YNU-HEPTh-06-103 KUNS-2017

The investigation of the photon structure has been an active field of research both theoretically and experimentally [1,2,3,4]. Also there has been growing interest in the study of the spin structure of photon. In particular, the first moment of the polarized photon structure function g 1 has attracted attention in connection with its relevance to the QED and QCD axial anomaly [5,6,7,8,9]. The polarized photon structure functions can be measured from two-photon processes in the polarized ee collider experiments as shown in Fig. 1, where −Q(−P ) is the mass squared of the probe (target) photon. For a real photon (P 2 = 0) target, there exists only one spin-dependent structure function g 1 (x,Q ). The QCD analysis for g 1 was performed in the leading order (LO) [10] and in the next-to-leading order (NLO) [11,12]. In the case of a virtual photon target (P 2 6= 0) there appear two spin-dependent structure functions, g 1 (x,Q , P ) and g 2 (x,Q , P ). The former has been investigated up to the NLO in QCD by the present authors in[13,14], and also in the second paper of [12]. In Ref.[13] the structure function g 1 (x,Q , P ) was analysed in the kinematical re-