Sea Quark or Anomalous Gluon Interpretation for g₁ᵖ(x)?

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Contrary to what has been often claimed in the literature, we clarify that the hard photon-gluon cross section ≫ hard(x) in polarized deep inelastic scattering calculated in the gauge-invariant factorization scheme does not involve any soft contributions and hence it is genuinely hard. We show that the polarized proton structure function g₁ᵖ(x) up to the next-to-leading order of αₛ is independent of the factorization convention, e.g., the gauge-invariant or chiral-invariant scheme, chosen in defining ≫ 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 Γ₁ᵖ, the first moment of g₁ᵖ(x), is purely factorization dependent. Nevertheless, we stress that even though hard gluons do not contribute to Γ₁ᵖ 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 Q² evolution of parton spin distributions to the next-to-leading order of QCD in the chiral-invariant factorization scheme.