Polarized and Unpolarized Structures of the Virtual Photon

As Maria Krawczyk remarked in her introductory talk on structure functions [1] , the virtual photon structure provides a unique test of QCD. In this talk I would like to discuss the polarized and unpolarized virtual photon structures. But because of the limitation of the allocated time, I will mainly focus my talk on the polarized virtual photon structure. Recently there has been growing interest in the polarized photon structure functions. Especially, the 1st moment of a photon structure function g 1 has attracted much attention in connection with its relevance for the axial anomaly, which has also played an important role in the QCD analysis of the nucleon spin structure functions. Now the information on the spin structure of the photon will be obtained from the resolved photon process in polarized electron and proton collision in the polarized version of the ep collider. More directly, the spin-dependent structure function of the photon can be measured by the polarized ee collision in the future linear colliders. Here we investigate two-photon process (Figure 1) with the kinematical region where the mass squared of the probe photon (Q) is much larger than that of the target photon (P ) which is in turn much bigger than the Λ, the QCD scale parameter squared. The advantage for studying the virtual photon target is that we can calculate whole structure functions up to next-leading-order (NLO), in contrast to the real photon target where there remain uncalculable non-perturbative pieces. This is true for summing up the QCD logarithmic terms due to twist-2 operators corresponding to the QCD parton picture. Here we neglect all the power corrections arising from the higher-twist effects and target mass effects of the form (P /Q)