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The process of elastic scattering of photons (light-by-light scattering)attracts a lot of attention in the last years. It goes via the loop and allcharged particles contributes to its cross section. Theoretical prediction ofthe cross section have existed for more than half a century, there are variousaccelerators with real and virtual photons, but only recently this process wasdiscovered at the LHC in ion-ion collisions. Hopes for further study of thisprocess are associated with high-luminosity $e^+e^-$ colliders (SuperKEKb, FCC,ILC, CLIC) and gamma-gamma colliders based on the Compton scattering of laserphotons on electrons. In this article, we show that there is very seriousbackground processes when the final pair of photons is created in theannihilation of real and virtual $e^+$ and $e^-$, and the remaining productsfly away from the detector at small angles.

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