Calculation of photon structure function in QCD

The structure function of a virtual photon measured in deep inelastic scattering of electrons on the photon is calculated in QCD by expanding into a series of inverse powers of photon virtuality p2. The calculation is performed for intermediate values of x and Q2 ∼ 10 GeV2 (x=Q2/2ν, Q2 is the square of the momentum transferred from the electron to the photon and ν is the transferred energy). A model is proposed which expresses the structure function obtained in terms of contributions from the physical states and which possesses the correct analytic properties with respect to p2. The model is used to extrapolate to the point p2=0, i.e. the structure function of a real photon is determined for intermediate values of x. Good agreement with the experimental data is observed without taking into account the QCD evolution. It is shown that higher terms of the order of 1/p2 (contribution of the gluon condensate) vanish in the structure function of a soft longitudinal photon and in the Callan-Gross relation