Qcd Analysis of Structure Functions of Real and Virtual Photons

The hadronic structure of real and virtual photons can be measured in electron positron scattering processes in which one lepton serves as a source of target photons with virtuality P 2 << Q where Q is the virtuality of the probing photon. The measured ee cross section can then be obtained by a convolution of a flux of target photons with the deep inelastic electron (positron) photon scattering cross section which is (completely analogous to the case of deep inelastic electron proton scattering) described by two structure functions F2,L. In the QCD impproved parton model the photon structure functions F γ(P ) 2,L (x,Q ) are given by a convolution of non-perturbative parton densities of the (real or virtual) photon with appropriate perturbatively calculable short distance coefficient functions. The photonic parton distributions are governed by inhomogenous evolution equations which have to be supplemented with appropriate boundary conditions. Here we briefly describe recently proposed parameter–free leading order (LO) and next–to–leading order (NLO) boundary conditions for real and virtual photons .