Sea Quark or Anomalous Gluon Interpretation for $g_1^p(x)$ ?

Contrary to what has been often claimed in the literature, we clarify that the hard photon-gluon cross section $\gg_{\rm hard}(x)$ in polarized deep inelastic scattering calculated in the gauge-invariant factorization scheme does {\it not} involve any soft contributions and hence it is genuinely {\it hard}. We show that the polarized proton structure function $g_1^p(x)$ up to the next-to-leading order of $\alpha_s$ is independent of the factorization convention, e.g., the gauge-invariant or chiral-invariant scheme, chosen in defining $\gg_{\rm hard}(x)$ and the quark spin density. Thereby, it is not pertinent to keep disputing which factorization prescription is correct or superior. The hard-gluonic contribution to $\Gamma_1^p$, the first moment of $g_1^p(x)$, is purely factorization dependent. Nevertheless, we stress that even though hard gluons do not contribute to $\Gamma_1^p$ in the gauge-invariant scheme, the gluon spin component in a proton, which is factorization independent, should be large enough to perturbatively generate a negative sea polarization via the axial anomaly. We briefly comment on how to study the $Q^2$ evolution of parton spin distributions to the next-to-leading order of QCD in the chiral-invariant factorization scheme.