Remarks on Next-to-Leading Order Analysis of Polarized Deep Inelastic Scattering Data

Since the x dependence of the axial-anomaly effect in inclusive polarized deep inelastic scattering is fixed, the transformation from the $\bar{MS}$ scheme to different factorization schemes are not arbitrary. If the quark spin distribution is demanded to be anomaly-free so that it does not evolve with $Q^2$ and hard gluons contribute to the first moment of $g_1(x)$, then all the moments of coefficient and splitting functions are fixed by perturbative QCD for a given $\gamma_5$ prescription, contrary to the commonly used Adler-Bardeen (AB) or AB-like scheme. It is urged that, in order to correctly demonstrate the effect of factorization scheme dependence, the QCD analysis of polarized structure functions in next-to-leading order should be performed, besides the $\bar{MS}$ scheme, in the chiral-invariant factorization scheme in which the axial anomaly resides in the gluon coefficient function, instead of the less consistent and ambiguous AB scheme.