Effects of gluon number fluctuations on photon - photon collisions at high energies

We investigate the effects of gluon number fluctuations on the total $\gamma\gamma$, $\gamma^*\gamma^*$ cross sections and the photon structure function $F_2^\gamma(x,Q^2)$. Considering a model which relates the dipole-dipole and dipole-hadron scattering amplitudes, we estimate these observables by using event-by-event and physical amplitudes. We demonstrate that both analyses are able to describe the LEP data, but predict different behaviours for the observables at high energies, with the gluon fluctuations effects decreasing the cross sections. We conclude that the study of $\gamma \gamma$ interactions can be useful to constrain the QCD dynamics.