NNLO QCD analysis of the virtual photon structure functions
  The next-to-next-to-leading order (NNLO) QCD analysis is performed for the virtual photon structure functions which can be measured in the double-tag events in two-photon processes in $e^+e^-$ collisions. We investigate the perturbative QCD evaluation of $F_2^\gamma(x,Q^2,P^2)$ to NNLO and $F_L^\gamma(x,Q^2,P^2)$ to NLO with and without taking into account the target mass effects, which are relevant for the large $x$ region. We also carry out the phenomenological analysis for the experimentally accessible effective structure function $F_{\rm eff}^\gamma=F_2^\gamma+(3/2)F_L^\gamma$. 
Ken Sasaki, Takahiro Ueda, Yoshio Kitadono and Tsuneo Uematsu