Polarized Parton Distributions in the Photon and Factorization Scheme Dependence

TL;DR

This paper investigates the spin-dependent parton distributions in polarized virtual photons within QCD at NLO, analyzing their dependence on factorization schemes and the effects of the axial anomaly.

Contribution

It provides a detailed analysis of the scheme dependence of polarized parton distributions in virtual photons at NLO, including the axial anomaly effects and large-x behavior.

Findings

Gluon distribution is scheme-independent at NLO.

Parton distributions are predictable up to NLO in the specified kinematic regime.

Scheme dependence affects quark distributions but not gluon distributions.

Abstract

Spin-dependent parton distributions in the polarized virtual photon are investigated in 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 the NLO, but they are factorization-scheme-dependent. Parton distributions are analyzed in four different factorization schemes and their scheme dependence are discussed. Particular attentions are paid to the axial anomaly effect on the first moments of quark parton distributions, and also to the large-$x$ behaviors of the parton distributions. Gluon distribution in the virtual photon is found to be factorization-scheme independent up to the NLO.