that the evolution of the quark spin contribution may actually be extended to the four-loop order, and that to all orders a single anomalous dimension governs the evolution of both Delta Sigma and Delta G. We present analytical solutions of the evolution equations for Delta Sigma and Delta G and investigate their scale dependence both to large and down to lower hadronic scales. We find that the solutions remain perturbatively stable even to low scales, where they come closer to simple quark model expectations. We discuss a curious scenario for the proton spin, in which even the gluon spin contribution is essentially scale independent and has a finite asymptotic value as the scale becomes large. We finally also show that perturbative three-loop evolution leads to a larger spin contribution of strange antiquarks than of strange quarks.