Factorization Scheme and Parton Distributions in the Polarized Virtual Photon Target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to NLO, but they are factorization-scheme-dependent.We analyze parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-$x$ behaviors of quark distributions in the virtual photon. Gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of gluon distribution is found to be factorization-scheme independent up to NLO.