Problems of studying $\gamma \gamma \to \gamma \gamma$ scattering at $e^{+}{e}^{-}$, $e^{-}{e}^{-}$ and $\gamma \gamma$ colliders

The process of elastic scattering of photons (scattering of light by light) has attracted much attention in recent years. It goes through a loop where all the charged particles contribute to the cross section. To date, this $\gamma \gamma \to \gamma \gamma$ process has been experimentally studied in the Delbrück scattering and splitting of photons in the Coulomb field of the nucleus, as well as at the LHC in the scattering of virtual photons in ion-ion collisions. Hopes for further study of this process are associated with high-luminosity $e^{+}{e}^{-}$ colliders (SuperKEKb, FCC, CEPC, ILC, CLIC) and gamma-gamma colliders based on the Compton scattering of laser photons on electrons. In this article, we show that there are some very serious background processes where the annihilation of electrons and positrons (real and virtual) produces a pair of photons flying into the detector, and the the remaining products fly away from the detector at small angles.