QCD saturation and γ*-γ* scattering

Two photon collisions at high energy have an important theoretical advantage: the simplicity of the initial state, which gives us a unique opportunity to calculate these processes for large virtualities of both photons in the perturbative QCD approach. In this paper we study QCD saturation in two photon collisions in the framework of the Glauber-Mueller approach. The Glauber-Mueller formula is derived emphasising the impact parameter dependence (b_t) of the dipole-dipole amplitude. It is shown that non-perturbative QCD contributions are needed to describe the large b_t behaviour, and the way how to deal with them is suggested. Our approach can be viewed as the model for the saturation in which the entire impact parameter dependence is determined by the initial conditions. The unitarity bound for the total cross section, its energy dependence as well as predictions for future experiments are discussed. It is argued that the total cross section increases faster than any power of ln(1/x) in a wide range of energy or x, namely σ(γ*-γ*) ∝ (1/Q²) exp(a√ln(1/x)) ≤ 1/m_π¹, where exp(a√ln(1/x)) reflects the x dependence of the gluon density xG ∝ exp(2a√ln(1/x)) and m_π is the pion mass.