Photon Structure Functions: Target Photon Mass Effects and QCD Corrections

We present a systematic analysis of the polarised and unpolarised processes $e^+ ~e^- \rightarrow e^+ ~e^- X$ in the deep inelastic limit and study the effects of target photon mass (virtuality) on the photon structure functions. The effect of target photon virtuality manifests as new singly polarised structure functions and also alters the physical interpretation of the unpolarised structure functions. The physical interpretation of these structure functions in terms of hadronic components is studied using the free field analysis. We also retrieve the real photon results in the limit the virtuality goes to zero. Assuming factorisation of the photon structure tensor, the relevant QCD corrections to the various twist two structure functions are evaluated.