Gluon Distributions in Real and Virtual Photon and the Photon Structure Function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in ref.[1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up to $x = 0.03 \div 0.05$ much lower than the corresponding values in the case of quark distributions.Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization point $Q^2 = Q^2_0 \sim 1 GeV^2$; (2) it is assumed that gluonic content of the photon at low $Q^2_0$ is described by gluonic content of vector mesons $\rho, \omega, \varphi$. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functions $F_2(x)$ for real and virual photon are calculated and it is shown that in the region $x \geq 0.2$ where QCD approach is valid, there is a good agreement with experiment.