Sum rules of polarized photon structure functions revisited: — NNLO corrections to the first moment of gγ1(x,Q2,P2) — ⁎

We present the next-to-next-to-leading order () corrections to the first moment of the polarized virtual photon structure function gγ1(x,Q2,P2) in the kinematical region Q2≫P2≫Λ2 in QCD. We find that the corrections are about 3% of the sum of the leading (α) and the next-to-leading (ααs) contributions, when Q2=30∼100GeV2 and P2=3GeV2.